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 -9/1 -8/1 -7/1 -6/1 -17/3 -5/1 -14/3 -13/3 -4/1 -11/3 -10/3 -3/1 -8/3 -18/7 -12/5 -2/1 -12/7 -8/5 -48/31 -10/7 -4/3 -6/5 -8/7 -1/1 -8/9 -4/5 -8/11 -12/17 -2/3 -12/19 -8/13 -4/7 -8/15 0/1 1/2 4/7 8/13 2/3 12/17 8/11 3/4 4/5 8/9 1/1 8/7 6/5 16/13 5/4 4/3 24/17 10/7 16/11 3/2 20/13 8/5 12/7 7/4 16/9 2/1 9/4 16/7 12/5 32/13 5/2 18/7 8/3 11/4 48/17 3/1 16/5 13/4 10/3 7/2 32/9 11/3 15/4 4/1 64/15 13/3 128/29 9/2 32/7 14/3 5/1 16/3 11/2 17/3 64/11 6/1 32/5 13/2 7/1 15/2 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 1/1 3/1 -8/1 1/0 -7/1 -5/1 -3/1 -13/2 -4/1 -6/1 -3/1 -2/1 1/0 -23/4 1/0 -17/3 -3/1 -1/1 -11/2 -2/1 -16/3 -3/1 -1/1 -5/1 -3/1 -1/1 -14/3 -2/1 -1/1 1/0 -9/2 0/1 -31/7 -3/1 -1/1 -53/12 1/0 -22/5 -1/1 0/1 1/0 -13/3 -1/1 1/1 -4/1 1/0 -19/5 -5/1 -3/1 -15/4 1/0 -41/11 -11/3 -3/1 -67/18 -4/1 -26/7 -4/1 -7/2 -3/1 -11/3 -3/1 -1/1 -18/5 -4/1 -3/1 1/0 -7/2 -2/1 -24/7 -2/1 -41/12 1/0 -17/5 -3/1 -1/1 -27/8 1/0 -10/3 -3/1 -2/1 1/0 -33/10 -2/1 -23/7 -5/3 -1/1 -13/4 1/0 -16/5 -3/1 -1/1 -3/1 -3/1 -1/1 -17/6 -4/3 -14/5 -1/1 0/1 1/0 -11/4 1/0 -8/3 1/0 -21/8 1/0 -34/13 -5/1 -4/1 1/0 -47/18 -4/1 -13/5 -5/1 -3/1 -31/12 1/0 -18/7 -4/1 -3/1 1/0 -5/2 -2/1 -22/9 -2/1 -1/1 1/0 -17/7 -3/1 -1/1 -29/12 1/0 -12/5 1/0 -31/13 -11/3 -3/1 -19/8 1/0 -26/11 -3/1 -5/2 -2/1 -7/3 -3/1 -1/1 -16/7 -3/1 -1/1 -9/4 1/0 -20/9 -2/1 -11/5 -3/1 -1/1 -13/6 -2/1 -2/1 -2/1 -1/1 1/0 -15/8 1/0 -13/7 -3/1 -1/1 -11/6 -2/1 -31/17 -5/3 -1/1 -20/11 1/0 -29/16 1/0 -9/5 -3/1 -1/1 -16/9 -3/1 -1/1 -7/4 1/0 -26/15 -3/1 -2/1 1/0 -45/26 -4/1 -64/37 -3/1 -19/11 -3/1 -7/3 -31/18 -2/1 -74/43 -3/1 -2/1 1/0 -117/68 1/0 -160/93 -3/1 -43/25 -3/1 -7/3 -12/7 -2/1 -41/24 -3/2 -70/41 -2/1 -3/2 -1/1 -99/58 -2/1 -128/75 -5/3 -1/1 -29/17 -5/3 -1/1 -17/10 0/1 -22/13 -3/1 -2/1 1/0 -27/16 1/0 -32/19 -3/1 -1/1 -5/3 -3/1 -1/1 -18/11 -3/1 -2/1 1/0 -49/30 -10/3 -80/49 -3/1 -31/19 -3/1 -19/7 -13/8 -5/2 -8/5 -2/1 -19/12 -3/2 -49/31 -5/3 -1/1 -128/81 -5/3 -1/1 -79/50 -2/1 -30/19 -2/1 -3/2 -1/1 -11/7 -5/3 -1/1 -14/9 -2/1 -1/1 1/0 -31/20 1/0 -48/31 -3/1 -1/1 -17/11 -3/1 -1/1 -3/2 -2/1 -16/11 -1/1 -13/9 -3/1 -1/1 -23/16 1/0 -33/23 -5/3 -1/1 -43/30 -2/1 -10/7 -2/1 -1/1 1/0 -37/26 -2/1 -64/45 -3/1 -1/1 -27/19 -3/1 -1/1 -17/12 -5/2 -41/29 -7/3 -11/5 -24/17 -2/1 -7/5 -5/3 -1/1 -32/23 -1/1 -25/18 0/1 -18/13 -2/1 -1/1 1/0 -11/8 1/0 -26/19 -2/1 -1/1 1/0 -67/49 -3/1 -1/1 -41/30 -2/1 -15/11 -3/1 -1/1 -4/3 -2/1 -17/13 -5/3 -1/1 -64/49 -5/3 -1/1 -47/36 -3/2 -30/23 -2/1 -5/3 -3/2 -13/10 -2/1 -22/17 -2/1 -5/3 -3/2 -75/58 -2/1 -128/99 -5/3 -53/41 -5/3 -11/7 -31/24 -3/2 -9/7 -7/5 -1/1 -32/25 -1/1 -23/18 0/1 -14/11 -2/1 -1/1 1/0 -5/4 -3/2 -16/13 -1/1 -11/9 -1/1 -1/3 -17/14 0/1 -23/19 -3/1 -1/1 -29/24 1/0 -64/53 -3/1 -1/1 -35/29 -3/1 -1/1 -6/5 -2/1 -1/1 1/0 -19/16 -3/2 -32/27 -1/1 -13/11 -1/1 1/1 -7/6 -2/1 -8/7 -2/1 -9/8 -3/2 -1/1 -3/1 -1/1 -9/10 0/1 -8/9 1/0 -7/8 1/0 -6/7 -2/1 -1/1 1/0 -11/13 -7/5 -1/1 -16/19 -1/1 -5/6 0/1 -14/17 -2/1 -1/1 1/0 -9/11 -1/1 -1/3 -13/16 1/0 -4/5 1/0 -19/24 1/0 -15/19 -3/1 -1/1 -11/14 -2/1 -18/23 -2/1 -1/1 1/0 -7/9 -1/1 1/1 -24/31 1/0 -41/53 -7/1 -5/1 -17/22 -4/1 -10/13 -2/1 -1/1 1/0 -13/17 -3/1 -1/1 -16/21 -1/1 -3/4 1/0 -17/23 -3/1 -1/1 -14/19 -2/1 -1/1 1/0 -11/15 -1/1 1/1 -8/11 1/0 -21/29 -5/1 -3/1 -13/18 -4/1 -31/43 -17/5 -3/1 -18/25 -3/1 -2/1 1/0 -5/7 -3/1 -1/1 -17/24 -3/2 -29/41 -1/1 1/1 -12/17 1/0 -31/44 1/0 -19/27 -5/1 -3/1 -7/10 -2/1 -16/23 -3/1 -1/1 -9/13 -3/1 -1/1 -20/29 -2/1 -11/16 1/0 -2/3 -2/1 -1/1 1/0 -11/17 -3/1 -1/1 -31/48 1/0 -20/31 1/0 -29/45 -3/1 -1/1 -9/14 -2/1 -16/25 -3/1 -1/1 -7/11 -3/1 -1/1 -19/30 -2/1 -31/49 -3/1 -13/5 -43/68 -5/2 -12/19 -2/1 -41/65 -3/1 -1/1 -29/46 -2/1 -17/27 -3/1 -1/1 -5/8 1/0 -18/29 -3/1 -5/2 -2/1 -49/79 -3/1 -7/3 -80/129 -3/1 -7/3 -31/50 -2/1 -13/21 -3/1 -7/3 -8/13 -2/1 -19/31 -5/3 -1/1 -11/18 -2/1 -14/23 -2/1 -3/2 -1/1 -31/51 -11/9 -1/1 -48/79 -1/1 -17/28 -1/2 -3/5 -3/1 -1/1 -16/27 -3/1 -1/1 -13/22 -2/1 -10/17 -3/1 -2/1 1/0 -17/29 -3/1 -1/1 -41/70 -2/1 -24/41 1/0 -7/12 1/0 -32/55 -3/1 -25/43 -3/1 -13/5 -18/31 -3/1 -5/2 -2/1 -11/19 -3/1 -1/1 -15/26 -2/1 -4/7 -2/1 -17/30 -2/1 -13/23 -5/3 -1/1 -9/16 -3/2 -32/57 -1/1 -23/41 -1/1 -1/3 -14/25 -2/1 -1/1 1/0 -5/9 -3/1 -1/1 -16/29 -3/1 -1/1 -11/20 1/0 -6/11 -3/1 -2/1 1/0 -7/13 -3/1 -7/3 -8/15 -2/1 -9/17 -9/5 -5/3 -1/2 -2/1 0/1 -1/1 1/2 0/1 7/13 1/3 1/1 6/11 0/1 1/1 1/0 11/20 1/0 5/9 -1/1 1/1 14/25 -1/1 0/1 1/0 9/16 -1/2 13/23 -1/1 -1/3 4/7 0/1 19/33 1/3 1/1 15/26 0/1 11/19 -1/1 1/1 7/12 1/0 24/41 1/0 17/29 -1/1 1/1 10/17 0/1 1/1 1/0 13/22 0/1 3/5 -1/1 1/1 17/28 -3/2 14/23 -1/1 -1/2 0/1 11/18 0/1 8/13 0/1 21/34 0/1 13/21 1/3 1/1 5/8 1/0 17/27 -1/1 1/1 12/19 0/1 31/49 3/5 1/1 19/30 0/1 7/11 -1/1 1/1 9/14 0/1 20/31 1/0 11/17 -1/1 1/1 2/3 -1/1 0/1 1/0 11/16 1/0 31/45 -3/1 -1/1 20/29 0/1 9/13 -1/1 1/1 7/10 0/1 19/27 1/1 3/1 12/17 1/0 41/58 -2/1 29/41 -3/1 -1/1 17/24 -1/2 5/7 -1/1 1/1 18/25 0/1 1/1 1/0 49/68 3/4 31/43 1/1 7/5 13/18 2/1 8/11 1/0 19/26 -2/1 11/15 -3/1 -1/1 3/4 1/0 13/17 -1/1 1/1 10/13 -1/1 0/1 1/0 17/22 2/1 7/9 -3/1 -1/1 18/23 -1/1 0/1 1/0 11/14 0/1 15/19 -1/1 1/1 4/5 1/0 17/21 -3/1 -1/1 13/16 1/0 9/11 -5/3 -1/1 5/6 -2/1 11/13 -1/1 -3/5 6/7 -1/1 0/1 1/0 7/8 1/0 8/9 1/0 1/1 -1/1 1/1 9/8 -1/2 8/7 0/1 7/6 0/1 13/11 -3/1 -1/1 6/5 -1/1 0/1 1/0 23/19 -1/1 1/1 17/14 -2/1 11/9 -5/3 -1/1 27/22 -6/5 16/13 -1/1 5/4 -1/2 19/15 -1/1 1/1 14/11 -1/1 0/1 1/0 9/7 -1/1 -3/5 31/24 -1/2 53/41 -3/7 -1/3 22/17 -1/2 -1/3 0/1 13/10 0/1 4/3 0/1 19/14 0/1 15/11 -1/1 1/1 56/41 1/0 41/30 0/1 67/49 -1/1 1/1 26/19 -1/1 0/1 1/0 11/8 1/0 18/13 -1/1 0/1 1/0 7/5 -1/1 -1/3 31/22 0/1 24/17 0/1 41/29 1/5 1/3 17/12 1/2 27/19 -1/1 1/1 10/7 -1/1 0/1 1/0 33/23 -1/1 -1/3 23/16 1/0 13/9 -1/1 1/1 29/20 1/0 16/11 -1/1 3/2 0/1 23/15 -1/1 1/1 20/13 0/1 17/11 -1/1 1/1 14/9 -1/1 0/1 1/0 39/25 -3/1 -1/1 25/16 -1/2 11/7 -1/1 -1/3 8/5 0/1 21/13 1/3 1/1 34/21 0/1 1/3 1/2 47/29 1/3 1/1 13/8 1/2 31/19 5/7 1/1 18/11 0/1 1/1 1/0 5/3 -1/1 1/1 22/13 0/1 1/1 1/0 17/10 -2/1 29/17 -1/1 -1/3 12/7 0/1 31/18 0/1 50/29 0/1 1/2 1/1 19/11 1/3 1/1 26/15 0/1 1/1 1/0 7/4 1/0 16/9 -1/1 1/1 25/14 0/1 9/5 -1/1 1/1 20/11 1/0 11/6 0/1 13/7 -1/1 1/1 2/1 -1/1 0/1 1/0 15/7 -1/1 1/1 13/6 0/1 11/5 -1/1 1/1 31/14 0/1 20/9 0/1 29/13 -1/1 1/1 9/4 1/0 16/7 -1/1 1/1 23/10 0/1 7/3 -1/1 1/1 26/11 0/1 1/2 1/1 45/19 3/5 1/1 64/27 1/1 19/8 1/0 31/13 1/1 5/3 74/31 1/1 2/1 1/0 117/49 -1/1 1/1 160/67 1/1 43/18 2/1 12/5 1/0 41/17 -1/1 1/1 70/29 -1/1 0/1 1/0 99/41 -1/1 1/1 128/53 -1/1 1/1 29/12 1/0 17/7 -1/1 1/1 22/9 -1/1 0/1 1/0 27/11 -1/1 1/1 32/13 -1/1 1/1 5/2 0/1 23/9 1/3 1/1 41/16 3/2 18/7 1/1 2/1 1/0 49/19 1/1 3/1 80/31 1/1 3/1 31/12 1/0 75/29 1/1 3/1 44/17 1/0 13/5 1/1 3/1 8/3 1/0 19/7 -3/1 -1/1 49/18 -2/1 128/47 -3/1 -1/1 79/29 -3/1 -1/1 30/11 -2/1 -1/1 1/0 11/4 1/0 14/5 -2/1 -1/1 1/0 31/11 -9/7 -1/1 79/28 -11/10 48/17 -1/1 17/6 -2/3 3/1 -1/1 1/1 19/6 0/1 16/5 -1/1 1/1 13/4 1/0 23/7 -1/1 -1/3 56/17 0/1 33/10 0/1 43/13 1/3 1/1 10/3 0/1 1/1 1/0 37/11 -1/1 1/1 64/19 -1/1 1/1 27/8 1/0 17/5 -1/1 1/1 41/12 1/0 24/7 0/1 7/2 0/1 32/9 1/1 57/16 5/4 25/7 1/1 5/3 18/5 1/1 2/1 1/0 65/18 2/1 112/31 1/1 3/1 47/13 1/1 3/1 29/8 1/0 11/3 -1/1 1/1 26/7 1/1 3/2 2/1 67/18 2/1 41/11 1/1 5/3 15/4 1/0 4/1 1/0 17/4 1/0 64/15 -3/1 -1/1 47/11 -3/1 -1/1 30/7 -3/1 -2/1 1/0 13/3 -3/1 -1/1 22/5 -2/1 -1/1 1/0 75/17 -5/3 -1/1 128/29 -1/1 53/12 1/0 31/7 -1/1 1/1 40/9 1/0 9/2 -2/1 32/7 -1/1 55/12 -5/6 23/5 -1/1 -3/5 14/3 -1/1 0/1 1/0 5/1 -1/1 1/1 21/4 1/0 16/3 -1/1 1/1 11/2 0/1 17/3 -1/1 1/1 23/4 1/0 29/5 -1/1 1/1 64/11 -1/1 1/1 35/6 0/1 6/1 0/1 1/1 1/0 19/3 1/3 1/1 32/5 1/1 13/2 2/1 7/1 1/1 3/1 15/2 6/1 8/1 1/0 17/2 -6/1 9/1 -5/1 -3/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(31,288,24,223) (-9/1,1/0) -> (9/7,31/24) Hyperbolic Matrix(65,544,-84,-703) (-9/1,-8/1) -> (-24/31,-41/53) Hyperbolic Matrix(31,224,-40,-289) (-8/1,-7/1) -> (-7/9,-24/31) Hyperbolic Matrix(33,224,52,353) (-7/1,-13/2) -> (19/30,7/11) Hyperbolic Matrix(97,608,-56,-351) (-13/2,-6/1) -> (-26/15,-45/26) Hyperbolic Matrix(321,1856,-188,-1087) (-6/1,-23/4) -> (-41/24,-70/41) Hyperbolic Matrix(191,1088,56,319) (-23/4,-17/3) -> (17/5,41/12) Hyperbolic Matrix(63,352,80,447) (-17/3,-11/2) -> (11/14,15/19) Hyperbolic Matrix(65,352,12,65) (-11/2,-16/3) -> (16/3,11/2) Hyperbolic Matrix(31,160,-56,-289) (-16/3,-5/1) -> (-5/9,-16/29) Hyperbolic Matrix(33,160,20,97) (-5/1,-14/3) -> (18/11,5/3) Hyperbolic Matrix(97,448,-76,-351) (-14/3,-9/2) -> (-23/18,-14/11) Hyperbolic Matrix(65,288,-72,-319) (-9/2,-31/7) -> (-1/1,-9/10) Hyperbolic Matrix(449,1984,652,2881) (-31/7,-53/12) -> (11/16,31/45) Hyperbolic Matrix(1473,6496,-856,-3775) (-53/12,-22/5) -> (-74/43,-117/68) Hyperbolic Matrix(95,416,124,543) (-22/5,-13/3) -> (13/17,10/13) Hyperbolic Matrix(31,128,-8,-33) (-13/3,-4/1) -> (-4/1,-19/5) Parabolic Matrix(127,480,-68,-257) (-19/5,-15/4) -> (-15/8,-13/7) Hyperbolic Matrix(351,1312,248,927) (-15/4,-41/11) -> (41/29,17/12) Hyperbolic Matrix(447,1664,292,1087) (-41/11,-67/18) -> (3/2,23/15) Hyperbolic Matrix(1953,7264,-1144,-4255) (-67/18,-26/7) -> (-70/41,-99/58) Hyperbolic Matrix(95,352,112,415) (-26/7,-11/3) -> (11/13,6/7) Hyperbolic Matrix(97,352,-132,-479) (-11/3,-18/5) -> (-14/19,-11/15) Hyperbolic Matrix(161,576,-116,-415) (-18/5,-7/2) -> (-25/18,-18/13) Hyperbolic Matrix(65,224,56,193) (-7/2,-24/7) -> (8/7,7/6) Hyperbolic Matrix(159,544,140,479) (-24/7,-41/12) -> (9/8,8/7) Hyperbolic Matrix(319,1088,56,191) (-41/12,-17/5) -> (17/3,23/4) Hyperbolic Matrix(161,544,256,865) (-17/5,-27/8) -> (5/8,17/27) Hyperbolic Matrix(257,864,-152,-511) (-27/8,-10/3) -> (-22/13,-27/16) Hyperbolic Matrix(833,2752,-484,-1599) (-10/3,-33/10) -> (-31/18,-74/43) Hyperbolic Matrix(97,320,-184,-607) (-33/10,-23/7) -> (-9/17,-1/2) Hyperbolic Matrix(127,416,156,511) (-23/7,-13/4) -> (13/16,9/11) Hyperbolic Matrix(129,416,40,129) (-13/4,-16/5) -> (16/5,13/4) Hyperbolic Matrix(31,96,-52,-161) (-16/5,-3/1) -> (-3/5,-16/27) Hyperbolic Matrix(191,544,112,319) (-3/1,-17/6) -> (17/10,29/17) Hyperbolic Matrix(353,992,-216,-607) (-17/6,-14/5) -> (-18/11,-49/30) Hyperbolic Matrix(127,352,92,255) (-14/5,-11/4) -> (11/8,18/13) Hyperbolic Matrix(95,256,-36,-97) (-11/4,-8/3) -> (-8/3,-21/8) Parabolic Matrix(159,416,232,607) (-21/8,-34/13) -> (2/3,11/16) Hyperbolic Matrix(1567,4096,-992,-2593) (-34/13,-47/18) -> (-79/50,-30/19) Hyperbolic Matrix(417,1088,724,1889) (-47/18,-13/5) -> (19/33,15/26) Hyperbolic Matrix(383,992,-544,-1409) (-13/5,-31/12) -> (-31/44,-19/27) Hyperbolic Matrix(385,992,-248,-639) (-31/12,-18/7) -> (-14/9,-31/20) Hyperbolic Matrix(63,160,-76,-193) (-18/7,-5/2) -> (-5/6,-14/17) Hyperbolic Matrix(353,864,-248,-607) (-5/2,-22/9) -> (-10/7,-37/26) Hyperbolic Matrix(223,544,380,927) (-22/9,-17/7) -> (17/29,10/17) Hyperbolic Matrix(225,544,-304,-735) (-17/7,-29/12) -> (-3/4,-17/23) Hyperbolic Matrix(385,928,-212,-511) (-29/12,-12/5) -> (-20/11,-29/16) Hyperbolic Matrix(415,992,-228,-545) (-12/5,-31/13) -> (-31/17,-20/11) Hyperbolic Matrix(417,992,256,609) (-31/13,-19/8) -> (13/8,31/19) Hyperbolic Matrix(257,608,-216,-511) (-19/8,-26/11) -> (-6/5,-19/16) Hyperbolic Matrix(95,224,176,415) (-26/11,-7/3) -> (7/13,6/11) Hyperbolic Matrix(97,224,-152,-351) (-7/3,-16/7) -> (-16/25,-7/11) Hyperbolic Matrix(127,288,56,127) (-16/7,-9/4) -> (9/4,16/7) Hyperbolic Matrix(417,928,-244,-543) (-9/4,-20/9) -> (-12/7,-41/24) Hyperbolic Matrix(447,992,-260,-577) (-20/9,-11/5) -> (-43/25,-12/7) Hyperbolic Matrix(161,352,220,481) (-11/5,-13/6) -> (19/26,11/15) Hyperbolic Matrix(193,416,-148,-319) (-13/6,-2/1) -> (-30/23,-13/10) Hyperbolic Matrix(287,544,-220,-417) (-2/1,-15/8) -> (-47/36,-30/23) Hyperbolic Matrix(225,416,364,673) (-13/7,-11/6) -> (21/34,13/21) Hyperbolic Matrix(929,1696,-648,-1183) (-11/6,-31/17) -> (-33/23,-43/30) Hyperbolic Matrix(513,928,-424,-767) (-29/16,-9/5) -> (-23/19,-29/24) Hyperbolic Matrix(161,288,-232,-415) (-9/5,-16/9) -> (-16/23,-9/13) Hyperbolic Matrix(127,224,72,127) (-16/9,-7/4) -> (7/4,16/9) Hyperbolic Matrix(129,224,148,257) (-7/4,-26/15) -> (6/7,7/8) Hyperbolic Matrix(1313,2272,204,353) (-45/26,-64/37) -> (32/5,13/2) Hyperbolic Matrix(2369,4096,1000,1729) (-64/37,-19/11) -> (45/19,64/27) Hyperbolic Matrix(575,992,-928,-1601) (-19/11,-31/18) -> (-31/50,-13/21) Hyperbolic Matrix(13633,23456,3088,5313) (-117/68,-160/93) -> (128/29,53/12) Hyperbolic Matrix(14881,25600,6232,10721) (-160/93,-43/25) -> (117/49,160/67) Hyperbolic Matrix(6337,10816,1088,1857) (-99/58,-128/75) -> (64/11,35/6) Hyperbolic Matrix(9601,16384,3976,6785) (-128/75,-29/17) -> (99/41,128/53) Hyperbolic Matrix(319,544,112,191) (-29/17,-17/10) -> (17/6,3/1) Hyperbolic Matrix(321,544,416,705) (-17/10,-22/13) -> (10/13,17/22) Hyperbolic Matrix(1537,2592,456,769) (-27/16,-32/19) -> (64/19,27/8) Hyperbolic Matrix(609,1024,248,417) (-32/19,-5/3) -> (27/11,32/13) Hyperbolic Matrix(97,160,20,33) (-5/3,-18/11) -> (14/3,5/1) Hyperbolic Matrix(2273,3712,804,1313) (-49/30,-80/49) -> (48/17,17/6) Hyperbolic Matrix(2431,3968,-4000,-6529) (-80/49,-31/19) -> (-31/51,-48/79) Hyperbolic Matrix(609,992,256,417) (-31/19,-13/8) -> (19/8,31/13) Hyperbolic Matrix(159,256,-100,-161) (-13/8,-8/5) -> (-8/5,-19/12) Parabolic Matrix(607,960,748,1183) (-19/12,-49/31) -> (17/21,13/16) Hyperbolic Matrix(5791,9152,1356,2143) (-49/31,-128/81) -> (64/15,47/11) Hyperbolic Matrix(10369,16384,3808,6017) (-128/81,-79/50) -> (49/18,128/47) Hyperbolic Matrix(223,352,344,543) (-30/19,-11/7) -> (11/17,2/3) Hyperbolic Matrix(225,352,-388,-607) (-11/7,-14/9) -> (-18/31,-11/19) Hyperbolic Matrix(2561,3968,992,1537) (-31/20,-48/31) -> (80/31,31/12) Hyperbolic Matrix(2399,3712,-3868,-5985) (-48/31,-17/11) -> (-49/79,-80/129) Hyperbolic Matrix(353,544,-560,-863) (-17/11,-3/2) -> (-29/46,-17/27) Hyperbolic Matrix(65,96,44,65) (-3/2,-16/11) -> (16/11,3/2) Hyperbolic Matrix(287,416,-376,-545) (-16/11,-13/9) -> (-13/17,-16/21) Hyperbolic Matrix(289,416,512,737) (-13/9,-23/16) -> (9/16,13/23) Hyperbolic Matrix(223,320,200,287) (-23/16,-33/23) -> (1/1,9/8) Hyperbolic Matrix(1185,1696,-916,-1311) (-43/30,-10/7) -> (-22/17,-75/58) Hyperbolic Matrix(1057,1504,428,609) (-37/26,-64/45) -> (32/13,5/2) Hyperbolic Matrix(2881,4096,856,1217) (-64/45,-27/19) -> (37/11,64/19) Hyperbolic Matrix(383,544,540,767) (-27/19,-17/12) -> (17/24,5/7) Hyperbolic Matrix(927,1312,248,351) (-17/12,-41/29) -> (41/11,15/4) Hyperbolic Matrix(385,544,-724,-1023) (-41/29,-24/17) -> (-8/15,-9/17) Hyperbolic Matrix(159,224,-296,-417) (-24/17,-7/5) -> (-7/13,-8/15) Hyperbolic Matrix(735,1024,-1264,-1761) (-7/5,-32/23) -> (-32/55,-25/43) Hyperbolic Matrix(737,1024,208,289) (-32/23,-25/18) -> (7/2,32/9) Hyperbolic Matrix(255,352,92,127) (-18/13,-11/8) -> (11/4,14/5) Hyperbolic Matrix(257,352,468,641) (-11/8,-26/19) -> (6/11,11/20) Hyperbolic Matrix(959,1312,-796,-1089) (-26/19,-67/49) -> (-35/29,-6/5) Hyperbolic Matrix(2879,3936,4072,5567) (-67/49,-41/30) -> (41/58,29/41) Hyperbolic Matrix(961,1312,-1640,-2239) (-41/30,-15/11) -> (-17/29,-41/70) Hyperbolic Matrix(95,128,-72,-97) (-15/11,-4/3) -> (-4/3,-17/13) Parabolic Matrix(5535,7232,2032,2655) (-17/13,-64/49) -> (128/47,79/29) Hyperbolic Matrix(3137,4096,736,961) (-64/49,-47/36) -> (17/4,64/15) Hyperbolic Matrix(321,416,544,705) (-13/10,-22/17) -> (10/17,13/22) Hyperbolic Matrix(13537,17504,5668,7329) (-75/58,-128/99) -> (160/67,43/18) Hyperbolic Matrix(12673,16384,2872,3713) (-128/99,-53/41) -> (75/17,128/29) Hyperbolic Matrix(3071,3968,1188,1535) (-53/41,-31/24) -> (31/12,75/29) Hyperbolic Matrix(223,288,24,31) (-31/24,-9/7) -> (9/1,1/0) Hyperbolic Matrix(799,1024,-1424,-1825) (-9/7,-32/25) -> (-32/57,-23/41) Hyperbolic Matrix(801,1024,176,225) (-32/25,-23/18) -> (9/2,32/7) Hyperbolic Matrix(127,160,-204,-257) (-14/11,-5/4) -> (-5/8,-18/29) Hyperbolic Matrix(129,160,104,129) (-5/4,-16/13) -> (16/13,5/4) Hyperbolic Matrix(287,352,-340,-417) (-16/13,-11/9) -> (-11/13,-16/19) Hyperbolic Matrix(289,352,500,609) (-11/9,-17/14) -> (15/26,11/19) Hyperbolic Matrix(897,1088,-1160,-1407) (-17/14,-23/19) -> (-41/53,-17/22) Hyperbolic Matrix(4609,5568,1908,2305) (-29/24,-64/53) -> (128/53,29/12) Hyperbolic Matrix(3393,4096,584,705) (-64/53,-35/29) -> (29/5,64/11) Hyperbolic Matrix(1537,1824,648,769) (-19/16,-32/27) -> (64/27,19/8) Hyperbolic Matrix(865,1024,136,161) (-32/27,-13/11) -> (19/3,32/5) Hyperbolic Matrix(191,224,272,319) (-13/11,-7/6) -> (7/10,19/27) Hyperbolic Matrix(193,224,56,65) (-7/6,-8/7) -> (24/7,7/2) Hyperbolic Matrix(479,544,140,159) (-8/7,-9/8) -> (41/12,24/7) Hyperbolic Matrix(287,320,200,223) (-9/8,-1/1) -> (33/23,23/16) Hyperbolic Matrix(929,832,680,609) (-9/10,-8/9) -> (56/41,41/30) Hyperbolic Matrix(255,224,436,383) (-8/9,-7/8) -> (7/12,24/41) Hyperbolic Matrix(257,224,148,129) (-7/8,-6/7) -> (26/15,7/4) Hyperbolic Matrix(415,352,112,95) (-6/7,-11/13) -> (11/3,26/7) Hyperbolic Matrix(609,512,496,417) (-16/19,-5/6) -> (27/22,16/13) Hyperbolic Matrix(545,448,-972,-799) (-14/17,-9/11) -> (-23/41,-14/25) Hyperbolic Matrix(511,416,156,127) (-9/11,-13/16) -> (13/4,23/7) Hyperbolic Matrix(159,128,-200,-161) (-13/16,-4/5) -> (-4/5,-19/24) Parabolic Matrix(1375,1088,848,671) (-19/24,-15/19) -> (47/29,13/8) Hyperbolic Matrix(447,352,80,63) (-15/19,-11/14) -> (11/2,17/3) Hyperbolic Matrix(449,352,736,577) (-11/14,-18/23) -> (14/23,11/18) Hyperbolic Matrix(737,576,-1268,-991) (-18/23,-7/9) -> (-25/43,-18/31) Hyperbolic Matrix(705,544,416,321) (-17/22,-10/13) -> (22/13,17/10) Hyperbolic Matrix(543,416,124,95) (-10/13,-13/17) -> (13/3,22/5) Hyperbolic Matrix(673,512,464,353) (-16/21,-3/4) -> (29/20,16/11) Hyperbolic Matrix(1345,992,-2168,-1599) (-17/23,-14/19) -> (-18/29,-49/79) Hyperbolic Matrix(351,256,-484,-353) (-11/15,-8/11) -> (-8/11,-21/29) Parabolic Matrix(575,416,264,191) (-21/29,-13/18) -> (13/6,11/5) Hyperbolic Matrix(1375,992,2172,1567) (-13/18,-31/43) -> (31/49,19/30) Hyperbolic Matrix(1377,992,-2264,-1631) (-31/43,-18/25) -> (-14/23,-31/51) Hyperbolic Matrix(223,160,400,287) (-18/25,-5/7) -> (5/9,14/25) Hyperbolic Matrix(767,544,540,383) (-5/7,-17/24) -> (17/12,27/19) Hyperbolic Matrix(769,544,1268,897) (-17/24,-29/41) -> (3/5,17/28) Hyperbolic Matrix(1313,928,-2036,-1439) (-29/41,-12/17) -> (-20/31,-29/45) Hyperbolic Matrix(1407,992,-2180,-1537) (-12/17,-31/44) -> (-31/48,-20/31) Hyperbolic Matrix(319,224,272,191) (-19/27,-7/10) -> (7/6,13/11) Hyperbolic Matrix(735,512,412,287) (-7/10,-16/23) -> (16/9,25/14) Hyperbolic Matrix(1345,928,-2132,-1471) (-9/13,-20/29) -> (-12/19,-41/65) Hyperbolic Matrix(1439,992,-2276,-1569) (-20/29,-11/16) -> (-43/68,-12/19) Hyperbolic Matrix(513,352,188,129) (-11/16,-2/3) -> (30/11,11/4) Hyperbolic Matrix(641,416,396,257) (-2/3,-11/17) -> (21/13,34/21) Hyperbolic Matrix(3071,1984,2376,1535) (-11/17,-31/48) -> (31/24,53/41) Hyperbolic Matrix(2783,1792,2036,1311) (-29/45,-9/14) -> (41/30,67/49) Hyperbolic Matrix(799,512,348,223) (-9/14,-16/25) -> (16/7,23/10) Hyperbolic Matrix(353,224,52,33) (-7/11,-19/30) -> (13/2,7/1) Hyperbolic Matrix(1567,992,2172,1375) (-19/30,-31/49) -> (31/43,13/18) Hyperbolic Matrix(4705,2976,1064,673) (-31/49,-43/68) -> (53/12,31/7) Hyperbolic Matrix(6241,3936,1676,1057) (-41/65,-29/46) -> (67/18,41/11) Hyperbolic Matrix(865,544,256,161) (-17/27,-5/8) -> (27/8,17/5) Hyperbolic Matrix(13985,8672,3872,2401) (-80/129,-31/50) -> (65/18,112/31) Hyperbolic Matrix(415,256,-676,-417) (-13/21,-8/13) -> (-8/13,-19/31) Parabolic Matrix(575,352,312,191) (-19/31,-11/18) -> (11/6,13/7) Hyperbolic Matrix(577,352,736,449) (-11/18,-14/23) -> (18/23,11/14) Hyperbolic Matrix(7585,4608,2688,1633) (-48/79,-17/28) -> (79/28,48/17) Hyperbolic Matrix(897,544,1268,769) (-17/28,-3/5) -> (29/41,17/24) Hyperbolic Matrix(865,512,272,161) (-16/27,-13/22) -> (19/6,16/5) Hyperbolic Matrix(705,416,544,321) (-13/22,-10/17) -> (22/17,13/10) Hyperbolic Matrix(927,544,380,223) (-10/17,-17/29) -> (17/7,22/9) Hyperbolic Matrix(3169,1856,712,417) (-41/70,-24/41) -> (40/9,9/2) Hyperbolic Matrix(383,224,436,255) (-24/41,-7/12) -> (7/8,8/9) Hyperbolic Matrix(3519,2048,988,575) (-7/12,-32/55) -> (32/9,57/16) Hyperbolic Matrix(609,352,500,289) (-11/19,-15/26) -> (17/14,11/9) Hyperbolic Matrix(223,128,-392,-225) (-15/26,-4/7) -> (-4/7,-17/30) Parabolic Matrix(1697,960,624,353) (-17/30,-13/23) -> (19/7,49/18) Hyperbolic Matrix(737,416,512,289) (-13/23,-9/16) -> (23/16,13/9) Hyperbolic Matrix(3647,2048,796,447) (-9/16,-32/57) -> (32/7,55/12) Hyperbolic Matrix(287,160,400,223) (-14/25,-5/9) -> (5/7,18/25) Hyperbolic Matrix(929,512,176,97) (-16/29,-11/20) -> (21/4,16/3) Hyperbolic Matrix(641,352,468,257) (-11/20,-6/11) -> (26/19,11/8) Hyperbolic Matrix(415,224,176,95) (-6/11,-7/13) -> (7/3,26/11) Hyperbolic Matrix(1,0,4,1) (-1/2,0/1) -> (0/1,1/2) Parabolic Matrix(417,-224,296,-159) (1/2,7/13) -> (7/5,31/22) Hyperbolic Matrix(289,-160,56,-31) (11/20,5/9) -> (5/1,21/4) Hyperbolic Matrix(1313,-736,512,-287) (14/25,9/16) -> (41/16,18/7) Hyperbolic Matrix(225,-128,392,-223) (13/23,4/7) -> (4/7,19/33) Parabolic Matrix(607,-352,388,-225) (11/19,7/12) -> (25/16,11/7) Hyperbolic Matrix(2239,-1312,1640,-961) (24/41,17/29) -> (15/11,56/41) Hyperbolic Matrix(161,-96,52,-31) (13/22,3/5) -> (3/1,19/6) Hyperbolic Matrix(1631,-992,2264,-1377) (17/28,14/23) -> (18/25,49/68) Hyperbolic Matrix(417,-256,676,-415) (11/18,8/13) -> (8/13,21/34) Parabolic Matrix(257,-160,204,-127) (13/21,5/8) -> (5/4,19/15) Hyperbolic Matrix(863,-544,560,-353) (17/27,12/19) -> (20/13,17/11) Hyperbolic Matrix(1569,-992,2276,-1439) (12/19,31/49) -> (31/45,20/29) Hyperbolic Matrix(351,-224,152,-97) (7/11,9/14) -> (23/10,7/3) Hyperbolic Matrix(1439,-928,2036,-1313) (9/14,20/31) -> (12/17,41/58) Hyperbolic Matrix(3073,-1984,1188,-767) (20/31,11/17) -> (75/29,44/17) Hyperbolic Matrix(927,-640,604,-417) (20/29,9/13) -> (23/15,20/13) Hyperbolic Matrix(415,-288,232,-161) (9/13,7/10) -> (25/14,9/5) Hyperbolic Matrix(1409,-992,544,-383) (19/27,12/17) -> (44/17,13/5) Hyperbolic Matrix(5505,-3968,1952,-1407) (49/68,31/43) -> (31/11,79/28) Hyperbolic Matrix(353,-256,484,-351) (13/18,8/11) -> (8/11,19/26) Parabolic Matrix(479,-352,132,-97) (11/15,3/4) -> (29/8,11/3) Hyperbolic Matrix(545,-416,376,-287) (3/4,13/17) -> (13/9,29/20) Hyperbolic Matrix(289,-224,40,-31) (17/22,7/9) -> (7/1,15/2) Hyperbolic Matrix(1023,-800,656,-513) (7/9,18/23) -> (14/9,39/25) Hyperbolic Matrix(161,-128,200,-159) (15/19,4/5) -> (4/5,17/21) Parabolic Matrix(193,-160,76,-63) (9/11,5/6) -> (5/2,23/9) Hyperbolic Matrix(417,-352,340,-287) (5/6,11/13) -> (11/9,27/22) Hyperbolic Matrix(319,-288,72,-65) (8/9,1/1) -> (31/7,40/9) Hyperbolic Matrix(511,-608,216,-257) (13/11,6/5) -> (26/11,45/19) Hyperbolic Matrix(1535,-1856,636,-769) (6/5,23/19) -> (41/17,70/29) Hyperbolic Matrix(449,-544,52,-63) (23/19,17/14) -> (17/2,9/1) Hyperbolic Matrix(959,-1216,556,-705) (19/15,14/11) -> (50/29,19/11) Hyperbolic Matrix(351,-448,76,-97) (14/11,9/7) -> (23/5,14/3) Hyperbolic Matrix(5023,-6496,2104,-2721) (53/41,22/17) -> (74/31,117/49) Hyperbolic Matrix(97,-128,72,-95) (13/10,4/3) -> (4/3,19/14) Parabolic Matrix(353,-480,164,-223) (19/14,15/11) -> (15/7,13/6) Hyperbolic Matrix(5311,-7264,2200,-3009) (67/49,26/19) -> (70/29,99/41) Hyperbolic Matrix(415,-576,116,-161) (18/13,7/5) -> (25/7,18/5) Hyperbolic Matrix(1793,-2528,544,-767) (31/22,24/17) -> (56/17,33/10) Hyperbolic Matrix(2015,-2848,612,-865) (24/17,41/29) -> (23/7,56/17) Hyperbolic Matrix(607,-864,248,-353) (27/19,10/7) -> (22/9,27/11) Hyperbolic Matrix(1919,-2752,804,-1153) (10/7,33/23) -> (31/13,74/31) Hyperbolic Matrix(639,-992,248,-385) (17/11,14/9) -> (18/7,49/19) Hyperbolic Matrix(1825,-2848,512,-799) (39/25,25/16) -> (57/16,25/7) Hyperbolic Matrix(161,-256,100,-159) (11/7,8/5) -> (8/5,21/13) Parabolic Matrix(2529,-4096,928,-1503) (34/21,47/29) -> (79/29,30/11) Hyperbolic Matrix(607,-992,216,-353) (31/19,18/11) -> (14/5,31/11) Hyperbolic Matrix(511,-864,152,-257) (5/3,22/13) -> (10/3,37/11) Hyperbolic Matrix(543,-928,244,-417) (29/17,12/7) -> (20/9,29/13) Hyperbolic Matrix(577,-992,260,-447) (12/7,31/18) -> (31/14,20/9) Hyperbolic Matrix(2209,-3808,612,-1055) (31/18,50/29) -> (18/5,65/18) Hyperbolic Matrix(351,-608,56,-97) (19/11,26/15) -> (6/1,19/3) Hyperbolic Matrix(511,-928,212,-385) (9/5,20/11) -> (12/5,41/17) Hyperbolic Matrix(545,-992,228,-415) (20/11,11/6) -> (43/18,12/5) Hyperbolic Matrix(223,-416,52,-97) (13/7,2/1) -> (30/7,13/3) Hyperbolic Matrix(257,-544,60,-127) (2/1,15/7) -> (47/11,30/7) Hyperbolic Matrix(767,-1696,232,-513) (11/5,31/14) -> (33/10,43/13) Hyperbolic Matrix(415,-928,72,-161) (29/13,9/4) -> (23/4,29/5) Hyperbolic Matrix(767,-1856,212,-513) (29/12,17/7) -> (47/13,29/8) Hyperbolic Matrix(863,-2208,188,-481) (23/9,41/16) -> (55/12,23/5) Hyperbolic Matrix(3585,-9248,992,-2559) (49/19,80/31) -> (112/31,47/13) Hyperbolic Matrix(97,-256,36,-95) (13/5,8/3) -> (8/3,19/7) Parabolic Matrix(511,-1696,116,-385) (43/13,10/3) -> (22/5,75/17) Hyperbolic Matrix(353,-1312,60,-223) (26/7,67/18) -> (35/6,6/1) Hyperbolic Matrix(33,-128,8,-31) (15/4,4/1) -> (4/1,17/4) Parabolic Matrix(33,-256,4,-31) (15/2,8/1) -> (8/1,17/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(31,288,24,223) -> Matrix(1,0,-2,1) Matrix(65,544,-84,-703) -> Matrix(1,-8,0,1) Matrix(31,224,-40,-289) -> Matrix(1,4,0,1) Matrix(33,224,52,353) -> Matrix(1,4,0,1) Matrix(97,608,-56,-351) -> Matrix(1,0,0,1) Matrix(321,1856,-188,-1087) -> Matrix(3,8,-2,-5) Matrix(191,1088,56,319) -> Matrix(1,2,0,1) Matrix(63,352,80,447) -> Matrix(1,2,0,1) Matrix(65,352,12,65) -> Matrix(1,2,0,1) Matrix(31,160,-56,-289) -> Matrix(1,0,0,1) Matrix(33,160,20,97) -> Matrix(1,2,0,1) Matrix(97,448,-76,-351) -> Matrix(1,0,0,1) Matrix(65,288,-72,-319) -> Matrix(1,0,0,1) Matrix(449,1984,652,2881) -> Matrix(1,0,0,1) Matrix(1473,6496,-856,-3775) -> Matrix(1,-2,0,1) Matrix(95,416,124,543) -> Matrix(1,0,0,1) Matrix(31,128,-8,-33) -> Matrix(1,-4,0,1) Matrix(127,480,-68,-257) -> Matrix(1,2,0,1) Matrix(351,1312,248,927) -> Matrix(1,4,2,9) Matrix(447,1664,292,1087) -> Matrix(1,4,-2,-7) Matrix(1953,7264,-1144,-4255) -> Matrix(1,2,0,1) Matrix(95,352,112,415) -> Matrix(1,4,-2,-7) Matrix(97,352,-132,-479) -> Matrix(1,2,0,1) Matrix(161,576,-116,-415) -> Matrix(1,2,0,1) Matrix(65,224,56,193) -> Matrix(1,2,0,1) Matrix(159,544,140,479) -> Matrix(1,2,-2,-3) Matrix(319,1088,56,191) -> Matrix(1,2,0,1) Matrix(161,544,256,865) -> Matrix(1,2,0,1) Matrix(257,864,-152,-511) -> Matrix(1,0,0,1) Matrix(833,2752,-484,-1599) -> Matrix(1,0,0,1) Matrix(97,320,-184,-607) -> Matrix(3,8,-2,-5) Matrix(127,416,156,511) -> Matrix(1,0,0,1) Matrix(129,416,40,129) -> Matrix(1,2,0,1) Matrix(31,96,-52,-161) -> Matrix(1,0,0,1) Matrix(191,544,112,319) -> Matrix(1,2,-2,-3) Matrix(353,992,-216,-607) -> Matrix(1,-2,0,1) Matrix(127,352,92,255) -> Matrix(1,0,0,1) Matrix(95,256,-36,-97) -> Matrix(1,-4,0,1) Matrix(159,416,232,607) -> Matrix(1,4,0,1) Matrix(1567,4096,-992,-2593) -> Matrix(3,14,-2,-9) Matrix(417,1088,724,1889) -> Matrix(1,4,2,9) Matrix(383,992,-544,-1409) -> Matrix(1,0,0,1) Matrix(385,992,-248,-639) -> Matrix(1,2,0,1) Matrix(63,160,-76,-193) -> Matrix(1,2,0,1) Matrix(353,864,-248,-607) -> Matrix(1,0,0,1) Matrix(223,544,380,927) -> Matrix(1,2,0,1) Matrix(225,544,-304,-735) -> Matrix(1,0,0,1) Matrix(385,928,-212,-511) -> Matrix(1,0,0,1) Matrix(415,992,-228,-545) -> Matrix(1,2,0,1) Matrix(417,992,256,609) -> Matrix(1,2,2,5) Matrix(257,608,-216,-511) -> Matrix(3,8,-2,-5) Matrix(95,224,176,415) -> Matrix(1,2,2,5) Matrix(97,224,-152,-351) -> Matrix(1,0,0,1) Matrix(127,288,56,127) -> Matrix(1,2,0,1) Matrix(417,928,-244,-543) -> Matrix(3,8,-2,-5) Matrix(447,992,-260,-577) -> Matrix(5,8,-2,-3) Matrix(161,352,220,481) -> Matrix(1,0,0,1) Matrix(193,416,-148,-319) -> Matrix(3,8,-2,-5) Matrix(287,544,-220,-417) -> Matrix(3,8,-2,-5) Matrix(225,416,364,673) -> Matrix(1,2,2,5) Matrix(929,1696,-648,-1183) -> Matrix(1,0,0,1) Matrix(513,928,-424,-767) -> Matrix(1,0,0,1) Matrix(161,288,-232,-415) -> Matrix(1,0,0,1) Matrix(127,224,72,127) -> Matrix(1,2,0,1) Matrix(129,224,148,257) -> Matrix(1,2,0,1) Matrix(1313,2272,204,353) -> Matrix(3,10,2,7) Matrix(2369,4096,1000,1729) -> Matrix(3,8,4,11) Matrix(575,992,-928,-1601) -> Matrix(1,0,0,1) Matrix(13633,23456,3088,5313) -> Matrix(1,2,0,1) Matrix(14881,25600,6232,10721) -> Matrix(1,2,2,5) Matrix(6337,10816,1088,1857) -> Matrix(1,2,-2,-3) Matrix(9601,16384,3976,6785) -> Matrix(1,2,-2,-3) Matrix(319,544,112,191) -> Matrix(1,2,-2,-3) Matrix(321,544,416,705) -> Matrix(1,2,0,1) Matrix(1537,2592,456,769) -> Matrix(1,2,0,1) Matrix(609,1024,248,417) -> Matrix(1,2,0,1) Matrix(97,160,20,33) -> Matrix(1,2,0,1) Matrix(2273,3712,804,1313) -> Matrix(5,16,-6,-19) Matrix(2431,3968,-4000,-6529) -> Matrix(9,26,-8,-23) Matrix(609,992,256,417) -> Matrix(1,2,2,5) Matrix(159,256,-100,-161) -> Matrix(7,16,-4,-9) Matrix(607,960,748,1183) -> Matrix(5,8,-2,-3) Matrix(5791,9152,1356,2143) -> Matrix(5,8,-2,-3) Matrix(10369,16384,3808,6017) -> Matrix(5,8,-2,-3) Matrix(223,352,344,543) -> Matrix(1,2,-2,-3) Matrix(225,352,-388,-607) -> Matrix(5,8,-2,-3) Matrix(2561,3968,992,1537) -> Matrix(1,4,0,1) Matrix(2399,3712,-3868,-5985) -> Matrix(5,8,-2,-3) Matrix(353,544,-560,-863) -> Matrix(1,0,0,1) Matrix(65,96,44,65) -> Matrix(1,2,-2,-3) Matrix(287,416,-376,-545) -> Matrix(1,0,0,1) Matrix(289,416,512,737) -> Matrix(1,2,-2,-3) Matrix(223,320,200,287) -> Matrix(1,2,-2,-3) Matrix(1185,1696,-916,-1311) -> Matrix(3,8,-2,-5) Matrix(1057,1504,428,609) -> Matrix(1,2,0,1) Matrix(2881,4096,856,1217) -> Matrix(1,2,0,1) Matrix(383,544,540,767) -> Matrix(1,2,0,1) Matrix(927,1312,248,351) -> Matrix(5,12,2,5) Matrix(385,544,-724,-1023) -> Matrix(15,32,-8,-17) Matrix(159,224,-296,-417) -> Matrix(9,16,-4,-7) Matrix(735,1024,-1264,-1761) -> Matrix(11,14,-4,-5) Matrix(737,1024,208,289) -> Matrix(1,0,2,1) Matrix(255,352,92,127) -> Matrix(1,0,0,1) Matrix(257,352,468,641) -> Matrix(1,2,0,1) Matrix(959,1312,-796,-1089) -> Matrix(1,0,0,1) Matrix(2879,3936,4072,5567) -> Matrix(1,0,0,1) Matrix(961,1312,-1640,-2239) -> Matrix(1,0,0,1) Matrix(95,128,-72,-97) -> Matrix(3,8,-2,-5) Matrix(5535,7232,2032,2655) -> Matrix(5,8,-2,-3) Matrix(3137,4096,736,961) -> Matrix(5,8,-2,-3) Matrix(321,416,544,705) -> Matrix(1,2,-2,-3) Matrix(13537,17504,5668,7329) -> Matrix(7,12,4,7) Matrix(12673,16384,2872,3713) -> Matrix(11,18,-8,-13) Matrix(3071,3968,1188,1535) -> Matrix(1,2,-2,-3) Matrix(223,288,24,31) -> Matrix(5,8,-2,-3) Matrix(799,1024,-1424,-1825) -> Matrix(3,4,-4,-5) Matrix(801,1024,176,225) -> Matrix(3,2,-2,-1) Matrix(127,160,-204,-257) -> Matrix(5,8,-2,-3) Matrix(129,160,104,129) -> Matrix(3,4,-4,-5) Matrix(287,352,-340,-417) -> Matrix(5,4,-4,-3) Matrix(289,352,500,609) -> Matrix(1,0,2,1) Matrix(897,1088,-1160,-1407) -> Matrix(1,-4,0,1) Matrix(4609,5568,1908,2305) -> Matrix(1,2,0,1) Matrix(3393,4096,584,705) -> Matrix(1,2,0,1) Matrix(1537,1824,648,769) -> Matrix(3,4,2,3) Matrix(865,1024,136,161) -> Matrix(1,0,2,1) Matrix(191,224,272,319) -> Matrix(1,2,0,1) Matrix(193,224,56,65) -> Matrix(1,2,0,1) Matrix(479,544,140,159) -> Matrix(1,2,-2,-3) Matrix(287,320,200,223) -> Matrix(1,2,-2,-3) Matrix(929,832,680,609) -> Matrix(1,0,0,1) Matrix(255,224,436,383) -> Matrix(1,2,0,1) Matrix(257,224,148,129) -> Matrix(1,2,0,1) Matrix(415,352,112,95) -> Matrix(3,4,2,3) Matrix(609,512,496,417) -> Matrix(7,6,-6,-5) Matrix(545,448,-972,-799) -> Matrix(1,0,0,1) Matrix(511,416,156,127) -> Matrix(1,0,0,1) Matrix(159,128,-200,-161) -> Matrix(1,-2,0,1) Matrix(1375,1088,848,671) -> Matrix(1,2,2,5) Matrix(447,352,80,63) -> Matrix(1,2,0,1) Matrix(449,352,736,577) -> Matrix(1,2,-2,-3) Matrix(737,576,-1268,-991) -> Matrix(5,8,-2,-3) Matrix(705,544,416,321) -> Matrix(1,2,0,1) Matrix(543,416,124,95) -> Matrix(1,0,0,1) Matrix(673,512,464,353) -> Matrix(1,0,0,1) Matrix(1345,992,-2168,-1599) -> Matrix(5,8,-2,-3) Matrix(351,256,-484,-353) -> Matrix(1,-4,0,1) Matrix(575,416,264,191) -> Matrix(1,4,0,1) Matrix(1375,992,2172,1567) -> Matrix(1,4,0,1) Matrix(1377,992,-2264,-1631) -> Matrix(3,8,-2,-5) Matrix(223,160,400,287) -> Matrix(1,2,0,1) Matrix(767,544,540,383) -> Matrix(1,2,0,1) Matrix(769,544,1268,897) -> Matrix(1,0,0,1) Matrix(1313,928,-2036,-1439) -> Matrix(1,-2,0,1) Matrix(1407,992,-2180,-1537) -> Matrix(1,2,0,1) Matrix(319,224,272,191) -> Matrix(1,2,0,1) Matrix(735,512,412,287) -> Matrix(1,2,0,1) Matrix(1345,928,-2132,-1471) -> Matrix(1,0,0,1) Matrix(1439,992,-2276,-1569) -> Matrix(5,8,-2,-3) Matrix(513,352,188,129) -> Matrix(1,0,0,1) Matrix(641,416,396,257) -> Matrix(1,2,2,5) Matrix(3071,1984,2376,1535) -> Matrix(1,0,-2,1) Matrix(2783,1792,2036,1311) -> Matrix(1,2,0,1) Matrix(799,512,348,223) -> Matrix(1,2,0,1) Matrix(353,224,52,33) -> Matrix(1,4,0,1) Matrix(1567,992,2172,1375) -> Matrix(1,4,0,1) Matrix(4705,2976,1064,673) -> Matrix(3,8,-2,-5) Matrix(6241,3936,1676,1057) -> Matrix(3,4,2,3) Matrix(865,544,256,161) -> Matrix(1,2,0,1) Matrix(13985,8672,3872,2401) -> Matrix(5,12,2,5) Matrix(415,256,-676,-417) -> Matrix(7,16,-4,-9) Matrix(575,352,312,191) -> Matrix(1,2,-2,-3) Matrix(577,352,736,449) -> Matrix(1,2,-2,-3) Matrix(7585,4608,2688,1633) -> Matrix(13,12,-12,-11) Matrix(897,544,1268,769) -> Matrix(1,0,0,1) Matrix(865,512,272,161) -> Matrix(1,2,0,1) Matrix(705,416,544,321) -> Matrix(1,2,-2,-3) Matrix(927,544,380,223) -> Matrix(1,2,0,1) Matrix(3169,1856,712,417) -> Matrix(1,0,0,1) Matrix(383,224,436,255) -> Matrix(1,2,0,1) Matrix(3519,2048,988,575) -> Matrix(5,16,4,13) Matrix(609,352,500,289) -> Matrix(3,8,-2,-5) Matrix(223,128,-392,-225) -> Matrix(7,16,-4,-9) Matrix(1697,960,624,353) -> Matrix(5,8,-2,-3) Matrix(737,416,512,289) -> Matrix(1,2,-2,-3) Matrix(3647,2048,796,447) -> Matrix(7,8,-8,-9) Matrix(287,160,400,223) -> Matrix(1,2,0,1) Matrix(929,512,176,97) -> Matrix(1,2,0,1) Matrix(641,352,468,257) -> Matrix(1,2,0,1) Matrix(415,224,176,95) -> Matrix(1,2,2,5) Matrix(1,0,4,1) -> Matrix(1,2,-2,-3) Matrix(417,-224,296,-159) -> Matrix(1,0,-4,1) Matrix(289,-160,56,-31) -> Matrix(1,0,0,1) Matrix(1313,-736,512,-287) -> Matrix(1,2,0,1) Matrix(225,-128,392,-223) -> Matrix(1,0,4,1) Matrix(607,-352,388,-225) -> Matrix(1,0,-2,1) Matrix(2239,-1312,1640,-961) -> Matrix(1,0,0,1) Matrix(161,-96,52,-31) -> Matrix(1,0,0,1) Matrix(1631,-992,2264,-1377) -> Matrix(1,0,2,1) Matrix(417,-256,676,-415) -> Matrix(1,0,4,1) Matrix(257,-160,204,-127) -> Matrix(1,0,-2,1) Matrix(863,-544,560,-353) -> Matrix(1,0,0,1) Matrix(1569,-992,2276,-1439) -> Matrix(1,0,-2,1) Matrix(351,-224,152,-97) -> Matrix(1,0,0,1) Matrix(1439,-928,2036,-1313) -> Matrix(1,-2,0,1) Matrix(3073,-1984,1188,-767) -> Matrix(1,2,0,1) Matrix(927,-640,604,-417) -> Matrix(1,0,0,1) Matrix(415,-288,232,-161) -> Matrix(1,0,0,1) Matrix(1409,-992,544,-383) -> Matrix(1,0,0,1) Matrix(5505,-3968,1952,-1407) -> Matrix(7,-8,-6,7) Matrix(353,-256,484,-351) -> Matrix(1,-4,0,1) Matrix(479,-352,132,-97) -> Matrix(1,2,0,1) Matrix(545,-416,376,-287) -> Matrix(1,0,0,1) Matrix(289,-224,40,-31) -> Matrix(1,4,0,1) Matrix(1023,-800,656,-513) -> Matrix(1,0,0,1) Matrix(161,-128,200,-159) -> Matrix(1,-2,0,1) Matrix(193,-160,76,-63) -> Matrix(1,2,0,1) Matrix(417,-352,340,-287) -> Matrix(5,4,-4,-3) Matrix(319,-288,72,-65) -> Matrix(1,0,0,1) Matrix(511,-608,216,-257) -> Matrix(1,0,2,1) Matrix(1535,-1856,636,-769) -> Matrix(1,0,0,1) Matrix(449,-544,52,-63) -> Matrix(1,-4,0,1) Matrix(959,-1216,556,-705) -> Matrix(1,0,2,1) Matrix(351,-448,76,-97) -> Matrix(1,0,0,1) Matrix(5023,-6496,2104,-2721) -> Matrix(5,2,2,1) Matrix(97,-128,72,-95) -> Matrix(1,0,2,1) Matrix(353,-480,164,-223) -> Matrix(1,0,0,1) Matrix(5311,-7264,2200,-3009) -> Matrix(1,0,0,1) Matrix(415,-576,116,-161) -> Matrix(1,2,0,1) Matrix(1793,-2528,544,-767) -> Matrix(1,0,6,1) Matrix(2015,-2848,612,-865) -> Matrix(1,0,-6,1) Matrix(607,-864,248,-353) -> Matrix(1,0,0,1) Matrix(1919,-2752,804,-1153) -> Matrix(1,2,0,1) Matrix(639,-992,248,-385) -> Matrix(1,2,0,1) Matrix(1825,-2848,512,-799) -> Matrix(3,4,2,3) Matrix(161,-256,100,-159) -> Matrix(1,0,4,1) Matrix(2529,-4096,928,-1503) -> Matrix(5,-2,-2,1) Matrix(607,-992,216,-353) -> Matrix(1,-2,0,1) Matrix(511,-864,152,-257) -> Matrix(1,0,0,1) Matrix(543,-928,244,-417) -> Matrix(1,0,2,1) Matrix(577,-992,260,-447) -> Matrix(1,0,-2,1) Matrix(2209,-3808,612,-1055) -> Matrix(3,-2,2,-1) Matrix(351,-608,56,-97) -> Matrix(1,0,0,1) Matrix(511,-928,212,-385) -> Matrix(1,0,0,1) Matrix(545,-992,228,-415) -> Matrix(1,2,0,1) Matrix(223,-416,52,-97) -> Matrix(1,-2,0,1) Matrix(257,-544,60,-127) -> Matrix(1,-2,0,1) Matrix(767,-1696,232,-513) -> Matrix(1,0,2,1) Matrix(415,-928,72,-161) -> Matrix(1,0,0,1) Matrix(767,-1856,212,-513) -> Matrix(1,2,0,1) Matrix(863,-2208,188,-481) -> Matrix(3,-2,-4,3) Matrix(3585,-9248,992,-2559) -> Matrix(1,0,0,1) Matrix(97,-256,36,-95) -> Matrix(1,-4,0,1) Matrix(511,-1696,116,-385) -> Matrix(1,-2,0,1) Matrix(353,-1312,60,-223) -> Matrix(1,-2,2,-3) Matrix(33,-128,8,-31) -> Matrix(1,-4,0,1) Matrix(33,-256,4,-31) -> Matrix(1,-12,0,1) 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): 42 Degree of the the map X: 42 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. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 768 Minimal number of generators: 129 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 56 Genus: 37 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -8/1 -6/1 -14/3 -4/1 -10/3 -8/3 -12/5 -2/1 -12/7 -8/5 -48/31 -4/3 -8/7 0/1 1/1 8/7 16/13 4/3 16/11 3/2 8/5 12/7 16/9 2/1 16/7 12/5 5/2 8/3 48/17 3/1 16/5 10/3 64/19 7/2 32/9 11/3 15/4 4/1 64/15 13/3 128/29 9/2 32/7 14/3 5/1 16/3 11/2 17/3 64/11 6/1 32/5 13/2 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -9/1 1/1 3/1 -8/1 1/0 -7/1 -5/1 -3/1 -6/1 -3/1 -2/1 1/0 -11/2 -2/1 -16/3 -3/1 -1/1 -5/1 -3/1 -1/1 -14/3 -2/1 -1/1 1/0 -9/2 0/1 -13/3 -1/1 1/1 -4/1 1/0 -19/5 -5/1 -3/1 -15/4 1/0 -11/3 -3/1 -1/1 -18/5 -4/1 -3/1 1/0 -7/2 -2/1 -24/7 -2/1 -41/12 1/0 -17/5 -3/1 -1/1 -10/3 -3/1 -2/1 1/0 -13/4 1/0 -16/5 -3/1 -1/1 -3/1 -3/1 -1/1 -17/6 -4/3 -14/5 -1/1 0/1 1/0 -11/4 1/0 -8/3 1/0 -21/8 1/0 -13/5 -5/1 -3/1 -31/12 1/0 -18/7 -4/1 -3/1 1/0 -5/2 -2/1 -22/9 -2/1 -1/1 1/0 -17/7 -3/1 -1/1 -29/12 1/0 -12/5 1/0 -31/13 -11/3 -3/1 -19/8 1/0 -26/11 -3/1 -5/2 -2/1 -7/3 -3/1 -1/1 -16/7 -3/1 -1/1 -9/4 1/0 -20/9 -2/1 -11/5 -3/1 -1/1 -2/1 -2/1 -1/1 1/0 -15/8 1/0 -13/7 -3/1 -1/1 -11/6 -2/1 -31/17 -5/3 -1/1 -20/11 1/0 -29/16 1/0 -9/5 -3/1 -1/1 -16/9 -3/1 -1/1 -7/4 1/0 -19/11 -3/1 -7/3 -31/18 -2/1 -43/25 -3/1 -7/3 -12/7 -2/1 -41/24 -3/2 -29/17 -5/3 -1/1 -17/10 0/1 -5/3 -3/1 -1/1 -18/11 -3/1 -2/1 1/0 -49/30 -10/3 -80/49 -3/1 -31/19 -3/1 -19/7 -13/8 -5/2 -8/5 -2/1 -19/12 -3/2 -30/19 -2/1 -3/2 -1/1 -11/7 -5/3 -1/1 -14/9 -2/1 -1/1 1/0 -31/20 1/0 -48/31 -3/1 -1/1 -17/11 -3/1 -1/1 -3/2 -2/1 -16/11 -1/1 -13/9 -3/1 -1/1 -23/16 1/0 -33/23 -5/3 -1/1 -43/30 -2/1 -10/7 -2/1 -1/1 1/0 -37/26 -2/1 -64/45 -3/1 -1/1 -27/19 -3/1 -1/1 -17/12 -5/2 -41/29 -7/3 -11/5 -24/17 -2/1 -7/5 -5/3 -1/1 -32/23 -1/1 -25/18 0/1 -18/13 -2/1 -1/1 1/0 -11/8 1/0 -26/19 -2/1 -1/1 1/0 -67/49 -3/1 -1/1 -41/30 -2/1 -15/11 -3/1 -1/1 -4/3 -2/1 -17/13 -5/3 -1/1 -64/49 -5/3 -1/1 -47/36 -3/2 -30/23 -2/1 -5/3 -3/2 -13/10 -2/1 -22/17 -2/1 -5/3 -3/2 -75/58 -2/1 -128/99 -5/3 -53/41 -5/3 -11/7 -31/24 -3/2 -9/7 -7/5 -1/1 -32/25 -1/1 -23/18 0/1 -14/11 -2/1 -1/1 1/0 -5/4 -3/2 -16/13 -1/1 -11/9 -1/1 -1/3 -17/14 0/1 -23/19 -3/1 -1/1 -29/24 1/0 -64/53 -3/1 -1/1 -35/29 -3/1 -1/1 -6/5 -2/1 -1/1 1/0 -19/16 -3/2 -32/27 -1/1 -13/11 -1/1 1/1 -7/6 -2/1 -8/7 -2/1 -9/8 -3/2 -1/1 -3/1 -1/1 0/1 -1/1 1/1 -1/1 1/1 9/8 -1/2 8/7 0/1 7/6 0/1 6/5 -1/1 0/1 1/0 11/9 -5/3 -1/1 16/13 -1/1 5/4 -1/2 14/11 -1/1 0/1 1/0 9/7 -1/1 -3/5 13/10 0/1 4/3 0/1 19/14 0/1 15/11 -1/1 1/1 11/8 1/0 18/13 -1/1 0/1 1/0 7/5 -1/1 -1/3 24/17 0/1 41/29 1/5 1/3 17/12 1/2 10/7 -1/1 0/1 1/0 13/9 -1/1 1/1 16/11 -1/1 3/2 0/1 17/11 -1/1 1/1 14/9 -1/1 0/1 1/0 11/7 -1/1 -1/3 8/5 0/1 21/13 1/3 1/1 13/8 1/2 31/19 5/7 1/1 18/11 0/1 1/1 1/0 5/3 -1/1 1/1 22/13 0/1 1/1 1/0 17/10 -2/1 29/17 -1/1 -1/3 12/7 0/1 31/18 0/1 19/11 1/3 1/1 26/15 0/1 1/1 1/0 7/4 1/0 16/9 -1/1 1/1 9/5 -1/1 1/1 20/11 1/0 11/6 0/1 2/1 -1/1 0/1 1/0 15/7 -1/1 1/1 13/6 0/1 11/5 -1/1 1/1 31/14 0/1 20/9 0/1 29/13 -1/1 1/1 9/4 1/0 16/7 -1/1 1/1 7/3 -1/1 1/1 19/8 1/0 31/13 1/1 5/3 43/18 2/1 12/5 1/0 41/17 -1/1 1/1 29/12 1/0 17/7 -1/1 1/1 5/2 0/1 18/7 1/1 2/1 1/0 49/19 1/1 3/1 80/31 1/1 3/1 31/12 1/0 13/5 1/1 3/1 8/3 1/0 19/7 -3/1 -1/1 30/11 -2/1 -1/1 1/0 11/4 1/0 14/5 -2/1 -1/1 1/0 31/11 -9/7 -1/1 48/17 -1/1 17/6 -2/3 3/1 -1/1 1/1 16/5 -1/1 1/1 13/4 1/0 23/7 -1/1 -1/3 33/10 0/1 43/13 1/3 1/1 10/3 0/1 1/1 1/0 37/11 -1/1 1/1 64/19 -1/1 1/1 27/8 1/0 17/5 -1/1 1/1 41/12 1/0 24/7 0/1 7/2 0/1 32/9 1/1 25/7 1/1 5/3 18/5 1/1 2/1 1/0 11/3 -1/1 1/1 26/7 1/1 3/2 2/1 67/18 2/1 41/11 1/1 5/3 15/4 1/0 4/1 1/0 17/4 1/0 64/15 -3/1 -1/1 47/11 -3/1 -1/1 30/7 -3/1 -2/1 1/0 13/3 -3/1 -1/1 22/5 -2/1 -1/1 1/0 75/17 -5/3 -1/1 128/29 -1/1 53/12 1/0 31/7 -1/1 1/1 9/2 -2/1 32/7 -1/1 23/5 -1/1 -3/5 14/3 -1/1 0/1 1/0 5/1 -1/1 1/1 16/3 -1/1 1/1 11/2 0/1 17/3 -1/1 1/1 23/4 1/0 29/5 -1/1 1/1 64/11 -1/1 1/1 35/6 0/1 6/1 0/1 1/1 1/0 19/3 1/3 1/1 32/5 1/1 13/2 2/1 7/1 1/1 3/1 8/1 1/0 9/1 -5/1 -3/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(33,320,10,97) (-9/1,1/0) -> (23/7,33/10) Hyperbolic Matrix(65,544,46,385) (-9/1,-8/1) -> (24/17,41/29) Hyperbolic Matrix(31,224,22,159) (-8/1,-7/1) -> (7/5,24/17) Hyperbolic Matrix(33,224,-14,-95) (-7/1,-6/1) -> (-26/11,-7/3) Hyperbolic Matrix(63,352,-46,-257) (-6/1,-11/2) -> (-11/8,-26/19) Hyperbolic Matrix(65,352,12,65) (-11/2,-16/3) -> (16/3,11/2) Hyperbolic Matrix(31,160,6,31) (-16/3,-5/1) -> (5/1,16/3) Hyperbolic Matrix(33,160,20,97) (-5/1,-14/3) -> (18/11,5/3) Hyperbolic Matrix(97,448,-76,-351) (-14/3,-9/2) -> (-23/18,-14/11) Hyperbolic Matrix(95,416,-66,-289) (-9/2,-13/3) -> (-13/9,-23/16) Hyperbolic Matrix(31,128,-8,-33) (-13/3,-4/1) -> (-4/1,-19/5) Parabolic Matrix(127,480,-68,-257) (-19/5,-15/4) -> (-15/8,-13/7) Hyperbolic Matrix(95,352,-78,-289) (-15/4,-11/3) -> (-11/9,-17/14) Hyperbolic Matrix(97,352,62,225) (-11/3,-18/5) -> (14/9,11/7) Hyperbolic Matrix(161,576,-116,-415) (-18/5,-7/2) -> (-25/18,-18/13) Hyperbolic Matrix(65,224,56,193) (-7/2,-24/7) -> (8/7,7/6) Hyperbolic Matrix(159,544,140,479) (-24/7,-41/12) -> (9/8,8/7) Hyperbolic Matrix(319,1088,56,191) (-41/12,-17/5) -> (17/3,23/4) Hyperbolic Matrix(161,544,-66,-223) (-17/5,-10/3) -> (-22/9,-17/7) Hyperbolic Matrix(127,416,-98,-321) (-10/3,-13/4) -> (-13/10,-22/17) Hyperbolic Matrix(129,416,40,129) (-13/4,-16/5) -> (16/5,13/4) Hyperbolic Matrix(31,96,10,31) (-16/5,-3/1) -> (3/1,16/5) Hyperbolic Matrix(191,544,112,319) (-3/1,-17/6) -> (17/10,29/17) Hyperbolic Matrix(353,992,-216,-607) (-17/6,-14/5) -> (-18/11,-49/30) Hyperbolic Matrix(127,352,92,255) (-14/5,-11/4) -> (11/8,18/13) Hyperbolic Matrix(95,256,-36,-97) (-11/4,-8/3) -> (-8/3,-21/8) Parabolic Matrix(159,416,-86,-225) (-21/8,-13/5) -> (-13/7,-11/6) Hyperbolic Matrix(383,992,222,575) (-13/5,-31/12) -> (31/18,19/11) Hyperbolic Matrix(385,992,-248,-639) (-31/12,-18/7) -> (-14/9,-31/20) Hyperbolic Matrix(63,160,50,127) (-18/7,-5/2) -> (5/4,14/11) Hyperbolic Matrix(353,864,-248,-607) (-5/2,-22/9) -> (-10/7,-37/26) Hyperbolic Matrix(225,544,146,353) (-17/7,-29/12) -> (3/2,17/11) Hyperbolic Matrix(385,928,-212,-511) (-29/12,-12/5) -> (-20/11,-29/16) Hyperbolic Matrix(415,992,-228,-545) (-12/5,-31/13) -> (-31/17,-20/11) Hyperbolic Matrix(417,992,256,609) (-31/13,-19/8) -> (13/8,31/19) Hyperbolic Matrix(257,608,-216,-511) (-19/8,-26/11) -> (-6/5,-19/16) Hyperbolic Matrix(97,224,42,97) (-7/3,-16/7) -> (16/7,7/3) Hyperbolic Matrix(127,288,56,127) (-16/7,-9/4) -> (9/4,16/7) Hyperbolic Matrix(417,928,-244,-543) (-9/4,-20/9) -> (-12/7,-41/24) Hyperbolic Matrix(447,992,-260,-577) (-20/9,-11/5) -> (-43/25,-12/7) Hyperbolic Matrix(161,352,-102,-223) (-11/5,-2/1) -> (-30/19,-11/7) Hyperbolic Matrix(287,544,-220,-417) (-2/1,-15/8) -> (-47/36,-30/23) Hyperbolic Matrix(929,1696,-648,-1183) (-11/6,-31/17) -> (-33/23,-43/30) Hyperbolic Matrix(513,928,-424,-767) (-29/16,-9/5) -> (-23/19,-29/24) Hyperbolic Matrix(161,288,90,161) (-9/5,-16/9) -> (16/9,9/5) Hyperbolic Matrix(127,224,72,127) (-16/9,-7/4) -> (7/4,16/9) Hyperbolic Matrix(129,224,-110,-191) (-7/4,-19/11) -> (-13/11,-7/6) Hyperbolic Matrix(575,992,222,383) (-19/11,-31/18) -> (31/12,13/5) Hyperbolic Matrix(1729,2976,-1338,-2303) (-31/18,-43/25) -> (-53/41,-31/24) Hyperbolic Matrix(2305,3936,-1686,-2879) (-41/24,-29/17) -> (-67/49,-41/30) Hyperbolic Matrix(319,544,112,191) (-29/17,-17/10) -> (17/6,3/1) Hyperbolic Matrix(321,544,-226,-383) (-17/10,-5/3) -> (-27/19,-17/12) Hyperbolic Matrix(97,160,20,33) (-5/3,-18/11) -> (14/3,5/1) Hyperbolic Matrix(2273,3712,804,1313) (-49/30,-80/49) -> (48/17,17/6) Hyperbolic Matrix(2431,3968,862,1407) (-80/49,-31/19) -> (31/11,48/17) Hyperbolic Matrix(609,992,256,417) (-31/19,-13/8) -> (19/8,31/13) Hyperbolic Matrix(159,256,-100,-161) (-13/8,-8/5) -> (-8/5,-19/12) Parabolic Matrix(607,960,-466,-737) (-19/12,-30/19) -> (-30/23,-13/10) Hyperbolic Matrix(225,352,62,97) (-11/7,-14/9) -> (18/5,11/3) Hyperbolic Matrix(2561,3968,992,1537) (-31/20,-48/31) -> (80/31,31/12) Hyperbolic Matrix(2399,3712,930,1439) (-48/31,-17/11) -> (49/19,80/31) Hyperbolic Matrix(353,544,146,225) (-17/11,-3/2) -> (29/12,17/7) Hyperbolic Matrix(65,96,44,65) (-3/2,-16/11) -> (16/11,3/2) Hyperbolic Matrix(287,416,198,287) (-16/11,-13/9) -> (13/9,16/11) Hyperbolic Matrix(223,320,200,287) (-23/16,-33/23) -> (1/1,9/8) Hyperbolic Matrix(1185,1696,-916,-1311) (-43/30,-10/7) -> (-22/17,-75/58) Hyperbolic Matrix(2879,4096,854,1215) (-37/26,-64/45) -> (64/19,27/8) Hyperbolic Matrix(2881,4096,856,1217) (-64/45,-27/19) -> (37/11,64/19) Hyperbolic Matrix(927,1312,248,351) (-17/12,-41/29) -> (41/11,15/4) Hyperbolic Matrix(385,544,46,65) (-41/29,-24/17) -> (8/1,9/1) Hyperbolic Matrix(159,224,22,31) (-24/17,-7/5) -> (7/1,8/1) Hyperbolic Matrix(735,1024,206,287) (-7/5,-32/23) -> (32/9,25/7) Hyperbolic Matrix(737,1024,208,289) (-32/23,-25/18) -> (7/2,32/9) Hyperbolic Matrix(255,352,92,127) (-18/13,-11/8) -> (11/4,14/5) Hyperbolic Matrix(959,1312,-796,-1089) (-26/19,-67/49) -> (-35/29,-6/5) Hyperbolic Matrix(961,1312,282,385) (-41/30,-15/11) -> (17/5,41/12) Hyperbolic Matrix(95,128,-72,-97) (-15/11,-4/3) -> (-4/3,-17/13) Parabolic Matrix(3135,4096,734,959) (-17/13,-64/49) -> (64/15,47/11) Hyperbolic Matrix(3137,4096,736,961) (-64/49,-47/36) -> (17/4,64/15) Hyperbolic Matrix(12671,16384,2870,3711) (-75/58,-128/99) -> (128/29,53/12) Hyperbolic Matrix(12673,16384,2872,3713) (-128/99,-53/41) -> (75/17,128/29) Hyperbolic Matrix(223,288,24,31) (-31/24,-9/7) -> (9/1,1/0) Hyperbolic Matrix(799,1024,174,223) (-9/7,-32/25) -> (32/7,23/5) Hyperbolic Matrix(801,1024,176,225) (-32/25,-23/18) -> (9/2,32/7) Hyperbolic Matrix(127,160,50,63) (-14/11,-5/4) -> (5/2,18/7) Hyperbolic Matrix(129,160,104,129) (-5/4,-16/13) -> (16/13,5/4) Hyperbolic Matrix(287,352,234,287) (-16/13,-11/9) -> (11/9,16/13) Hyperbolic Matrix(897,1088,634,769) (-17/14,-23/19) -> (41/29,17/12) Hyperbolic Matrix(3391,4096,582,703) (-29/24,-64/53) -> (64/11,35/6) Hyperbolic Matrix(3393,4096,584,705) (-64/53,-35/29) -> (29/5,64/11) Hyperbolic Matrix(863,1024,134,159) (-19/16,-32/27) -> (32/5,13/2) Hyperbolic Matrix(865,1024,136,161) (-32/27,-13/11) -> (19/3,32/5) Hyperbolic Matrix(193,224,56,65) (-7/6,-8/7) -> (24/7,7/2) Hyperbolic Matrix(479,544,140,159) (-8/7,-9/8) -> (41/12,24/7) Hyperbolic Matrix(257,288,58,65) (-9/8,-1/1) -> (31/7,9/2) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(191,-224,110,-129) (7/6,6/5) -> (26/15,7/4) Hyperbolic Matrix(289,-352,78,-95) (6/5,11/9) -> (11/3,26/7) Hyperbolic Matrix(351,-448,76,-97) (14/11,9/7) -> (23/5,14/3) Hyperbolic Matrix(321,-416,98,-127) (9/7,13/10) -> (13/4,23/7) Hyperbolic Matrix(97,-128,72,-95) (13/10,4/3) -> (4/3,19/14) Parabolic Matrix(353,-480,164,-223) (19/14,15/11) -> (15/7,13/6) Hyperbolic Matrix(257,-352,46,-63) (15/11,11/8) -> (11/2,17/3) Hyperbolic Matrix(415,-576,116,-161) (18/13,7/5) -> (25/7,18/5) Hyperbolic Matrix(383,-544,226,-321) (17/12,10/7) -> (22/13,17/10) Hyperbolic Matrix(289,-416,66,-95) (10/7,13/9) -> (13/3,22/5) Hyperbolic Matrix(639,-992,248,-385) (17/11,14/9) -> (18/7,49/19) Hyperbolic Matrix(161,-256,100,-159) (11/7,8/5) -> (8/5,21/13) Parabolic Matrix(257,-416,118,-191) (21/13,13/8) -> (13/6,11/5) Hyperbolic Matrix(607,-992,216,-353) (31/19,18/11) -> (14/5,31/11) Hyperbolic Matrix(511,-864,152,-257) (5/3,22/13) -> (10/3,37/11) Hyperbolic Matrix(543,-928,244,-417) (29/17,12/7) -> (20/9,29/13) Hyperbolic Matrix(577,-992,260,-447) (12/7,31/18) -> (31/14,20/9) Hyperbolic Matrix(351,-608,56,-97) (19/11,26/15) -> (6/1,19/3) Hyperbolic Matrix(511,-928,212,-385) (9/5,20/11) -> (12/5,41/17) Hyperbolic Matrix(545,-992,228,-415) (20/11,11/6) -> (43/18,12/5) Hyperbolic Matrix(191,-352,70,-129) (11/6,2/1) -> (30/11,11/4) Hyperbolic Matrix(257,-544,60,-127) (2/1,15/7) -> (47/11,30/7) Hyperbolic Matrix(767,-1696,232,-513) (11/5,31/14) -> (33/10,43/13) Hyperbolic Matrix(415,-928,72,-161) (29/13,9/4) -> (23/4,29/5) Hyperbolic Matrix(95,-224,14,-33) (7/3,19/8) -> (13/2,7/1) Hyperbolic Matrix(1247,-2976,282,-673) (31/13,43/18) -> (53/12,31/7) Hyperbolic Matrix(1631,-3936,438,-1057) (41/17,29/12) -> (67/18,41/11) Hyperbolic Matrix(223,-544,66,-161) (17/7,5/2) -> (27/8,17/5) Hyperbolic Matrix(97,-256,36,-95) (13/5,8/3) -> (8/3,19/7) Parabolic Matrix(353,-960,82,-223) (19/7,30/11) -> (30/7,13/3) Hyperbolic Matrix(511,-1696,116,-385) (43/13,10/3) -> (22/5,75/17) Hyperbolic Matrix(353,-1312,60,-223) (26/7,67/18) -> (35/6,6/1) Hyperbolic Matrix(33,-128,8,-31) (15/4,4/1) -> (4/1,17/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(33,320,10,97) -> Matrix(0,-1,1,0) Matrix(65,544,46,385) -> Matrix(0,1,-1,6) Matrix(31,224,22,159) -> Matrix(0,-1,1,6) Matrix(33,224,-14,-95) -> Matrix(2,9,-1,-4) Matrix(63,352,-46,-257) -> Matrix(2,5,-1,-2) Matrix(65,352,12,65) -> Matrix(1,2,0,1) Matrix(31,160,6,31) -> Matrix(0,-1,1,2) Matrix(33,160,20,97) -> Matrix(1,2,0,1) Matrix(97,448,-76,-351) -> Matrix(1,0,0,1) Matrix(95,416,-66,-289) -> Matrix(2,1,-1,0) Matrix(31,128,-8,-33) -> Matrix(1,-4,0,1) Matrix(127,480,-68,-257) -> Matrix(1,2,0,1) Matrix(95,352,-78,-289) -> Matrix(0,-1,1,4) Matrix(97,352,62,225) -> Matrix(0,-1,1,4) Matrix(161,576,-116,-415) -> Matrix(1,2,0,1) Matrix(65,224,56,193) -> Matrix(1,2,0,1) Matrix(159,544,140,479) -> Matrix(1,2,-2,-3) Matrix(319,1088,56,191) -> Matrix(1,2,0,1) Matrix(161,544,-66,-223) -> Matrix(2,5,-1,-2) Matrix(127,416,-98,-321) -> Matrix(2,1,-1,0) Matrix(129,416,40,129) -> Matrix(1,2,0,1) Matrix(31,96,10,31) -> Matrix(0,-1,1,2) Matrix(191,544,112,319) -> Matrix(1,2,-2,-3) Matrix(353,992,-216,-607) -> Matrix(1,-2,0,1) Matrix(127,352,92,255) -> Matrix(1,0,0,1) Matrix(95,256,-36,-97) -> Matrix(1,-4,0,1) Matrix(159,416,-86,-225) -> Matrix(2,9,-1,-4) Matrix(383,992,222,575) -> Matrix(0,-1,1,2) Matrix(385,992,-248,-639) -> Matrix(1,2,0,1) Matrix(63,160,50,127) -> Matrix(0,-1,1,4) Matrix(353,864,-248,-607) -> Matrix(1,0,0,1) Matrix(225,544,146,353) -> Matrix(0,-1,1,2) Matrix(385,928,-212,-511) -> Matrix(1,0,0,1) Matrix(415,992,-228,-545) -> Matrix(1,2,0,1) Matrix(417,992,256,609) -> Matrix(1,2,2,5) Matrix(257,608,-216,-511) -> Matrix(3,8,-2,-5) Matrix(97,224,42,97) -> Matrix(0,-1,1,2) Matrix(127,288,56,127) -> Matrix(1,2,0,1) Matrix(417,928,-244,-543) -> Matrix(3,8,-2,-5) Matrix(447,992,-260,-577) -> Matrix(5,8,-2,-3) Matrix(161,352,-102,-223) -> Matrix(2,1,-1,0) Matrix(287,544,-220,-417) -> Matrix(3,8,-2,-5) Matrix(929,1696,-648,-1183) -> Matrix(1,0,0,1) Matrix(513,928,-424,-767) -> Matrix(1,0,0,1) Matrix(161,288,90,161) -> Matrix(0,-1,1,2) Matrix(127,224,72,127) -> Matrix(1,2,0,1) Matrix(129,224,-110,-191) -> Matrix(2,5,-1,-2) Matrix(575,992,222,383) -> Matrix(0,-1,1,2) Matrix(1729,2976,-1338,-2303) -> Matrix(2,1,-1,0) Matrix(2305,3936,-1686,-2879) -> Matrix(0,-1,1,2) Matrix(319,544,112,191) -> Matrix(1,2,-2,-3) Matrix(321,544,-226,-383) -> Matrix(2,5,-1,-2) Matrix(97,160,20,33) -> Matrix(1,2,0,1) Matrix(2273,3712,804,1313) -> Matrix(5,16,-6,-19) Matrix(2431,3968,862,1407) -> Matrix(8,23,-7,-20) Matrix(609,992,256,417) -> Matrix(1,2,2,5) Matrix(159,256,-100,-161) -> Matrix(7,16,-4,-9) Matrix(607,960,-466,-737) -> Matrix(8,13,-5,-8) Matrix(225,352,62,97) -> Matrix(2,3,1,2) Matrix(2561,3968,992,1537) -> Matrix(1,4,0,1) Matrix(2399,3712,930,1439) -> Matrix(2,3,1,2) Matrix(353,544,146,225) -> Matrix(0,-1,1,2) Matrix(65,96,44,65) -> Matrix(1,2,-2,-3) Matrix(287,416,198,287) -> Matrix(0,-1,1,2) Matrix(223,320,200,287) -> Matrix(1,2,-2,-3) Matrix(1185,1696,-916,-1311) -> Matrix(3,8,-2,-5) Matrix(2879,4096,854,1215) -> Matrix(0,-1,1,2) Matrix(2881,4096,856,1217) -> Matrix(1,2,0,1) Matrix(927,1312,248,351) -> Matrix(5,12,2,5) Matrix(385,544,46,65) -> Matrix(8,17,-1,-2) Matrix(159,224,22,31) -> Matrix(4,7,1,2) Matrix(735,1024,206,287) -> Matrix(4,5,3,4) Matrix(737,1024,208,289) -> Matrix(1,0,2,1) Matrix(255,352,92,127) -> Matrix(1,0,0,1) Matrix(959,1312,-796,-1089) -> Matrix(1,0,0,1) Matrix(961,1312,282,385) -> Matrix(0,-1,1,2) Matrix(95,128,-72,-97) -> Matrix(3,8,-2,-5) Matrix(3135,4096,734,959) -> Matrix(0,-1,1,2) Matrix(3137,4096,736,961) -> Matrix(5,8,-2,-3) Matrix(12671,16384,2870,3711) -> Matrix(2,3,1,2) Matrix(12673,16384,2872,3713) -> Matrix(11,18,-8,-13) Matrix(223,288,24,31) -> Matrix(5,8,-2,-3) Matrix(799,1024,174,223) -> Matrix(4,5,-5,-6) Matrix(801,1024,176,225) -> Matrix(3,2,-2,-1) Matrix(127,160,50,63) -> Matrix(2,3,1,2) Matrix(129,160,104,129) -> Matrix(3,4,-4,-5) Matrix(287,352,234,287) -> Matrix(4,3,-3,-2) Matrix(897,1088,634,769) -> Matrix(0,1,-1,2) Matrix(3391,4096,582,703) -> Matrix(0,-1,1,2) Matrix(3393,4096,584,705) -> Matrix(1,2,0,1) Matrix(863,1024,134,159) -> Matrix(4,5,3,4) Matrix(865,1024,136,161) -> Matrix(1,0,2,1) Matrix(193,224,56,65) -> Matrix(1,2,0,1) Matrix(479,544,140,159) -> Matrix(1,2,-2,-3) Matrix(257,288,58,65) -> Matrix(0,-1,1,2) Matrix(1,0,2,1) -> Matrix(0,-1,1,2) Matrix(191,-224,110,-129) -> Matrix(0,-1,1,0) Matrix(289,-352,78,-95) -> Matrix(2,3,1,2) Matrix(351,-448,76,-97) -> Matrix(1,0,0,1) Matrix(321,-416,98,-127) -> Matrix(2,1,-1,0) Matrix(97,-128,72,-95) -> Matrix(1,0,2,1) Matrix(353,-480,164,-223) -> Matrix(1,0,0,1) Matrix(257,-352,46,-63) -> Matrix(0,-1,1,0) Matrix(415,-576,116,-161) -> Matrix(1,2,0,1) Matrix(383,-544,226,-321) -> Matrix(0,-1,1,0) Matrix(289,-416,66,-95) -> Matrix(2,1,-1,0) Matrix(639,-992,248,-385) -> Matrix(1,2,0,1) Matrix(161,-256,100,-159) -> Matrix(1,0,4,1) Matrix(257,-416,118,-191) -> Matrix(2,-1,1,0) Matrix(607,-992,216,-353) -> Matrix(1,-2,0,1) Matrix(511,-864,152,-257) -> Matrix(1,0,0,1) Matrix(543,-928,244,-417) -> Matrix(1,0,2,1) Matrix(577,-992,260,-447) -> Matrix(1,0,-2,1) Matrix(351,-608,56,-97) -> Matrix(1,0,0,1) Matrix(511,-928,212,-385) -> Matrix(1,0,0,1) Matrix(545,-992,228,-415) -> Matrix(1,2,0,1) Matrix(191,-352,70,-129) -> Matrix(2,1,-1,0) Matrix(257,-544,60,-127) -> Matrix(1,-2,0,1) Matrix(767,-1696,232,-513) -> Matrix(1,0,2,1) Matrix(415,-928,72,-161) -> Matrix(1,0,0,1) Matrix(95,-224,14,-33) -> Matrix(2,-1,1,0) Matrix(1247,-2976,282,-673) -> Matrix(2,-3,-1,2) Matrix(1631,-3936,438,-1057) -> Matrix(2,3,1,2) Matrix(223,-544,66,-161) -> Matrix(0,-1,1,0) Matrix(97,-256,36,-95) -> Matrix(1,-4,0,1) Matrix(353,-960,82,-223) -> Matrix(2,5,-1,-2) Matrix(511,-1696,116,-385) -> Matrix(1,-2,0,1) Matrix(353,-1312,60,-223) -> Matrix(1,-2,2,-3) Matrix(33,-128,8,-31) -> Matrix(1,-4,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 42 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 -1/1 1 2 1/1 (-1/1,1/1) 0 16 9/8 -1/2 1 16 8/7 0/1 1 2 7/6 0/1 1 16 6/5 0 8 11/9 (-5/3,-1/1) 0 16 16/13 -1/1 7 2 5/4 -1/2 1 16 14/11 0 8 9/7 (-1/1,-3/5) 0 16 13/10 0/1 1 16 4/3 0/1 1 4 19/14 0/1 1 16 15/11 (-1/1,1/1) 0 16 11/8 1/0 1 16 18/13 0 8 7/5 (-1/1,-1/3) 0 16 24/17 0/1 6 2 41/29 (1/5,1/3) 0 16 17/12 1/2 1 16 10/7 0 8 13/9 (-1/1,1/1) 0 16 16/11 -1/1 1 2 3/2 0/1 1 16 17/11 (-1/1,1/1) 0 16 14/9 0 8 11/7 (-1/1,-1/3) 0 16 8/5 0/1 2 2 21/13 (1/3,1/1) 0 16 13/8 1/2 1 16 31/19 (5/7,1/1) 0 16 18/11 0 8 5/3 (-1/1,1/1) 0 16 22/13 0 8 17/10 -2/1 1 16 29/17 (-1/1,-1/3) 0 16 12/7 0/1 2 4 31/18 0/1 1 16 19/11 (1/3,1/1) 0 16 26/15 0 8 7/4 1/0 1 16 16/9 (-1/1,1/1).(0/1,1/0) 0 2 9/5 (-1/1,1/1) 0 16 20/11 1/0 1 4 11/6 0/1 1 16 2/1 0 8 15/7 (-1/1,1/1) 0 16 13/6 0/1 1 16 11/5 (-1/1,1/1) 0 16 31/14 0/1 1 16 20/9 0/1 2 4 29/13 (-1/1,1/1) 0 16 9/4 1/0 1 16 16/7 (-1/1,1/1).(0/1,1/0) 0 2 7/3 (-1/1,1/1) 0 16 19/8 1/0 1 16 31/13 (1/1,5/3) 0 16 43/18 2/1 1 16 12/5 1/0 1 4 41/17 (-1/1,1/1) 0 16 29/12 1/0 1 16 17/7 (-1/1,1/1) 0 16 5/2 0/1 1 16 18/7 0 8 49/19 (1/1,3/1) 0 16 80/31 (1/1,3/1).(2/1,1/0) 0 2 31/12 1/0 1 16 13/5 (1/1,3/1) 0 16 8/3 1/0 2 2 19/7 (-3/1,-1/1) 0 16 30/11 0 8 11/4 1/0 1 16 14/5 0 8 31/11 (-9/7,-1/1) 0 16 48/17 -1/1 13 2 17/6 -2/3 1 16 3/1 (-1/1,1/1) 0 16 16/5 (-1/1,1/1).(0/1,1/0) 0 2 13/4 1/0 1 16 23/7 (-1/1,-1/3) 0 16 33/10 0/1 1 16 43/13 (1/3,1/1) 0 16 10/3 0 8 37/11 (-1/1,1/1) 0 16 64/19 (-1/1,1/1).(0/1,1/0) 0 2 27/8 1/0 1 16 17/5 (-1/1,1/1) 0 16 41/12 1/0 1 16 24/7 0/1 1 2 7/2 0/1 1 16 32/9 1/1 5 2 25/7 (1/1,5/3) 0 16 18/5 0 8 11/3 (-1/1,1/1) 0 16 26/7 0 8 67/18 2/1 1 16 41/11 (1/1,5/3) 0 16 15/4 1/0 1 16 4/1 1/0 2 4 17/4 1/0 1 16 64/15 (-3/1,-1/1).(-2/1,1/0) 0 2 47/11 (-3/1,-1/1) 0 16 30/7 0 8 13/3 (-3/1,-1/1) 0 16 22/5 0 8 75/17 (-5/3,-1/1) 0 16 128/29 -1/1 3 2 53/12 1/0 1 16 31/7 (-1/1,1/1) 0 16 9/2 -2/1 1 16 32/7 -1/1 7 2 23/5 (-1/1,-3/5) 0 16 14/3 0 8 5/1 (-1/1,1/1) 0 16 16/3 (-1/1,1/1).(0/1,1/0) 0 2 11/2 0/1 1 16 17/3 (-1/1,1/1) 0 16 23/4 1/0 1 16 29/5 (-1/1,1/1) 0 16 64/11 (-1/1,1/1).(0/1,1/0) 0 2 35/6 0/1 1 16 6/1 0 8 19/3 (1/3,1/1) 0 16 32/5 1/1 5 2 13/2 2/1 1 16 7/1 (1/1,3/1) 0 16 8/1 1/0 6 2 9/1 (-5/1,-3/1) 0 16 1/0 1/0 1 16 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(257,-288,58,-65) (1/1,9/8) -> (31/7,9/2) Glide Reflection Matrix(479,-544,140,-159) (9/8,8/7) -> (41/12,24/7) Glide Reflection Matrix(193,-224,56,-65) (8/7,7/6) -> (24/7,7/2) Glide Reflection Matrix(191,-224,110,-129) (7/6,6/5) -> (26/15,7/4) Hyperbolic Matrix(289,-352,78,-95) (6/5,11/9) -> (11/3,26/7) Hyperbolic Matrix(287,-352,234,-287) (11/9,16/13) -> (11/9,16/13) Reflection Matrix(129,-160,104,-129) (16/13,5/4) -> (16/13,5/4) Reflection Matrix(127,-160,50,-63) (5/4,14/11) -> (5/2,18/7) Glide Reflection Matrix(351,-448,76,-97) (14/11,9/7) -> (23/5,14/3) Hyperbolic Matrix(321,-416,98,-127) (9/7,13/10) -> (13/4,23/7) Hyperbolic Matrix(97,-128,72,-95) (13/10,4/3) -> (4/3,19/14) Parabolic Matrix(353,-480,164,-223) (19/14,15/11) -> (15/7,13/6) Hyperbolic Matrix(257,-352,46,-63) (15/11,11/8) -> (11/2,17/3) Hyperbolic Matrix(255,-352,92,-127) (11/8,18/13) -> (11/4,14/5) Glide Reflection Matrix(415,-576,116,-161) (18/13,7/5) -> (25/7,18/5) Hyperbolic Matrix(159,-224,22,-31) (7/5,24/17) -> (7/1,8/1) Glide Reflection Matrix(385,-544,46,-65) (24/17,41/29) -> (8/1,9/1) Glide Reflection Matrix(927,-1312,248,-351) (41/29,17/12) -> (41/11,15/4) Glide Reflection Matrix(383,-544,226,-321) (17/12,10/7) -> (22/13,17/10) Hyperbolic Matrix(289,-416,66,-95) (10/7,13/9) -> (13/3,22/5) Hyperbolic Matrix(287,-416,198,-287) (13/9,16/11) -> (13/9,16/11) Reflection Matrix(65,-96,44,-65) (16/11,3/2) -> (16/11,3/2) Reflection Matrix(353,-544,146,-225) (3/2,17/11) -> (29/12,17/7) Glide Reflection Matrix(639,-992,248,-385) (17/11,14/9) -> (18/7,49/19) Hyperbolic Matrix(225,-352,62,-97) (14/9,11/7) -> (18/5,11/3) Glide Reflection Matrix(161,-256,100,-159) (11/7,8/5) -> (8/5,21/13) Parabolic Matrix(257,-416,118,-191) (21/13,13/8) -> (13/6,11/5) Hyperbolic Matrix(609,-992,256,-417) (13/8,31/19) -> (19/8,31/13) Glide Reflection Matrix(607,-992,216,-353) (31/19,18/11) -> (14/5,31/11) Hyperbolic Matrix(97,-160,20,-33) (18/11,5/3) -> (14/3,5/1) Glide Reflection Matrix(511,-864,152,-257) (5/3,22/13) -> (10/3,37/11) Hyperbolic Matrix(319,-544,112,-191) (17/10,29/17) -> (17/6,3/1) Glide Reflection Matrix(543,-928,244,-417) (29/17,12/7) -> (20/9,29/13) Hyperbolic Matrix(577,-992,260,-447) (12/7,31/18) -> (31/14,20/9) Hyperbolic Matrix(575,-992,222,-383) (31/18,19/11) -> (31/12,13/5) Glide Reflection Matrix(351,-608,56,-97) (19/11,26/15) -> (6/1,19/3) Hyperbolic Matrix(127,-224,72,-127) (7/4,16/9) -> (7/4,16/9) Reflection Matrix(161,-288,90,-161) (16/9,9/5) -> (16/9,9/5) Reflection Matrix(511,-928,212,-385) (9/5,20/11) -> (12/5,41/17) Hyperbolic Matrix(545,-992,228,-415) (20/11,11/6) -> (43/18,12/5) Hyperbolic Matrix(191,-352,70,-129) (11/6,2/1) -> (30/11,11/4) Hyperbolic Matrix(257,-544,60,-127) (2/1,15/7) -> (47/11,30/7) Hyperbolic Matrix(767,-1696,232,-513) (11/5,31/14) -> (33/10,43/13) Hyperbolic Matrix(415,-928,72,-161) (29/13,9/4) -> (23/4,29/5) Hyperbolic Matrix(127,-288,56,-127) (9/4,16/7) -> (9/4,16/7) Reflection Matrix(97,-224,42,-97) (16/7,7/3) -> (16/7,7/3) Reflection Matrix(95,-224,14,-33) (7/3,19/8) -> (13/2,7/1) Hyperbolic Matrix(1247,-2976,282,-673) (31/13,43/18) -> (53/12,31/7) Hyperbolic Matrix(1631,-3936,438,-1057) (41/17,29/12) -> (67/18,41/11) Hyperbolic Matrix(223,-544,66,-161) (17/7,5/2) -> (27/8,17/5) Hyperbolic Matrix(3039,-7840,1178,-3039) (49/19,80/31) -> (49/19,80/31) Reflection Matrix(1921,-4960,744,-1921) (80/31,31/12) -> (80/31,31/12) Reflection Matrix(97,-256,36,-95) (13/5,8/3) -> (8/3,19/7) Parabolic Matrix(353,-960,82,-223) (19/7,30/11) -> (30/7,13/3) Hyperbolic Matrix(1055,-2976,374,-1055) (31/11,48/17) -> (31/11,48/17) Reflection Matrix(577,-1632,204,-577) (48/17,17/6) -> (48/17,17/6) Reflection Matrix(31,-96,10,-31) (3/1,16/5) -> (3/1,16/5) Reflection Matrix(129,-416,40,-129) (16/5,13/4) -> (16/5,13/4) Reflection Matrix(97,-320,10,-33) (23/7,33/10) -> (9/1,1/0) Glide Reflection Matrix(511,-1696,116,-385) (43/13,10/3) -> (22/5,75/17) Hyperbolic Matrix(1407,-4736,418,-1407) (37/11,64/19) -> (37/11,64/19) Reflection Matrix(1025,-3456,304,-1025) (64/19,27/8) -> (64/19,27/8) Reflection Matrix(319,-1088,56,-191) (17/5,41/12) -> (17/3,23/4) Glide Reflection Matrix(127,-448,36,-127) (7/2,32/9) -> (7/2,32/9) Reflection Matrix(449,-1600,126,-449) (32/9,25/7) -> (32/9,25/7) Reflection Matrix(353,-1312,60,-223) (26/7,67/18) -> (35/6,6/1) Hyperbolic Matrix(33,-128,8,-31) (15/4,4/1) -> (4/1,17/4) Parabolic Matrix(511,-2176,120,-511) (17/4,64/15) -> (17/4,64/15) Reflection Matrix(1409,-6016,330,-1409) (64/15,47/11) -> (64/15,47/11) Reflection Matrix(4351,-19200,986,-4351) (75/17,128/29) -> (75/17,128/29) Reflection Matrix(3073,-13568,696,-3073) (128/29,53/12) -> (128/29,53/12) Reflection Matrix(127,-576,28,-127) (9/2,32/7) -> (9/2,32/7) Reflection Matrix(321,-1472,70,-321) (32/7,23/5) -> (32/7,23/5) Reflection Matrix(31,-160,6,-31) (5/1,16/3) -> (5/1,16/3) Reflection Matrix(65,-352,12,-65) (16/3,11/2) -> (16/3,11/2) Reflection Matrix(639,-3712,110,-639) (29/5,64/11) -> (29/5,64/11) Reflection Matrix(769,-4480,132,-769) (64/11,35/6) -> (64/11,35/6) Reflection Matrix(191,-1216,30,-191) (19/3,32/5) -> (19/3,32/5) Reflection Matrix(129,-832,20,-129) (32/5,13/2) -> (32/5,13/2) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,2,0,-1) (0/1,1/0) -> (-1/1,1/0) Matrix(1,0,2,-1) -> Matrix(0,1,1,0) (0/1,1/1) -> (-1/1,1/1) Matrix(257,-288,58,-65) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(479,-544,140,-159) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(193,-224,56,-65) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(191,-224,110,-129) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(289,-352,78,-95) -> Matrix(2,3,1,2) Matrix(287,-352,234,-287) -> Matrix(4,5,-3,-4) (11/9,16/13) -> (-5/3,-1/1) Matrix(129,-160,104,-129) -> Matrix(3,2,-4,-3) (16/13,5/4) -> (-1/1,-1/2) Matrix(127,-160,50,-63) -> Matrix(2,1,1,0) Matrix(351,-448,76,-97) -> Matrix(1,0,0,1) Matrix(321,-416,98,-127) -> Matrix(2,1,-1,0) -1/1 Matrix(97,-128,72,-95) -> Matrix(1,0,2,1) 0/1 Matrix(353,-480,164,-223) -> Matrix(1,0,0,1) Matrix(257,-352,46,-63) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(255,-352,92,-127) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(415,-576,116,-161) -> Matrix(1,2,0,1) 1/0 Matrix(159,-224,22,-31) -> Matrix(4,1,1,0) Matrix(385,-544,46,-65) -> Matrix(-8,1,1,0) Matrix(927,-1312,248,-351) -> Matrix(5,-2,2,-1) Matrix(383,-544,226,-321) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(289,-416,66,-95) -> Matrix(2,1,-1,0) -1/1 Matrix(287,-416,198,-287) -> Matrix(0,1,1,0) (13/9,16/11) -> (-1/1,1/1) Matrix(65,-96,44,-65) -> Matrix(-1,0,2,1) (16/11,3/2) -> (-1/1,0/1) Matrix(353,-544,146,-225) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(639,-992,248,-385) -> Matrix(1,2,0,1) 1/0 Matrix(225,-352,62,-97) -> Matrix(2,1,1,0) Matrix(161,-256,100,-159) -> Matrix(1,0,4,1) 0/1 Matrix(257,-416,118,-191) -> Matrix(2,-1,1,0) 1/1 Matrix(609,-992,256,-417) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(607,-992,216,-353) -> Matrix(1,-2,0,1) 1/0 Matrix(97,-160,20,-33) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(511,-864,152,-257) -> Matrix(1,0,0,1) Matrix(319,-544,112,-191) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(543,-928,244,-417) -> Matrix(1,0,2,1) 0/1 Matrix(577,-992,260,-447) -> Matrix(1,0,-2,1) 0/1 Matrix(575,-992,222,-383) -> Matrix(0,1,1,0) *** -> (-1/1,1/1) Matrix(351,-608,56,-97) -> Matrix(1,0,0,1) Matrix(127,-224,72,-127) -> Matrix(1,0,0,-1) (7/4,16/9) -> (0/1,1/0) Matrix(161,-288,90,-161) -> Matrix(0,1,1,0) (16/9,9/5) -> (-1/1,1/1) Matrix(511,-928,212,-385) -> Matrix(1,0,0,1) Matrix(545,-992,228,-415) -> Matrix(1,2,0,1) 1/0 Matrix(191,-352,70,-129) -> Matrix(2,1,-1,0) -1/1 Matrix(257,-544,60,-127) -> Matrix(1,-2,0,1) 1/0 Matrix(767,-1696,232,-513) -> Matrix(1,0,2,1) 0/1 Matrix(415,-928,72,-161) -> Matrix(1,0,0,1) Matrix(127,-288,56,-127) -> Matrix(1,0,0,-1) (9/4,16/7) -> (0/1,1/0) Matrix(97,-224,42,-97) -> Matrix(0,1,1,0) (16/7,7/3) -> (-1/1,1/1) Matrix(95,-224,14,-33) -> Matrix(2,-1,1,0) 1/1 Matrix(1247,-2976,282,-673) -> Matrix(2,-3,-1,2) Matrix(1631,-3936,438,-1057) -> Matrix(2,3,1,2) Matrix(223,-544,66,-161) -> Matrix(0,-1,1,0) (-1/1,1/1).(0/1,1/0) Matrix(3039,-7840,1178,-3039) -> Matrix(2,-3,1,-2) (49/19,80/31) -> (1/1,3/1) Matrix(1921,-4960,744,-1921) -> Matrix(-1,4,0,1) (80/31,31/12) -> (2/1,1/0) Matrix(97,-256,36,-95) -> Matrix(1,-4,0,1) 1/0 Matrix(353,-960,82,-223) -> Matrix(2,5,-1,-2) (-3/1,-1/1).(-2/1,1/0) Matrix(1055,-2976,374,-1055) -> Matrix(8,9,-7,-8) (31/11,48/17) -> (-9/7,-1/1) Matrix(577,-1632,204,-577) -> Matrix(5,4,-6,-5) (48/17,17/6) -> (-1/1,-2/3) Matrix(31,-96,10,-31) -> Matrix(0,1,1,0) (3/1,16/5) -> (-1/1,1/1) Matrix(129,-416,40,-129) -> Matrix(1,0,0,-1) (16/5,13/4) -> (0/1,1/0) Matrix(97,-320,10,-33) -> Matrix(-2,1,1,0) Matrix(511,-1696,116,-385) -> Matrix(1,-2,0,1) 1/0 Matrix(1407,-4736,418,-1407) -> Matrix(0,1,1,0) (37/11,64/19) -> (-1/1,1/1) Matrix(1025,-3456,304,-1025) -> Matrix(1,0,0,-1) (64/19,27/8) -> (0/1,1/0) Matrix(319,-1088,56,-191) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(127,-448,36,-127) -> Matrix(1,0,2,-1) (7/2,32/9) -> (0/1,1/1) Matrix(449,-1600,126,-449) -> Matrix(4,-5,3,-4) (32/9,25/7) -> (1/1,5/3) Matrix(353,-1312,60,-223) -> Matrix(1,-2,2,-3) 1/1 Matrix(33,-128,8,-31) -> Matrix(1,-4,0,1) 1/0 Matrix(511,-2176,120,-511) -> Matrix(1,4,0,-1) (17/4,64/15) -> (-2/1,1/0) Matrix(1409,-6016,330,-1409) -> Matrix(2,3,-1,-2) (64/15,47/11) -> (-3/1,-1/1) Matrix(4351,-19200,986,-4351) -> Matrix(4,5,-3,-4) (75/17,128/29) -> (-5/3,-1/1) Matrix(3073,-13568,696,-3073) -> Matrix(1,2,0,-1) (128/29,53/12) -> (-1/1,1/0) Matrix(127,-576,28,-127) -> Matrix(3,4,-2,-3) (9/2,32/7) -> (-2/1,-1/1) Matrix(321,-1472,70,-321) -> Matrix(4,3,-5,-4) (32/7,23/5) -> (-1/1,-3/5) Matrix(31,-160,6,-31) -> Matrix(0,1,1,0) (5/1,16/3) -> (-1/1,1/1) Matrix(65,-352,12,-65) -> Matrix(1,0,0,-1) (16/3,11/2) -> (0/1,1/0) Matrix(639,-3712,110,-639) -> Matrix(0,1,1,0) (29/5,64/11) -> (-1/1,1/1) Matrix(769,-4480,132,-769) -> Matrix(1,0,0,-1) (64/11,35/6) -> (0/1,1/0) Matrix(191,-1216,30,-191) -> Matrix(2,-1,3,-2) (19/3,32/5) -> (1/3,1/1) Matrix(129,-832,20,-129) -> Matrix(3,-4,2,-3) (32/5,13/2) -> (1/1,2/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.