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): 1944 Minimal number of generators: 325 Number of equivalence classes of cusps: 90 Genus: 118 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -8/17 -7/16 -2/5 -5/14 -4/13 -1/4 -2/11 0/1 1/8 1/5 5/22 2/7 4/11 5/13 8/19 1/2 10/17 8/13 7/11 11/16 5/7 4/5 1/1 8/7 5/4 47/34 7/5 16/11 3/2 11/7 50/31 13/8 17/10 35/19 2/1 37/17 56/25 113/49 19/8 17/7 5/2 136/53 13/5 137/52 79/29 11/4 119/43 20/7 3/1 41/13 16/5 55/17 10/3 7/2 11/3 85/23 19/5 107/28 4/1 17/4 73/17 13/3 22/5 9/2 37/8 14/3 19/4 67/14 5/1 68/13 21/4 16/3 11/2 17/3 23/4 6/1 19/3 13/2 20/3 47/7 7/1 15/2 23/3 8/1 17/2 26/3 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 1/2 -8/17 1/2 -7/15 2/3 -13/28 1/2 -6/13 1/3 -11/24 9/16 -5/11 2/3 -14/31 1/1 -9/20 1/2 -13/29 6/11 -17/38 1/2 -4/9 3/5 -15/34 1/2 -26/59 3/5 -11/25 4/5 -18/41 1/1 -7/16 1/2 -24/55 3/5 -17/39 4/7 -10/23 7/11 -13/30 1/2 -3/7 2/3 -14/33 1/1 -25/59 4/7 -11/26 1/2 -19/45 12/17 -8/19 1/1 -13/31 2/3 -5/12 1/2 -17/41 4/5 -12/29 1/1 -7/17 0/1 -9/22 5/6 -11/27 2/3 -13/32 3/4 -2/5 1/1 -13/33 2/1 -11/28 1/2 -9/23 4/5 -7/18 1/2 -19/49 2/3 -12/31 1/1 -5/13 2/1 -18/47 -1/3 -13/34 1/2 -34/89 1/1 -21/55 4/5 -8/21 3/1 -11/29 0/1 -3/8 1/2 -13/35 4/3 -23/62 3/2 -10/27 1/1 -17/46 5/2 -7/19 0/1 -18/49 1/1 -11/30 1/0 -26/71 1/0 -15/41 -4/3 -19/52 -1/2 -4/11 1/3 -13/36 1/0 -22/61 1/3 -9/25 2/3 -14/39 1/3 -5/14 1/1 -16/45 3/1 -11/31 2/1 -6/17 1/1 -7/20 -1/4 -1/3 0/1 -6/19 1/7 -5/16 1/2 -9/29 2/5 -4/13 1/2 -15/49 0/1 -11/36 1/0 -7/23 2/3 -17/56 1/0 -27/89 0/1 -10/33 1/3 -13/43 2/3 -3/10 1/0 -17/57 2/15 -14/47 1/5 -11/37 4/15 -19/64 1/3 -8/27 1/3 -21/71 0/1 -13/44 1/2 -5/17 0/1 -12/41 5/13 -19/65 4/9 -7/24 1/2 -16/55 3/7 -9/31 4/9 -2/7 1/1 -7/25 0/1 -5/18 3/8 -18/65 7/15 -13/47 4/7 -34/123 1/1 -55/199 0/1 -21/76 1/2 -8/29 1/1 -11/40 1/6 -14/51 1/3 -3/11 2/5 -7/26 1/2 -18/67 5/9 -11/41 2/3 -4/15 1/1 -5/19 4/7 -6/23 1/1 -13/50 1/4 -7/27 2/5 -1/4 1/2 -6/25 3/5 -11/46 3/4 -5/21 2/3 -4/17 5/9 -3/13 0/1 -5/22 1/2 -7/31 4/7 -9/40 5/8 -2/9 1/1 -5/23 2/3 -3/14 1/2 -10/47 3/5 -7/33 12/19 -4/19 1/1 -9/43 4/5 -14/67 1/1 -19/91 0/1 -5/24 1/2 -6/29 1/1 -1/5 2/3 -4/21 1/1 -3/16 7/10 -5/27 4/5 -2/11 1/1 -7/39 2/3 -5/28 1/2 -3/17 4/7 -13/74 17/26 -10/57 13/19 -7/40 3/4 -4/23 1/1 -5/29 0/1 -1/6 3/4 -4/25 1/1 -3/19 6/7 -2/13 1/1 -5/33 2/7 -3/20 1/2 -1/7 2/3 -2/15 9/11 -3/23 10/11 -1/8 1/0 -2/17 1/1 -3/26 5/8 -4/35 9/13 -1/9 2/3 -1/10 1/1 0/1 1/1 1/9 0/1 2/17 1/1 1/8 1/1 1/7 2/1 2/13 1/1 1/6 1/2 2/11 9/7 5/27 2/1 3/16 3/2 4/21 1/1 1/5 2/1 5/24 1/0 4/19 1/1 7/33 2/3 3/14 1/0 2/9 1/1 5/22 1/1 8/35 1/1 3/13 6/5 4/17 1/1 1/4 3/2 4/15 1/1 11/41 2/1 7/26 3/2 3/11 4/1 5/18 1/0 2/7 1/1 7/24 3/2 19/65 0/1 12/41 1/1 17/58 5/4 5/17 4/3 8/27 1/1 19/64 3/2 11/37 4/3 3/10 7/4 4/13 1/1 5/16 3/2 6/19 13/7 1/3 2/1 5/14 1/0 9/25 4/3 13/36 7/4 4/11 1/1 19/52 3/2 15/41 2/1 11/30 15/8 7/19 12/5 3/8 1/0 11/29 2/3 19/50 5/4 27/71 4/3 8/21 1/1 21/55 2/1 34/89 5/3 13/34 7/4 5/13 2/1 7/18 5/2 16/41 3/1 25/64 1/0 9/23 2/1 2/5 1/1 7/17 4/1 5/12 1/0 8/19 1/0 11/26 1/0 3/7 0/1 13/30 3/2 10/23 1/1 27/62 1/0 17/39 2/1 7/16 1/0 4/9 5/1 5/11 2/1 6/13 3/1 7/15 4/1 8/17 5/1 1/2 1/0 7/13 -2/1 6/11 1/1 17/31 0/1 28/51 1/1 11/20 1/0 5/9 4/1 19/34 1/0 33/59 -6/1 14/25 -3/1 37/66 -9/4 23/41 -2/1 9/16 1/0 13/23 0/1 4/7 1/1 11/19 2/1 7/12 1/0 10/17 1/0 13/22 1/0 3/5 -2/1 11/18 -1/4 19/31 0/1 27/44 1/2 35/57 2/3 8/13 1/1 37/60 3/2 29/47 2/1 21/34 1/0 13/21 4/1 5/8 -3/2 17/27 -2/3 46/73 -1/3 75/119 0/1 29/46 -1/2 41/65 0/1 12/19 -1/1 31/49 -6/13 50/79 -1/3 19/30 -1/2 7/11 0/1 16/25 3/7 9/14 1/2 20/31 1/1 31/48 5/6 11/17 6/5 2/3 1/1 11/16 1/0 20/29 -9/1 9/13 -4/1 16/23 -3/1 7/10 1/0 12/17 -5/3 29/41 -4/3 17/24 -7/6 22/31 -1/1 5/7 0/1 23/32 1/0 18/25 -1/1 31/43 0/1 44/61 -1/1 13/18 1/0 8/11 -1/1 27/37 -2/1 46/63 -1/1 19/26 -1/1 11/15 -4/7 14/19 -1/3 3/4 1/2 10/13 -1/1 17/22 1/2 41/53 8/9 24/31 1/1 7/9 2/1 18/23 5/1 47/60 1/0 29/37 -2/1 11/14 1/2 4/5 1/0 13/16 -3/2 48/59 -1/1 35/43 -2/3 22/27 -1/3 53/65 0/1 31/38 1/0 9/11 -2/1 23/28 1/0 60/73 3/1 37/45 -8/1 14/17 -1/1 19/23 -2/1 24/29 -1/1 5/6 1/0 6/7 -1/5 13/15 2/11 7/8 1/2 1/1 0/1 10/9 1/1 9/8 1/0 8/7 -1/1 15/13 -2/9 22/19 -1/15 7/6 1/6 20/17 1/3 13/11 0/1 6/5 1/1 23/19 2/3 17/14 1/2 11/9 2/3 5/4 1/1 19/15 0/1 52/41 1/1 33/26 5/2 47/37 4/1 14/11 -1/1 9/7 2/1 31/24 1/0 22/17 -1/1 35/27 0/1 13/10 1/2 30/23 1/1 17/13 2/1 4/3 -1/1 23/17 2/13 19/14 1/4 15/11 4/11 26/19 1/2 63/46 1/2 37/27 2/3 11/8 1/2 29/21 0/1 47/34 1/2 65/47 2/3 18/13 1/1 43/31 0/1 25/18 1/2 57/41 4/5 32/23 1/1 7/5 0/1 38/27 1/3 69/49 4/9 31/22 1/2 55/39 12/25 79/56 1/2 24/17 7/13 41/29 4/7 17/12 5/8 27/19 4/5 37/26 1/1 47/33 -2/1 10/7 1/1 33/23 2/3 23/16 3/4 13/9 4/5 16/11 1/1 19/13 6/5 3/2 1/0 20/13 1/1 17/11 6/1 31/20 1/0 45/29 0/1 14/9 -1/1 11/7 0/1 30/19 1/3 79/50 1/4 49/31 6/19 19/12 1/2 46/29 1/3 73/46 1/4 100/63 1/3 27/17 2/5 8/5 3/5 29/18 7/8 50/31 1/1 71/44 15/14 21/13 4/3 55/34 1/0 89/55 0/1 34/21 1/1 81/50 3/2 47/29 2/1 13/8 1/0 57/35 -2/1 101/62 1/0 44/27 -1/1 31/19 0/1 49/30 -1/8 67/41 0/1 18/11 1/5 23/14 1/2 5/3 2/3 17/10 1/1 29/17 12/11 12/7 1/1 31/18 5/4 81/47 10/7 50/29 13/9 19/11 2/1 45/26 3/2 26/15 9/5 7/4 1/0 16/9 1/1 57/32 1/2 41/23 2/3 25/14 3/4 59/33 6/7 93/52 5/6 34/19 1/1 43/24 15/16 52/29 1/1 9/5 4/3 11/6 1/0 35/19 0/1 59/32 1/6 24/13 1/3 13/7 2/3 15/8 1/2 17/9 8/9 2/1 1/1 13/6 3/2 37/17 2/1 61/28 9/4 24/11 3/1 11/5 2/1 20/9 -1/1 29/13 2/3 38/17 1/1 47/21 14/15 56/25 1/1 9/4 5/4 25/11 2/1 16/7 1/1 55/24 1/0 94/41 1/1 39/17 2/1 101/44 1/0 62/27 1/1 23/10 1/0 53/23 2/1 83/36 7/4 113/49 2/1 30/13 3/1 7/3 0/1 19/8 1/1 31/13 10/9 12/5 1/1 29/12 13/10 46/19 7/5 17/7 4/3 56/23 19/13 39/16 3/2 61/25 8/5 22/9 5/3 5/2 1/0 28/11 1/1 23/9 2/1 41/16 3/2 59/23 28/19 136/53 3/2 77/30 3/2 18/7 5/3 31/12 7/4 13/5 2/1 34/13 7/3 89/34 5/2 55/21 2/1 21/8 1/0 92/35 3/1 71/27 4/1 192/73 27/7 121/46 17/4 50/19 5/1 79/30 1/0 108/41 17/1 137/52 1/0 29/11 -2/1 8/3 1/1 27/10 3/2 73/27 10/7 46/17 3/2 19/7 12/7 49/18 27/14 79/29 2/1 109/40 57/28 30/11 15/7 41/15 2/1 93/34 5/2 52/19 3/1 11/4 1/0 47/17 2/1 83/30 15/8 119/43 2/1 155/56 29/14 36/13 7/3 25/9 4/1 39/14 1/0 53/19 0/1 120/43 1/1 67/24 1/0 14/5 1/1 17/6 1/0 20/7 1/1 23/8 3/2 3/1 2/1 22/7 13/7 41/13 2/1 19/6 13/6 16/5 3/1 29/9 4/1 42/13 3/1 55/17 4/1 68/21 3/1 13/4 1/0 23/7 2/1 33/10 3/2 10/3 7/3 37/11 4/1 27/8 1/0 44/13 3/1 105/31 26/9 166/49 3/1 61/18 7/2 17/5 4/1 7/2 1/0 25/7 2/1 118/33 5/3 211/59 2/1 93/26 5/2 68/19 3/1 43/12 1/0 190/53 1/0 147/41 -18/1 104/29 -7/1 61/17 -2/1 18/5 1/1 47/13 0/1 29/8 1/0 11/3 4/3 48/13 17/9 85/23 2/1 122/33 43/21 37/10 13/6 26/7 3/1 67/18 1/0 108/29 3/1 41/11 2/1 56/15 3/1 127/34 1/0 71/19 2/1 15/4 1/0 19/5 0/1 42/11 1/1 107/28 1/1 172/45 1/1 65/17 16/15 23/6 5/4 27/7 4/3 4/1 3/1 21/5 16/5 17/4 1/0 30/7 5/1 103/24 1/0 73/17 6/1 43/10 1/0 13/3 6/1 22/5 1/0 31/7 -8/1 9/2 1/0 23/5 2/5 37/8 1/1 51/11 4/3 14/3 1/1 33/7 -2/1 19/4 1/0 43/9 2/1 67/14 1/0 91/19 0/1 24/5 1/1 29/6 1/0 5/1 2/1 26/5 3/1 47/9 2/1 68/13 3/1 21/4 1/0 37/7 2/1 16/3 3/1 43/8 1/0 27/5 2/1 11/2 9/2 17/3 10/1 23/4 1/0 29/5 -12/1 6/1 -1/1 19/3 0/1 13/2 1/0 20/3 5/3 47/7 2/1 74/11 23/11 27/4 9/4 7/1 2/1 15/2 1/0 23/3 20/3 8/1 1/0 17/2 1/0 26/3 -1/1 9/1 0/1 10/1 3/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(1123,530,820,387) (-1/2,-8/17) -> (26/19,63/46) Hyperbolic Matrix(1931,906,714,335) (-8/17,-7/15) -> (73/27,46/17) Hyperbolic Matrix(1011,470,-3332,-1549) (-7/15,-13/28) -> (-17/56,-27/89) Hyperbolic Matrix(2109,976,806,373) (-13/28,-6/13) -> (34/13,89/34) Hyperbolic Matrix(497,228,-1794,-823) (-6/13,-11/24) -> (-5/18,-18/65) Hyperbolic Matrix(297,136,998,457) (-11/24,-5/11) -> (11/37,3/10) Hyperbolic Matrix(593,268,1082,489) (-5/11,-14/31) -> (6/11,17/31) Hyperbolic Matrix(293,132,-1374,-619) (-14/31,-9/20) -> (-3/14,-10/47) Hyperbolic Matrix(881,396,198,89) (-9/20,-13/29) -> (31/7,9/2) Hyperbolic Matrix(2543,1138,1562,699) (-13/29,-17/38) -> (13/8,57/35) Hyperbolic Matrix(1851,826,1172,523) (-17/38,-4/9) -> (30/19,79/50) Hyperbolic Matrix(675,298,-2512,-1109) (-4/9,-15/34) -> (-7/26,-18/67) Hyperbolic Matrix(1933,852,4440,1957) (-15/34,-26/59) -> (10/23,27/62) Hyperbolic Matrix(1353,596,-4538,-1999) (-26/59,-11/25) -> (-17/57,-14/47) Hyperbolic Matrix(387,170,1828,803) (-11/25,-18/41) -> (4/19,7/33) Hyperbolic Matrix(671,294,-1536,-673) (-18/41,-7/16) -> (-7/16,-24/55) Parabolic Matrix(4213,1838,1726,753) (-24/55,-17/39) -> (61/25,22/9) Hyperbolic Matrix(193,84,1050,457) (-17/39,-10/23) -> (2/11,5/27) Hyperbolic Matrix(1815,788,1048,455) (-10/23,-13/30) -> (45/26,26/15) Hyperbolic Matrix(759,328,1238,535) (-13/30,-3/7) -> (19/31,27/44) Hyperbolic Matrix(749,318,-2532,-1075) (-3/7,-14/33) -> (-8/27,-21/71) Hyperbolic Matrix(2435,1032,-8808,-3733) (-14/33,-25/59) -> (-13/47,-34/123) Hyperbolic Matrix(2063,874,2528,1071) (-25/59,-11/26) -> (31/38,9/11) Hyperbolic Matrix(653,276,750,317) (-11/26,-19/45) -> (13/15,7/8) Hyperbolic Matrix(185,78,-1212,-511) (-19/45,-8/19) -> (-2/13,-5/33) Hyperbolic Matrix(371,156,654,275) (-8/19,-13/31) -> (13/23,4/7) Hyperbolic Matrix(463,194,1210,507) (-13/31,-5/12) -> (13/34,5/13) Hyperbolic Matrix(279,116,-926,-385) (-5/12,-17/41) -> (-13/43,-3/10) Hyperbolic Matrix(1197,496,1016,421) (-17/41,-12/29) -> (20/17,13/11) Hyperbolic Matrix(1103,456,462,191) (-12/29,-7/17) -> (31/13,12/5) Hyperbolic Matrix(459,188,730,299) (-7/17,-9/22) -> (5/8,17/27) Hyperbolic Matrix(1097,448,1550,633) (-9/22,-11/27) -> (29/41,17/24) Hyperbolic Matrix(457,186,-1914,-779) (-11/27,-13/32) -> (-11/46,-5/21) Hyperbolic Matrix(637,258,1632,661) (-13/32,-2/5) -> (16/41,25/64) Hyperbolic Matrix(1607,634,2228,879) (-2/5,-13/33) -> (31/43,44/61) Hyperbolic Matrix(625,246,-2406,-947) (-13/33,-11/28) -> (-13/50,-7/27) Hyperbolic Matrix(265,104,1246,489) (-11/28,-9/23) -> (7/33,3/14) Hyperbolic Matrix(267,104,706,275) (-9/23,-7/18) -> (3/8,11/29) Hyperbolic Matrix(2031,788,616,239) (-7/18,-19/49) -> (23/7,33/10) Hyperbolic Matrix(351,136,-2026,-785) (-19/49,-12/31) -> (-4/23,-5/29) Hyperbolic Matrix(1055,408,618,239) (-12/31,-5/13) -> (29/17,12/7) Hyperbolic Matrix(1049,402,-3588,-1375) (-5/13,-18/47) -> (-12/41,-19/65) Hyperbolic Matrix(439,168,1398,535) (-18/47,-13/34) -> (5/16,6/19) Hyperbolic Matrix(1921,734,6556,2505) (-13/34,-34/89) -> (12/41,17/58) Hyperbolic Matrix(1571,600,-7512,-2869) (-34/89,-21/55) -> (-9/43,-14/67) Hyperbolic Matrix(173,66,-1308,-499) (-21/55,-8/21) -> (-2/15,-3/23) Hyperbolic Matrix(611,232,956,363) (-8/21,-11/29) -> (7/11,16/25) Hyperbolic Matrix(607,230,958,363) (-11/29,-3/8) -> (19/30,7/11) Hyperbolic Matrix(257,96,174,65) (-3/8,-13/35) -> (19/13,3/2) Hyperbolic Matrix(6525,2422,2492,925) (-13/35,-23/62) -> (89/34,55/21) Hyperbolic Matrix(3521,1306,1286,477) (-23/62,-10/27) -> (52/19,11/4) Hyperbolic Matrix(941,348,-3426,-1267) (-10/27,-17/46) -> (-11/40,-14/51) Hyperbolic Matrix(1543,570,1968,727) (-17/46,-7/19) -> (29/37,11/14) Hyperbolic Matrix(1197,440,1450,533) (-7/19,-18/49) -> (14/17,19/23) Hyperbolic Matrix(425,156,-2046,-751) (-18/49,-11/30) -> (-5/24,-6/29) Hyperbolic Matrix(1447,530,172,63) (-11/30,-26/71) -> (8/1,17/2) Hyperbolic Matrix(1961,718,254,93) (-26/71,-15/41) -> (23/3,8/1) Hyperbolic Matrix(5787,2116,3662,1339) (-15/41,-19/52) -> (79/50,49/31) Hyperbolic Matrix(597,218,-3404,-1243) (-19/52,-4/11) -> (-10/57,-7/40) Hyperbolic Matrix(171,62,-764,-277) (-4/11,-13/36) -> (-9/40,-2/9) Hyperbolic Matrix(255,92,-2198,-793) (-13/36,-22/61) -> (-2/17,-3/26) Hyperbolic Matrix(2363,852,4224,1523) (-22/61,-9/25) -> (33/59,14/25) Hyperbolic Matrix(1431,514,2024,727) (-9/25,-14/39) -> (12/17,29/41) Hyperbolic Matrix(419,150,-1176,-421) (-14/39,-5/14) -> (-5/14,-16/45) Parabolic Matrix(5195,1846,3014,1071) (-16/45,-11/31) -> (81/47,50/29) Hyperbolic Matrix(1085,384,1506,533) (-11/31,-6/17) -> (18/25,31/43) Hyperbolic Matrix(1413,496,584,205) (-6/17,-7/20) -> (29/12,46/19) Hyperbolic Matrix(333,116,910,317) (-7/20,-1/3) -> (15/41,11/30) Hyperbolic Matrix(869,276,318,101) (-1/3,-6/19) -> (30/11,41/15) Hyperbolic Matrix(787,248,238,75) (-6/19,-5/16) -> (33/10,10/3) Hyperbolic Matrix(1413,440,1018,317) (-5/16,-9/29) -> (43/31,25/18) Hyperbolic Matrix(311,96,-1014,-313) (-9/29,-4/13) -> (-4/13,-15/49) Parabolic Matrix(2099,642,546,167) (-15/49,-11/36) -> (23/6,27/7) Hyperbolic Matrix(1867,570,1320,403) (-11/36,-7/23) -> (41/29,17/12) Hyperbolic Matrix(3879,1178,2170,659) (-7/23,-17/56) -> (25/14,59/33) Hyperbolic Matrix(389,118,-3412,-1035) (-27/89,-10/33) -> (-4/35,-1/9) Hyperbolic Matrix(2787,844,776,235) (-10/33,-13/43) -> (61/17,18/5) Hyperbolic Matrix(771,230,-4388,-1309) (-3/10,-17/57) -> (-3/17,-13/74) Hyperbolic Matrix(3307,984,5226,1555) (-14/47,-11/37) -> (31/49,50/79) Hyperbolic Matrix(4377,1300,3074,913) (-11/37,-19/64) -> (37/26,47/33) Hyperbolic Matrix(155,46,1304,387) (-19/64,-8/27) -> (2/17,1/8) Hyperbolic Matrix(1765,522,612,181) (-21/71,-13/44) -> (23/8,3/1) Hyperbolic Matrix(1301,384,1074,317) (-13/44,-5/17) -> (23/19,17/14) Hyperbolic Matrix(1529,448,686,201) (-5/17,-12/41) -> (20/9,29/13) Hyperbolic Matrix(3507,1024,1298,379) (-19/65,-7/24) -> (27/10,73/27) Hyperbolic Matrix(1141,332,3124,909) (-7/24,-16/55) -> (4/11,19/52) Hyperbolic Matrix(2209,642,5784,1681) (-16/55,-9/31) -> (21/55,34/89) Hyperbolic Matrix(683,198,990,287) (-9/31,-2/7) -> (20/29,9/13) Hyperbolic Matrix(827,232,524,147) (-2/7,-7/25) -> (11/7,30/19) Hyperbolic Matrix(675,188,298,83) (-7/25,-5/18) -> (9/4,25/11) Hyperbolic Matrix(2167,600,372,103) (-18/65,-13/47) -> (29/5,6/1) Hyperbolic Matrix(20297,5610,6270,1733) (-34/123,-55/199) -> (55/17,68/21) Hyperbolic Matrix(30669,8476,8210,2269) (-55/199,-21/76) -> (127/34,71/19) Hyperbolic Matrix(6415,1772,1792,495) (-21/76,-8/29) -> (68/19,43/12) Hyperbolic Matrix(1191,328,374,103) (-8/29,-11/40) -> (19/6,16/5) Hyperbolic Matrix(2755,756,594,163) (-14/51,-3/11) -> (51/11,14/3) Hyperbolic Matrix(221,60,372,101) (-3/11,-7/26) -> (13/22,3/5) Hyperbolic Matrix(3247,872,3988,1071) (-18/67,-11/41) -> (35/43,22/27) Hyperbolic Matrix(2141,574,884,237) (-11/41,-4/15) -> (46/19,17/7) Hyperbolic Matrix(587,156,222,59) (-4/15,-5/19) -> (29/11,8/3) Hyperbolic Matrix(1025,268,218,57) (-5/19,-6/23) -> (14/3,33/7) Hyperbolic Matrix(2557,666,1386,361) (-6/23,-13/50) -> (59/32,24/13) Hyperbolic Matrix(1017,262,656,169) (-7/27,-1/4) -> (31/20,45/29) Hyperbolic Matrix(1139,274,212,51) (-1/4,-6/25) -> (16/3,43/8) Hyperbolic Matrix(2629,630,1206,289) (-6/25,-11/46) -> (61/28,24/11) Hyperbolic Matrix(1201,284,850,201) (-5/21,-4/17) -> (24/17,41/29) Hyperbolic Matrix(563,132,354,83) (-4/17,-3/13) -> (27/17,8/5) Hyperbolic Matrix(209,48,492,113) (-3/13,-5/22) -> (11/26,3/7) Hyperbolic Matrix(1813,410,1048,237) (-5/22,-7/31) -> (19/11,45/26) Hyperbolic Matrix(977,220,3344,753) (-7/31,-9/40) -> (7/24,19/65) Hyperbolic Matrix(899,196,344,75) (-2/9,-5/23) -> (13/5,34/13) Hyperbolic Matrix(895,194,346,75) (-5/23,-3/14) -> (31/12,13/5) Hyperbolic Matrix(2539,540,1782,379) (-10/47,-7/33) -> (47/33,10/7) Hyperbolic Matrix(549,116,478,101) (-7/33,-4/19) -> (8/7,15/13) Hyperbolic Matrix(2597,544,2048,429) (-4/19,-9/43) -> (19/15,52/41) Hyperbolic Matrix(14471,3022,5186,1083) (-14/67,-19/91) -> (53/19,120/43) Hyperbolic Matrix(11125,2322,2592,541) (-19/91,-5/24) -> (103/24,73/17) Hyperbolic Matrix(1975,408,1428,295) (-6/29,-1/5) -> (65/47,18/13) Hyperbolic Matrix(871,168,534,103) (-1/5,-4/21) -> (44/27,31/19) Hyperbolic Matrix(467,88,398,75) (-4/21,-3/16) -> (7/6,20/17) Hyperbolic Matrix(729,136,134,25) (-3/16,-5/27) -> (27/5,11/2) Hyperbolic Matrix(131,24,-726,-133) (-5/27,-2/11) -> (-2/11,-7/39) Parabolic Matrix(4475,802,2762,495) (-7/39,-5/28) -> (81/50,47/29) Hyperbolic Matrix(1247,222,264,47) (-5/28,-3/17) -> (33/7,19/4) Hyperbolic Matrix(11137,1956,3012,529) (-13/74,-10/57) -> (122/33,37/10) Hyperbolic Matrix(3009,526,1310,229) (-7/40,-4/23) -> (62/27,23/10) Hyperbolic Matrix(1239,212,976,167) (-5/29,-1/6) -> (33/26,47/37) Hyperbolic Matrix(775,126,1224,199) (-1/6,-4/25) -> (50/79,19/30) Hyperbolic Matrix(1027,164,1672,267) (-4/25,-3/19) -> (35/57,8/13) Hyperbolic Matrix(191,30,834,131) (-3/19,-2/13) -> (8/35,3/13) Hyperbolic Matrix(955,144,126,19) (-5/33,-3/20) -> (15/2,23/3) Hyperbolic Matrix(1143,170,316,47) (-3/20,-1/7) -> (47/13,29/8) Hyperbolic Matrix(625,84,186,25) (-1/7,-2/15) -> (10/3,37/11) Hyperbolic Matrix(1801,234,1116,145) (-3/23,-1/8) -> (71/44,21/13) Hyperbolic Matrix(493,60,1290,157) (-1/8,-2/17) -> (34/89,13/34) Hyperbolic Matrix(2869,330,426,49) (-3/26,-4/35) -> (74/11,27/4) Hyperbolic Matrix(843,88,182,19) (-1/9,-1/10) -> (37/8,51/11) Hyperbolic Matrix(479,46,656,63) (-1/10,0/1) -> (46/63,19/26) Hyperbolic Matrix(345,-32,248,-23) (0/1,1/9) -> (57/41,32/23) Hyperbolic Matrix(2035,-234,774,-89) (1/9,2/17) -> (92/35,71/27) Hyperbolic Matrix(475,-64,334,-45) (1/8,1/7) -> (27/19,37/26) Hyperbolic Matrix(609,-92,470,-71) (1/7,2/13) -> (22/17,35/27) Hyperbolic Matrix(233,-38,92,-15) (2/13,1/6) -> (5/2,28/11) Hyperbolic Matrix(367,-66,228,-41) (1/6,2/11) -> (8/5,29/18) Hyperbolic Matrix(819,-152,2096,-389) (5/27,3/16) -> (25/64,9/23) Hyperbolic Matrix(1453,-276,816,-155) (3/16,4/21) -> (16/9,57/32) Hyperbolic Matrix(497,-96,906,-175) (4/21,1/5) -> (17/31,28/51) Hyperbolic Matrix(359,-74,1208,-249) (1/5,5/24) -> (19/64,11/37) Hyperbolic Matrix(1429,-300,624,-131) (5/24,4/19) -> (16/7,55/24) Hyperbolic Matrix(355,-78,132,-29) (3/14,2/9) -> (8/3,27/10) Hyperbolic Matrix(221,-50,968,-219) (2/9,5/22) -> (5/22,8/35) Parabolic Matrix(701,-164,218,-51) (3/13,4/17) -> (16/5,29/9) Hyperbolic Matrix(131,-32,86,-21) (4/17,1/4) -> (3/2,20/13) Hyperbolic Matrix(513,-136,298,-79) (1/4,4/15) -> (12/7,31/18) Hyperbolic Matrix(425,-114,384,-103) (4/15,11/41) -> (1/1,10/9) Hyperbolic Matrix(2255,-606,3576,-961) (11/41,7/26) -> (29/46,41/65) Hyperbolic Matrix(807,-218,596,-161) (7/26,3/11) -> (23/17,19/14) Hyperbolic Matrix(211,-58,382,-105) (3/11,5/18) -> (11/20,5/9) Hyperbolic Matrix(85,-24,294,-83) (5/18,2/7) -> (2/7,7/24) Parabolic Matrix(4555,-1332,5598,-1637) (19/65,12/41) -> (48/59,35/43) Hyperbolic Matrix(4843,-1420,7684,-2253) (17/58,5/17) -> (75/119,29/46) Hyperbolic Matrix(291,-86,626,-185) (5/17,8/27) -> (6/13,7/15) Hyperbolic Matrix(6455,-1916,2456,-729) (8/27,19/64) -> (21/8,92/35) Hyperbolic Matrix(497,-152,206,-63) (3/10,4/13) -> (12/5,29/12) Hyperbolic Matrix(701,-218,164,-51) (4/13,5/16) -> (17/4,30/7) Hyperbolic Matrix(123,-40,40,-13) (6/19,1/3) -> (3/1,22/7) Hyperbolic Matrix(439,-156,318,-113) (1/3,5/14) -> (11/8,29/21) Hyperbolic Matrix(1669,-600,1032,-371) (5/14,9/25) -> (21/13,55/34) Hyperbolic Matrix(3691,-1332,2142,-773) (9/25,13/36) -> (31/18,81/47) Hyperbolic Matrix(911,-330,1626,-589) (13/36,4/11) -> (14/25,37/66) Hyperbolic Matrix(6169,-2256,2688,-983) (19/52,15/41) -> (39/17,101/44) Hyperbolic Matrix(1501,-552,552,-203) (11/30,7/19) -> (19/7,49/18) Hyperbolic Matrix(355,-132,78,-29) (7/19,3/8) -> (9/2,23/5) Hyperbolic Matrix(2543,-966,3288,-1249) (11/29,19/50) -> (17/22,41/53) Hyperbolic Matrix(4851,-1844,5948,-2261) (19/50,27/71) -> (53/65,31/38) Hyperbolic Matrix(2035,-774,234,-89) (27/71,8/21) -> (26/3,9/1) Hyperbolic Matrix(587,-224,1250,-477) (8/21,21/55) -> (7/15,8/17) Hyperbolic Matrix(351,-136,622,-241) (5/13,7/18) -> (9/16,13/23) Hyperbolic Matrix(1631,-636,2526,-985) (7/18,16/41) -> (20/31,31/48) Hyperbolic Matrix(233,-92,38,-15) (9/23,2/5) -> (6/1,19/3) Hyperbolic Matrix(153,-62,116,-47) (2/5,7/17) -> (17/13,4/3) Hyperbolic Matrix(497,-206,152,-63) (7/17,5/12) -> (13/4,23/7) Hyperbolic Matrix(305,-128,722,-303) (5/12,8/19) -> (8/19,11/26) Parabolic Matrix(1885,-816,1356,-587) (3/7,13/30) -> (25/18,57/41) Hyperbolic Matrix(1091,-474,1770,-769) (13/30,10/23) -> (8/13,37/60) Hyperbolic Matrix(6169,-2688,2256,-983) (27/62,17/39) -> (41/15,93/34) Hyperbolic Matrix(1429,-624,300,-131) (17/39,7/16) -> (19/4,43/9) Hyperbolic Matrix(337,-148,526,-231) (7/16,4/9) -> (16/25,9/14) Hyperbolic Matrix(261,-118,334,-151) (4/9,5/11) -> (7/9,18/23) Hyperbolic Matrix(407,-186,186,-85) (5/11,6/13) -> (24/11,11/5) Hyperbolic Matrix(511,-244,622,-297) (8/17,1/2) -> (23/28,60/73) Hyperbolic Matrix(317,-170,386,-207) (1/2,7/13) -> (9/11,23/28) Hyperbolic Matrix(455,-246,246,-133) (7/13,6/11) -> (24/13,13/7) Hyperbolic Matrix(5577,-3064,1498,-823) (28/51,11/20) -> (67/18,108/29) Hyperbolic Matrix(2149,-1200,1524,-851) (5/9,19/34) -> (31/22,55/39) Hyperbolic Matrix(7897,-4416,4848,-2711) (19/34,33/59) -> (57/35,101/62) Hyperbolic Matrix(6505,-3648,2352,-1319) (37/66,23/41) -> (47/17,83/30) Hyperbolic Matrix(1453,-816,276,-155) (23/41,9/16) -> (21/4,37/7) Hyperbolic Matrix(205,-118,172,-99) (4/7,11/19) -> (13/11,6/5) Hyperbolic Matrix(513,-298,136,-79) (11/19,7/12) -> (15/4,19/5) Hyperbolic Matrix(341,-200,578,-339) (7/12,10/17) -> (10/17,13/22) Parabolic Matrix(571,-348,402,-245) (3/5,11/18) -> (17/12,27/19) Hyperbolic Matrix(2077,-1272,1272,-779) (11/18,19/31) -> (31/19,49/30) Hyperbolic Matrix(7897,-4848,4416,-2711) (27/44,35/57) -> (59/33,93/52) Hyperbolic Matrix(7081,-4368,3072,-1895) (37/60,29/47) -> (53/23,83/36) Hyperbolic Matrix(3907,-2412,1602,-989) (29/47,21/34) -> (39/16,61/25) Hyperbolic Matrix(1669,-1032,600,-371) (21/34,13/21) -> (25/9,39/14) Hyperbolic Matrix(367,-228,66,-41) (13/21,5/8) -> (11/2,17/3) Hyperbolic Matrix(6063,-3820,4306,-2713) (17/27,46/73) -> (38/27,69/49) Hyperbolic Matrix(15867,-10000,4438,-2797) (46/73,75/119) -> (25/7,118/33) Hyperbolic Matrix(2583,-1630,496,-313) (41/65,12/19) -> (26/5,47/9) Hyperbolic Matrix(1389,-878,1688,-1067) (12/19,31/49) -> (37/45,14/17) Hyperbolic Matrix(1019,-656,1412,-909) (9/14,20/31) -> (44/61,13/18) Hyperbolic Matrix(3511,-2268,918,-593) (31/48,11/17) -> (65/17,23/6) Hyperbolic Matrix(131,-86,32,-21) (11/17,2/3) -> (4/1,21/5) Hyperbolic Matrix(353,-242,512,-351) (2/3,11/16) -> (11/16,20/29) Parabolic Matrix(893,-620,350,-243) (9/13,16/23) -> (28/11,23/9) Hyperbolic Matrix(287,-200,254,-177) (16/23,7/10) -> (9/8,8/7) Hyperbolic Matrix(571,-402,348,-245) (7/10,12/17) -> (18/11,23/14) Hyperbolic Matrix(2149,-1524,1200,-851) (17/24,22/31) -> (34/19,43/24) Hyperbolic Matrix(757,-538,916,-651) (22/31,5/7) -> (19/23,24/29) Hyperbolic Matrix(1257,-902,1604,-1151) (5/7,23/32) -> (47/60,29/37) Hyperbolic Matrix(345,-248,32,-23) (23/32,18/25) -> (10/1,1/0) Hyperbolic Matrix(439,-318,156,-113) (13/18,8/11) -> (14/5,17/6) Hyperbolic Matrix(999,-728,188,-137) (8/11,27/37) -> (37/7,16/3) Hyperbolic Matrix(5401,-3942,3402,-2483) (27/37,46/63) -> (100/63,27/17) Hyperbolic Matrix(1153,-844,250,-183) (19/26,11/15) -> (23/5,37/8) Hyperbolic Matrix(623,-458,404,-297) (11/15,14/19) -> (20/13,17/11) Hyperbolic Matrix(807,-596,218,-161) (14/19,3/4) -> (37/10,26/7) Hyperbolic Matrix(153,-116,62,-47) (3/4,10/13) -> (22/9,5/2) Hyperbolic Matrix(609,-470,92,-71) (10/13,17/22) -> (13/2,20/3) Hyperbolic Matrix(3471,-2686,1552,-1201) (41/53,24/31) -> (38/17,47/21) Hyperbolic Matrix(1277,-990,396,-307) (24/31,7/9) -> (29/9,42/13) Hyperbolic Matrix(8297,-6498,3150,-2467) (18/23,47/60) -> (79/30,108/41) Hyperbolic Matrix(121,-96,150,-119) (11/14,4/5) -> (4/5,13/16) Parabolic Matrix(6255,-5086,1846,-1501) (13/16,48/59) -> (166/49,61/18) Hyperbolic Matrix(14397,-11738,5474,-4463) (22/27,53/65) -> (71/27,192/73) Hyperbolic Matrix(15411,-12668,4298,-3533) (60/73,37/45) -> (147/41,104/29) Hyperbolic Matrix(2717,-2252,1712,-1419) (24/29,5/6) -> (73/46,100/63) Hyperbolic Matrix(205,-172,118,-99) (5/6,6/7) -> (26/15,7/4) Hyperbolic Matrix(435,-376,376,-325) (6/7,13/15) -> (15/13,22/19) Hyperbolic Matrix(287,-254,200,-177) (7/8,1/1) -> (33/23,23/16) Hyperbolic Matrix(715,-796,256,-285) (10/9,9/8) -> (67/24,14/5) Hyperbolic Matrix(2251,-2608,826,-957) (22/19,7/6) -> (109/40,30/11) Hyperbolic Matrix(757,-916,538,-651) (6/5,23/19) -> (7/5,38/27) Hyperbolic Matrix(317,-386,170,-207) (17/14,11/9) -> (13/7,15/8) Hyperbolic Matrix(121,-150,96,-119) (11/9,5/4) -> (5/4,19/15) Parabolic Matrix(6261,-7942,2380,-3019) (52/41,33/26) -> (121/46,50/19) Hyperbolic Matrix(4519,-5742,1260,-1601) (47/37,14/11) -> (104/29,61/17) Hyperbolic Matrix(261,-334,118,-151) (14/11,9/7) -> (11/5,20/9) Hyperbolic Matrix(613,-790,142,-183) (9/7,31/24) -> (43/10,13/3) Hyperbolic Matrix(2543,-3288,966,-1249) (31/24,22/17) -> (50/19,79/30) Hyperbolic Matrix(799,-1036,118,-153) (35/27,13/10) -> (27/4,7/1) Hyperbolic Matrix(2203,-2872,1360,-1773) (13/10,30/23) -> (34/21,81/50) Hyperbolic Matrix(983,-1284,258,-337) (30/23,17/13) -> (19/5,42/11) Hyperbolic Matrix(849,-1148,230,-311) (4/3,23/17) -> (11/3,48/13) Hyperbolic Matrix(481,-654,114,-155) (19/14,15/11) -> (21/5,17/4) Hyperbolic Matrix(867,-1184,320,-437) (15/11,26/19) -> (46/17,19/7) Hyperbolic Matrix(4011,-5494,2848,-3901) (63/46,37/27) -> (69/49,31/22) Hyperbolic Matrix(1867,-2560,1048,-1437) (37/27,11/8) -> (57/32,41/23) Hyperbolic Matrix(3197,-4418,2312,-3195) (29/21,47/34) -> (47/34,65/47) Parabolic Matrix(1019,-1412,656,-909) (18/13,43/31) -> (45/29,14/9) Hyperbolic Matrix(857,-1194,384,-535) (32/23,7/5) -> (29/13,38/17) Hyperbolic Matrix(6967,-9826,2644,-3729) (55/39,79/56) -> (137/52,29/11) Hyperbolic Matrix(8377,-11820,3180,-4487) (79/56,24/17) -> (108/41,137/52) Hyperbolic Matrix(1575,-2258,422,-605) (10/7,33/23) -> (41/11,56/15) Hyperbolic Matrix(421,-606,66,-95) (23/16,13/9) -> (19/3,13/2) Hyperbolic Matrix(353,-512,242,-351) (13/9,16/11) -> (16/11,19/13) Parabolic Matrix(1631,-2526,636,-985) (17/11,31/20) -> (41/16,59/23) Hyperbolic Matrix(337,-526,148,-231) (14/9,11/7) -> (25/11,16/7) Hyperbolic Matrix(669,-1058,356,-563) (49/31,19/12) -> (15/8,17/9) Hyperbolic Matrix(2255,-3576,606,-961) (19/12,46/29) -> (26/7,67/18) Hyperbolic Matrix(5825,-9242,1628,-2583) (46/29,73/46) -> (93/26,68/19) Hyperbolic Matrix(3101,-5000,1922,-3099) (29/18,50/31) -> (50/31,71/44) Parabolic Matrix(3239,-5240,866,-1401) (55/34,89/55) -> (71/19,15/4) Hyperbolic Matrix(3465,-5608,1072,-1735) (89/55,34/21) -> (42/13,55/17) Hyperbolic Matrix(1091,-1770,474,-769) (47/29,13/8) -> (23/10,53/23) Hyperbolic Matrix(6901,-11244,1848,-3011) (101/62,44/27) -> (56/15,127/34) Hyperbolic Matrix(2009,-3282,636,-1039) (49/30,67/41) -> (41/13,19/6) Hyperbolic Matrix(1353,-2212,430,-703) (67/41,18/11) -> (22/7,41/13) Hyperbolic Matrix(143,-236,20,-33) (23/14,5/3) -> (7/1,15/2) Hyperbolic Matrix(341,-578,200,-339) (5/3,17/10) -> (17/10,29/17) Parabolic Matrix(1109,-1914,456,-787) (50/29,19/11) -> (17/7,56/23) Hyperbolic Matrix(351,-622,136,-241) (7/4,16/9) -> (18/7,31/12) Hyperbolic Matrix(911,-1626,330,-589) (41/23,25/14) -> (11/4,47/17) Hyperbolic Matrix(7513,-13438,2692,-4815) (93/52,34/19) -> (120/43,67/24) Hyperbolic Matrix(1605,-2876,716,-1283) (43/24,52/29) -> (56/25,9/4) Hyperbolic Matrix(1643,-2948,734,-1317) (52/29,9/5) -> (47/21,56/25) Hyperbolic Matrix(211,-382,58,-105) (9/5,11/6) -> (29/8,11/3) Hyperbolic Matrix(1331,-2450,722,-1329) (11/6,35/19) -> (35/19,59/32) Parabolic Matrix(501,-958,148,-283) (17/9,2/1) -> (44/13,105/31) Hyperbolic Matrix(291,-626,86,-185) (2/1,13/6) -> (27/8,44/13) Hyperbolic Matrix(1259,-2738,578,-1257) (13/6,37/17) -> (37/17,61/28) Parabolic Matrix(2493,-5714,476,-1091) (55/24,94/41) -> (68/13,21/4) Hyperbolic Matrix(3083,-7070,590,-1353) (94/41,39/17) -> (47/9,68/13) Hyperbolic Matrix(3343,-7674,1032,-2369) (101/44,62/27) -> (68/21,13/4) Hyperbolic Matrix(12153,-28022,3398,-7835) (83/36,113/49) -> (211/59,93/26) Hyperbolic Matrix(8525,-19664,2384,-5499) (113/49,30/13) -> (118/33,211/59) Hyperbolic Matrix(147,-340,16,-37) (30/13,7/3) -> (9/1,10/1) Hyperbolic Matrix(305,-722,128,-303) (7/3,19/8) -> (19/8,31/13) Parabolic Matrix(2059,-5014,802,-1953) (56/23,39/16) -> (77/30,18/7) Hyperbolic Matrix(819,-2096,152,-389) (23/9,41/16) -> (43/8,27/5) Hyperbolic Matrix(12161,-31202,3392,-8703) (59/23,136/53) -> (190/53,147/41) Hyperbolic Matrix(7979,-20478,2226,-5713) (136/53,77/30) -> (43/12,190/53) Hyperbolic Matrix(1417,-3712,418,-1095) (55/21,21/8) -> (61/18,17/5) Hyperbolic Matrix(12971,-34116,4686,-12325) (192/73,121/46) -> (155/56,36/13) Hyperbolic Matrix(4583,-12482,1682,-4581) (49/18,79/29) -> (79/29,109/40) Parabolic Matrix(2977,-8146,694,-1899) (93/34,52/19) -> (30/7,103/24) Hyperbolic Matrix(10235,-28322,3698,-10233) (83/30,119/43) -> (119/43,155/56) Parabolic Matrix(387,-1072,100,-277) (36/13,25/9) -> (27/7,4/1) Hyperbolic Matrix(1839,-5126,428,-1193) (39/14,53/19) -> (73/17,43/10) Hyperbolic Matrix(281,-800,98,-279) (17/6,20/7) -> (20/7,23/8) Parabolic Matrix(359,-1208,74,-249) (37/11,27/8) -> (29/6,5/1) Hyperbolic Matrix(8517,-28850,2228,-7547) (105/31,166/49) -> (172/45,65/17) Hyperbolic Matrix(85,-294,24,-83) (17/5,7/2) -> (7/2,25/7) Parabolic Matrix(363,-1312,70,-253) (18/5,47/13) -> (5/1,26/5) Hyperbolic Matrix(3911,-14450,1058,-3909) (48/13,85/23) -> (85/23,122/33) Parabolic Matrix(2903,-10812,606,-2257) (108/29,41/11) -> (91/19,24/5) Hyperbolic Matrix(5993,-22898,1568,-5991) (42/11,107/28) -> (107/28,172/45) Parabolic Matrix(221,-968,50,-219) (13/3,22/5) -> (22/5,31/7) Parabolic Matrix(1877,-8978,392,-1875) (43/9,67/14) -> (67/14,91/19) Parabolic Matrix(241,-1162,28,-135) (24/5,29/6) -> (17/2,26/3) Hyperbolic Matrix(185,-1058,32,-183) (17/3,23/4) -> (23/4,29/5) Parabolic Matrix(659,-4418,98,-657) (20/3,47/7) -> (47/7,74/11) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(1123,530,820,387) -> Matrix(5,-2,8,-3) Matrix(1931,906,714,335) -> Matrix(29,-16,20,-11) Matrix(1011,470,-3332,-1549) -> Matrix(3,-2,2,-1) Matrix(2109,976,806,373) -> Matrix(1,2,0,1) Matrix(497,228,-1794,-823) -> Matrix(11,-6,24,-13) Matrix(297,136,998,457) -> Matrix(17,-10,12,-7) Matrix(593,268,1082,489) -> Matrix(3,-2,2,-1) Matrix(293,132,-1374,-619) -> Matrix(5,-2,8,-3) Matrix(881,396,198,89) -> Matrix(5,-2,-2,1) Matrix(2543,1138,1562,699) -> Matrix(7,-4,2,-1) Matrix(1851,826,1172,523) -> Matrix(3,-2,14,-9) Matrix(675,298,-2512,-1109) -> Matrix(5,-2,8,-3) Matrix(1933,852,4440,1957) -> Matrix(7,-4,2,-1) Matrix(1353,596,-4538,-1999) -> Matrix(3,-2,20,-13) Matrix(387,170,1828,803) -> Matrix(3,-2,2,-1) Matrix(671,294,-1536,-673) -> Matrix(5,-2,8,-3) Matrix(4213,1838,1726,753) -> Matrix(5,-4,4,-3) Matrix(193,84,1050,457) -> Matrix(17,-10,12,-7) Matrix(1815,788,1048,455) -> Matrix(5,-4,4,-3) Matrix(759,328,1238,535) -> Matrix(3,-2,8,-5) Matrix(749,318,-2532,-1075) -> Matrix(3,-2,8,-5) Matrix(2435,1032,-8808,-3733) -> Matrix(1,0,0,1) Matrix(2063,874,2528,1071) -> Matrix(3,-2,2,-1) Matrix(653,276,750,317) -> Matrix(3,-2,8,-5) Matrix(185,78,-1212,-511) -> Matrix(3,-2,2,-1) Matrix(371,156,654,275) -> Matrix(3,-2,2,-1) Matrix(463,194,1210,507) -> Matrix(17,-12,10,-7) Matrix(279,116,-926,-385) -> Matrix(3,-2,2,-1) Matrix(1197,496,1016,421) -> Matrix(5,-4,14,-11) Matrix(1103,456,462,191) -> Matrix(11,-10,10,-9) Matrix(459,188,730,299) -> Matrix(3,-2,-4,3) Matrix(1097,448,1550,633) -> Matrix(1,-2,0,1) Matrix(457,186,-1914,-779) -> Matrix(1,0,0,1) Matrix(637,258,1632,661) -> Matrix(13,-10,4,-3) Matrix(1607,634,2228,879) -> Matrix(1,-2,0,1) Matrix(625,246,-2406,-947) -> Matrix(1,0,2,1) Matrix(265,104,1246,489) -> Matrix(3,-2,2,-1) Matrix(267,104,706,275) -> Matrix(3,-2,2,-1) Matrix(2031,788,616,239) -> Matrix(5,-4,4,-3) Matrix(351,136,-2026,-785) -> Matrix(3,-2,2,-1) Matrix(1055,408,618,239) -> Matrix(11,-10,10,-9) Matrix(1049,402,-3588,-1375) -> Matrix(1,2,2,5) Matrix(439,168,1398,535) -> Matrix(7,-2,4,-1) Matrix(1921,734,6556,2505) -> Matrix(7,-6,6,-5) Matrix(1571,600,-7512,-2869) -> Matrix(1,0,0,1) Matrix(173,66,-1308,-499) -> Matrix(5,-6,6,-7) Matrix(611,232,956,363) -> Matrix(1,0,2,1) Matrix(607,230,958,363) -> Matrix(1,0,-4,1) Matrix(257,96,174,65) -> Matrix(3,-2,2,-1) Matrix(6525,2422,2492,925) -> Matrix(11,-14,4,-5) Matrix(3521,1306,1286,477) -> Matrix(5,-8,2,-3) Matrix(941,348,-3426,-1267) -> Matrix(1,-2,4,-7) Matrix(1543,570,1968,727) -> Matrix(1,-2,0,1) Matrix(1197,440,1450,533) -> Matrix(1,-2,0,1) Matrix(425,156,-2046,-751) -> Matrix(1,-2,2,-3) Matrix(1447,530,172,63) -> Matrix(1,-2,0,1) Matrix(1961,718,254,93) -> Matrix(1,8,0,1) Matrix(5787,2116,3662,1339) -> Matrix(3,2,10,7) Matrix(597,218,-3404,-1243) -> Matrix(7,2,10,3) Matrix(171,62,-764,-277) -> Matrix(5,-2,8,-3) Matrix(255,92,-2198,-793) -> Matrix(5,-2,8,-3) Matrix(2363,852,4224,1523) -> Matrix(9,-4,-2,1) Matrix(1431,514,2024,727) -> Matrix(1,-2,0,1) Matrix(419,150,-1176,-421) -> Matrix(3,-2,2,-1) Matrix(5195,1846,3014,1071) -> Matrix(3,4,2,3) Matrix(1085,384,1506,533) -> Matrix(1,-2,0,1) Matrix(1413,496,584,205) -> Matrix(3,4,2,3) Matrix(333,116,910,317) -> Matrix(7,-2,4,-1) Matrix(869,276,318,101) -> Matrix(1,2,0,1) Matrix(787,248,238,75) -> Matrix(7,-2,4,-1) Matrix(1413,440,1018,317) -> Matrix(5,-2,8,-3) Matrix(311,96,-1014,-313) -> Matrix(5,-2,8,-3) Matrix(2099,642,546,167) -> Matrix(5,-4,4,-3) Matrix(1867,570,1320,403) -> Matrix(5,-2,8,-3) Matrix(3879,1178,2170,659) -> Matrix(3,-4,4,-5) Matrix(389,118,-3412,-1035) -> Matrix(3,2,4,3) Matrix(2787,844,776,235) -> Matrix(1,0,-2,1) Matrix(771,230,-4388,-1309) -> Matrix(17,-2,26,-3) Matrix(3307,984,5226,1555) -> Matrix(9,-2,-22,5) Matrix(4377,1300,3074,913) -> Matrix(7,-2,4,-1) Matrix(155,46,1304,387) -> Matrix(5,-2,8,-3) Matrix(1765,522,612,181) -> Matrix(7,-2,4,-1) Matrix(1301,384,1074,317) -> Matrix(5,-2,8,-3) Matrix(1529,448,686,201) -> Matrix(5,-2,8,-3) Matrix(3507,1024,1298,379) -> Matrix(7,-2,4,-1) Matrix(1141,332,3124,909) -> Matrix(19,-8,12,-5) Matrix(2209,642,5784,1681) -> Matrix(31,-14,20,-9) Matrix(683,198,990,287) -> Matrix(17,-8,-2,1) Matrix(827,232,524,147) -> Matrix(1,0,2,1) Matrix(675,188,298,83) -> Matrix(7,-2,4,-1) Matrix(2167,600,372,103) -> Matrix(17,-8,-2,1) Matrix(20297,5610,6270,1733) -> Matrix(7,-4,2,-1) Matrix(30669,8476,8210,2269) -> Matrix(3,-2,2,-1) Matrix(6415,1772,1792,495) -> Matrix(7,-4,2,-1) Matrix(1191,328,374,103) -> Matrix(1,2,0,1) Matrix(2755,756,594,163) -> Matrix(7,-2,4,-1) Matrix(221,60,372,101) -> Matrix(9,-4,-2,1) Matrix(3247,872,3988,1071) -> Matrix(7,-4,-12,7) Matrix(2141,574,884,237) -> Matrix(17,-10,12,-7) Matrix(587,156,222,59) -> Matrix(3,-2,2,-1) Matrix(1025,268,218,57) -> Matrix(3,-2,2,-1) Matrix(2557,666,1386,361) -> Matrix(1,0,2,1) Matrix(1017,262,656,169) -> Matrix(5,-2,-2,1) Matrix(1139,274,212,51) -> Matrix(11,-6,2,-1) Matrix(2629,630,1206,289) -> Matrix(19,-12,8,-5) Matrix(1201,284,850,201) -> Matrix(5,-2,8,-3) Matrix(563,132,354,83) -> Matrix(3,-2,8,-5) Matrix(209,48,492,113) -> Matrix(1,0,-2,1) Matrix(1813,410,1048,237) -> Matrix(17,-10,12,-7) Matrix(977,220,3344,753) -> Matrix(7,-4,2,-1) Matrix(899,196,344,75) -> Matrix(19,-12,8,-5) Matrix(895,194,346,75) -> Matrix(17,-12,10,-7) Matrix(2539,540,1782,379) -> Matrix(3,-2,8,-5) Matrix(549,116,478,101) -> Matrix(3,-2,-4,3) Matrix(2597,544,2048,429) -> Matrix(5,-4,4,-3) Matrix(14471,3022,5186,1083) -> Matrix(1,0,0,1) Matrix(11125,2322,2592,541) -> Matrix(11,-6,2,-1) Matrix(1975,408,1428,295) -> Matrix(1,0,0,1) Matrix(871,168,534,103) -> Matrix(3,-2,-4,3) Matrix(467,88,398,75) -> Matrix(3,-2,8,-5) Matrix(729,136,134,25) -> Matrix(13,-10,4,-3) Matrix(131,24,-726,-133) -> Matrix(3,-2,2,-1) Matrix(4475,802,2762,495) -> Matrix(5,-4,4,-3) Matrix(1247,222,264,47) -> Matrix(3,-2,2,-1) Matrix(11137,1956,3012,529) -> Matrix(91,-60,44,-29) Matrix(3009,526,1310,229) -> Matrix(5,-4,4,-3) Matrix(1239,212,976,167) -> Matrix(7,-4,2,-1) Matrix(775,126,1224,199) -> Matrix(3,-2,-10,7) Matrix(1027,164,1672,267) -> Matrix(5,-4,4,-3) Matrix(191,30,834,131) -> Matrix(13,-12,12,-11) Matrix(955,144,126,19) -> Matrix(11,-6,2,-1) Matrix(1143,170,316,47) -> Matrix(3,-2,2,-1) Matrix(625,84,186,25) -> Matrix(13,-10,4,-3) Matrix(1801,234,1116,145) -> Matrix(15,-14,14,-13) Matrix(493,60,1290,157) -> Matrix(7,-2,4,-1) Matrix(2869,330,426,49) -> Matrix(43,-28,20,-13) Matrix(843,88,182,19) -> Matrix(7,-6,6,-5) Matrix(479,46,656,63) -> Matrix(1,-2,0,1) Matrix(345,-32,248,-23) -> Matrix(3,-4,4,-5) Matrix(2035,-234,774,-89) -> Matrix(7,-4,2,-1) Matrix(475,-64,334,-45) -> Matrix(5,-6,6,-7) Matrix(609,-92,470,-71) -> Matrix(1,-2,0,1) Matrix(233,-38,92,-15) -> Matrix(3,-2,2,-1) Matrix(367,-66,228,-41) -> Matrix(5,-6,6,-7) Matrix(819,-152,2096,-389) -> Matrix(5,-8,2,-3) Matrix(1453,-276,816,-155) -> Matrix(3,-4,4,-5) Matrix(497,-96,906,-175) -> Matrix(1,-2,2,-3) Matrix(359,-74,1208,-249) -> Matrix(3,-2,2,-1) Matrix(1429,-300,624,-131) -> Matrix(1,0,0,1) Matrix(355,-78,132,-29) -> Matrix(3,-2,2,-1) Matrix(221,-50,968,-219) -> Matrix(15,-14,14,-13) Matrix(701,-164,218,-51) -> Matrix(11,-14,4,-5) Matrix(131,-32,86,-21) -> Matrix(1,-2,2,-3) Matrix(513,-136,298,-79) -> Matrix(3,-2,2,-1) Matrix(425,-114,384,-103) -> Matrix(1,-2,2,-3) Matrix(2255,-606,3576,-961) -> Matrix(1,-2,0,1) Matrix(807,-218,596,-161) -> Matrix(1,-2,6,-11) Matrix(211,-58,382,-105) -> Matrix(1,0,0,1) Matrix(85,-24,294,-83) -> Matrix(3,-2,2,-1) Matrix(4555,-1332,5598,-1637) -> Matrix(3,-2,-4,3) Matrix(4843,-1420,7684,-2253) -> Matrix(3,-4,-2,3) Matrix(291,-86,626,-185) -> Matrix(5,-8,2,-3) Matrix(6455,-1916,2456,-729) -> Matrix(5,-8,2,-3) Matrix(497,-152,206,-63) -> Matrix(3,-2,2,-1) Matrix(701,-218,164,-51) -> Matrix(9,-14,2,-3) Matrix(123,-40,40,-13) -> Matrix(1,0,0,1) Matrix(439,-156,318,-113) -> Matrix(1,-2,2,-3) Matrix(1669,-600,1032,-371) -> Matrix(1,0,0,1) Matrix(3691,-1332,2142,-773) -> Matrix(11,-18,8,-13) Matrix(911,-330,1626,-589) -> Matrix(1,-4,0,1) Matrix(6169,-2256,2688,-983) -> Matrix(5,-8,2,-3) Matrix(1501,-552,552,-203) -> Matrix(11,-24,6,-13) Matrix(355,-132,78,-29) -> Matrix(1,-2,0,1) Matrix(2543,-966,3288,-1249) -> Matrix(5,-6,6,-7) Matrix(4851,-1844,5948,-2261) -> Matrix(3,-4,4,-5) Matrix(2035,-774,234,-89) -> Matrix(3,-4,-2,3) Matrix(587,-224,1250,-477) -> Matrix(9,-14,2,-3) Matrix(351,-136,622,-241) -> Matrix(1,-2,-2,5) Matrix(1631,-636,2526,-985) -> Matrix(3,-10,4,-13) Matrix(233,-92,38,-15) -> Matrix(1,-2,0,1) Matrix(153,-62,116,-47) -> Matrix(1,-2,0,1) Matrix(497,-206,152,-63) -> Matrix(1,-2,0,1) Matrix(305,-128,722,-303) -> Matrix(1,-10,0,1) Matrix(1885,-816,1356,-587) -> Matrix(3,-4,4,-5) Matrix(1091,-474,1770,-769) -> Matrix(1,0,0,1) Matrix(6169,-2688,2256,-983) -> Matrix(5,-8,2,-3) Matrix(1429,-624,300,-131) -> Matrix(1,0,0,1) Matrix(337,-148,526,-231) -> Matrix(1,-2,2,-3) Matrix(261,-118,334,-151) -> Matrix(1,0,0,1) Matrix(407,-186,186,-85) -> Matrix(1,0,0,1) Matrix(511,-244,622,-297) -> Matrix(1,-2,0,1) Matrix(317,-170,386,-207) -> Matrix(1,0,0,1) Matrix(455,-246,246,-133) -> Matrix(1,0,2,1) Matrix(5577,-3064,1498,-823) -> Matrix(1,2,0,1) Matrix(2149,-1200,1524,-851) -> Matrix(1,8,2,17) Matrix(7897,-4416,4848,-2711) -> Matrix(1,4,0,1) Matrix(6505,-3648,2352,-1319) -> Matrix(7,12,4,7) Matrix(1453,-816,276,-155) -> Matrix(1,4,0,1) Matrix(205,-118,172,-99) -> Matrix(1,-2,2,-3) Matrix(513,-298,136,-79) -> Matrix(1,-2,0,1) Matrix(341,-200,578,-339) -> Matrix(1,-14,0,1) Matrix(571,-348,402,-245) -> Matrix(3,2,4,3) Matrix(2077,-1272,1272,-779) -> Matrix(1,0,-4,1) Matrix(7897,-4848,4416,-2711) -> Matrix(3,-4,4,-5) Matrix(7081,-4368,3072,-1895) -> Matrix(3,-8,2,-5) Matrix(3907,-2412,1602,-989) -> Matrix(3,-14,2,-9) Matrix(1669,-1032,600,-371) -> Matrix(1,0,0,1) Matrix(367,-228,66,-41) -> Matrix(1,6,0,1) Matrix(6063,-3820,4306,-2713) -> Matrix(5,2,12,5) Matrix(15867,-10000,4438,-2797) -> Matrix(1,2,0,1) Matrix(2583,-1630,496,-313) -> Matrix(5,2,2,1) Matrix(1389,-878,1688,-1067) -> Matrix(3,2,-2,-1) Matrix(1019,-656,1412,-909) -> Matrix(1,0,-2,1) Matrix(3511,-2268,918,-593) -> Matrix(11,-10,10,-9) Matrix(131,-86,32,-21) -> Matrix(1,2,0,1) Matrix(353,-242,512,-351) -> Matrix(1,-10,0,1) Matrix(893,-620,350,-243) -> Matrix(3,10,2,7) Matrix(287,-200,254,-177) -> Matrix(1,2,0,1) Matrix(571,-402,348,-245) -> Matrix(1,2,2,5) Matrix(2149,-1524,1200,-851) -> Matrix(9,8,10,9) Matrix(757,-538,916,-651) -> Matrix(3,2,-2,-1) Matrix(1257,-902,1604,-1151) -> Matrix(1,-2,0,1) Matrix(345,-248,32,-23) -> Matrix(1,4,0,1) Matrix(439,-318,156,-113) -> Matrix(1,2,0,1) Matrix(999,-728,188,-137) -> Matrix(1,4,0,1) Matrix(5401,-3942,3402,-2483) -> Matrix(3,4,8,11) Matrix(1153,-844,250,-183) -> Matrix(3,2,4,3) Matrix(623,-458,404,-297) -> Matrix(5,2,2,1) Matrix(807,-596,218,-161) -> Matrix(9,2,4,1) Matrix(153,-116,62,-47) -> Matrix(3,-2,2,-1) Matrix(609,-470,92,-71) -> Matrix(3,-2,2,-1) Matrix(3471,-2686,1552,-1201) -> Matrix(5,-6,6,-7) Matrix(1277,-990,396,-307) -> Matrix(1,2,0,1) Matrix(8297,-6498,3150,-2467) -> Matrix(1,12,0,1) Matrix(121,-96,150,-119) -> Matrix(1,-2,0,1) Matrix(6255,-5086,1846,-1501) -> Matrix(13,16,4,5) Matrix(14397,-11738,5474,-4463) -> Matrix(15,-4,4,-1) Matrix(15411,-12668,4298,-3533) -> Matrix(1,-10,0,1) Matrix(2717,-2252,1712,-1419) -> Matrix(1,0,4,1) Matrix(205,-172,118,-99) -> Matrix(1,2,0,1) Matrix(435,-376,376,-325) -> Matrix(1,0,-10,1) Matrix(287,-254,200,-177) -> Matrix(1,-2,2,-3) Matrix(715,-796,256,-285) -> Matrix(1,0,0,1) Matrix(2251,-2608,826,-957) -> Matrix(45,2,22,1) Matrix(757,-916,538,-651) -> Matrix(3,-2,8,-5) Matrix(317,-386,170,-207) -> Matrix(1,0,0,1) Matrix(121,-150,96,-119) -> Matrix(3,-2,2,-1) Matrix(6261,-7942,2380,-3019) -> Matrix(9,-14,2,-3) Matrix(4519,-5742,1260,-1601) -> Matrix(1,-6,0,1) Matrix(261,-334,118,-151) -> Matrix(1,0,0,1) Matrix(613,-790,142,-183) -> Matrix(1,4,0,1) Matrix(2543,-3288,966,-1249) -> Matrix(1,6,0,1) Matrix(799,-1036,118,-153) -> Matrix(5,2,2,1) Matrix(2203,-2872,1360,-1773) -> Matrix(5,-4,4,-3) Matrix(983,-1284,258,-337) -> Matrix(1,-2,2,-3) Matrix(849,-1148,230,-311) -> Matrix(15,-2,8,-1) Matrix(481,-654,114,-155) -> Matrix(15,-4,4,-1) Matrix(867,-1184,320,-437) -> Matrix(19,-8,12,-5) Matrix(4011,-5494,2848,-3901) -> Matrix(11,-6,24,-13) Matrix(1867,-2560,1048,-1437) -> Matrix(1,0,0,1) Matrix(3197,-4418,2312,-3195) -> Matrix(5,-2,8,-3) Matrix(1019,-1412,656,-909) -> Matrix(1,0,-2,1) Matrix(857,-1194,384,-535) -> Matrix(1,-2,2,-3) Matrix(6967,-9826,2644,-3729) -> Matrix(29,-14,-2,1) Matrix(8377,-11820,3180,-4487) -> Matrix(47,-24,2,-1) Matrix(1575,-2258,422,-605) -> Matrix(7,-4,2,-1) Matrix(421,-606,66,-95) -> Matrix(5,-4,4,-3) Matrix(353,-512,242,-351) -> Matrix(11,-10,10,-9) Matrix(1631,-2526,636,-985) -> Matrix(3,10,2,7) Matrix(337,-526,148,-231) -> Matrix(1,2,0,1) Matrix(669,-1058,356,-563) -> Matrix(5,-2,8,-3) Matrix(2255,-3576,606,-961) -> Matrix(3,-2,2,-1) Matrix(5825,-9242,1628,-2583) -> Matrix(3,-2,2,-1) Matrix(3101,-5000,1922,-3099) -> Matrix(23,-22,22,-21) Matrix(3239,-5240,866,-1401) -> Matrix(1,2,0,1) Matrix(3465,-5608,1072,-1735) -> Matrix(7,-4,2,-1) Matrix(1091,-1770,474,-769) -> Matrix(1,0,0,1) Matrix(6901,-11244,1848,-3011) -> Matrix(1,4,0,1) Matrix(2009,-3282,636,-1039) -> Matrix(29,2,14,1) Matrix(1353,-2212,430,-703) -> Matrix(23,-2,12,-1) Matrix(143,-236,20,-33) -> Matrix(7,-4,2,-1) Matrix(341,-578,200,-339) -> Matrix(15,-14,14,-13) Matrix(1109,-1914,456,-787) -> Matrix(11,-18,8,-13) Matrix(351,-622,136,-241) -> Matrix(7,-2,4,-1) Matrix(911,-1626,330,-589) -> Matrix(5,-4,4,-3) Matrix(7513,-13438,2692,-4815) -> Matrix(7,-6,6,-5) Matrix(1605,-2876,716,-1283) -> Matrix(21,-20,20,-19) Matrix(1643,-2948,734,-1317) -> Matrix(17,-18,18,-19) Matrix(211,-382,58,-105) -> Matrix(1,0,0,1) Matrix(1331,-2450,722,-1329) -> Matrix(1,0,6,1) Matrix(501,-958,148,-283) -> Matrix(1,2,0,1) Matrix(291,-626,86,-185) -> Matrix(5,-8,2,-3) Matrix(1259,-2738,578,-1257) -> Matrix(13,-24,6,-11) Matrix(2493,-5714,476,-1091) -> Matrix(1,2,0,1) Matrix(3083,-7070,590,-1353) -> Matrix(5,-8,2,-3) Matrix(3343,-7674,1032,-2369) -> Matrix(1,2,0,1) Matrix(12153,-28022,3398,-7835) -> Matrix(13,-24,6,-11) Matrix(8525,-19664,2384,-5499) -> Matrix(7,-16,4,-9) Matrix(147,-340,16,-37) -> Matrix(1,0,0,1) Matrix(305,-722,128,-303) -> Matrix(11,-10,10,-9) Matrix(2059,-5014,802,-1953) -> Matrix(49,-72,32,-47) Matrix(819,-2096,152,-389) -> Matrix(5,-8,2,-3) Matrix(12161,-31202,3392,-8703) -> Matrix(55,-82,-2,3) Matrix(7979,-20478,2226,-5713) -> Matrix(37,-56,2,-3) Matrix(1417,-3712,418,-1095) -> Matrix(7,-18,2,-5) Matrix(12971,-34116,4686,-12325) -> Matrix(21,-82,10,-39) Matrix(4583,-12482,1682,-4581) -> Matrix(85,-168,42,-83) Matrix(2977,-8146,694,-1899) -> Matrix(11,-28,2,-5) Matrix(10235,-28322,3698,-10233) -> Matrix(45,-88,22,-43) Matrix(387,-1072,100,-277) -> Matrix(3,-8,2,-5) Matrix(1839,-5126,428,-1193) -> Matrix(1,6,0,1) Matrix(281,-800,98,-279) -> Matrix(3,-2,2,-1) Matrix(359,-1208,74,-249) -> Matrix(1,-2,0,1) Matrix(8517,-28850,2228,-7547) -> Matrix(25,-74,24,-71) Matrix(85,-294,24,-83) -> Matrix(1,-2,0,1) Matrix(363,-1312,70,-253) -> Matrix(1,2,0,1) Matrix(3911,-14450,1058,-3909) -> Matrix(61,-120,30,-59) Matrix(2903,-10812,606,-2257) -> Matrix(1,-2,0,1) Matrix(5993,-22898,1568,-5991) -> Matrix(47,-46,46,-45) Matrix(221,-968,50,-219) -> Matrix(1,-14,0,1) Matrix(1877,-8978,392,-1875) -> Matrix(1,-2,0,1) Matrix(241,-1162,28,-135) -> Matrix(1,-2,0,1) Matrix(185,-1058,32,-183) -> Matrix(1,-22,0,1) Matrix(659,-4418,98,-657) -> Matrix(29,-56,14,-27) 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): 108 Degree of the the map X: 108 Degree of the the map Y: 324 ----------------------------------------------------------------------- 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, lambda2 The subgroup of modular group liftables which arise from translations is isomorphic to Z/2Z. ----------------------------------------------------------------------- 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): 972 Minimal number of generators: 163 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: 60 Genus: 52 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/8 1/5 2/7 5/13 1/2 7/11 5/7 4/5 1/1 5/4 7/5 16/11 11/7 67/41 17/10 52/29 35/19 2/1 37/17 113/49 19/8 17/7 13/5 79/29 11/4 119/43 20/7 3/1 16/5 55/17 7/2 11/3 85/23 19/5 107/28 4/1 21/5 17/4 73/17 13/3 22/5 67/14 5/1 21/4 16/3 11/2 17/3 23/4 6/1 19/3 13/2 20/3 47/7 7/1 15/2 8/1 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 0/1 1/1 1/9 0/1 1/8 1/1 1/7 2/1 2/13 1/1 1/6 1/2 2/11 9/7 3/16 3/2 4/21 1/1 1/5 2/1 5/24 1/0 4/19 1/1 3/14 1/0 2/9 1/1 5/22 1/1 3/13 6/5 4/17 1/1 1/4 3/2 4/15 1/1 11/41 2/1 7/26 3/2 3/11 4/1 5/18 1/0 2/7 1/1 7/24 3/2 12/41 1/1 5/17 4/3 8/27 1/1 3/10 7/4 4/13 1/1 5/16 3/2 1/3 2/1 5/14 1/0 9/25 4/3 13/36 7/4 4/11 1/1 11/30 15/8 7/19 12/5 3/8 1/0 8/21 1/1 5/13 2/1 7/18 5/2 16/41 3/1 9/23 2/1 2/5 1/1 7/17 4/1 5/12 1/0 8/19 1/0 3/7 0/1 13/30 3/2 10/23 1/1 17/39 2/1 7/16 1/0 4/9 5/1 5/11 2/1 6/13 3/1 7/15 4/1 1/2 1/0 7/13 -2/1 6/11 1/1 11/20 1/0 5/9 4/1 19/34 1/0 14/25 -3/1 37/66 -9/4 23/41 -2/1 9/16 1/0 4/7 1/1 11/19 2/1 7/12 1/0 10/17 1/0 3/5 -2/1 11/18 -1/4 19/31 0/1 8/13 1/1 37/60 3/2 29/47 2/1 21/34 1/0 13/21 4/1 5/8 -3/2 12/19 -1/1 7/11 0/1 9/14 1/2 20/31 1/1 31/48 5/6 11/17 6/5 2/3 1/1 11/16 1/0 9/13 -4/1 16/23 -3/1 7/10 1/0 12/17 -5/3 17/24 -7/6 22/31 -1/1 5/7 0/1 23/32 1/0 18/25 -1/1 13/18 1/0 8/11 -1/1 27/37 -2/1 19/26 -1/1 11/15 -4/7 14/19 -1/3 3/4 1/2 10/13 -1/1 17/22 1/2 24/31 1/1 7/9 2/1 18/23 5/1 11/14 1/2 4/5 1/0 13/16 -3/2 22/27 -1/3 9/11 -2/1 23/28 1/0 14/17 -1/1 5/6 1/0 6/7 -1/5 7/8 1/2 1/1 0/1 10/9 1/1 9/8 1/0 8/7 -1/1 7/6 1/6 13/11 0/1 6/5 1/1 17/14 1/2 11/9 2/3 5/4 1/1 19/15 0/1 33/26 5/2 14/11 -1/1 9/7 2/1 31/24 1/0 22/17 -1/1 35/27 0/1 13/10 1/2 30/23 1/1 17/13 2/1 4/3 -1/1 23/17 2/13 19/14 1/4 15/11 4/11 26/19 1/2 37/27 2/3 11/8 1/2 29/21 0/1 47/34 1/2 18/13 1/1 25/18 1/2 57/41 4/5 32/23 1/1 7/5 0/1 31/22 1/2 55/39 12/25 79/56 1/2 24/17 7/13 17/12 5/8 27/19 4/5 37/26 1/1 10/7 1/1 33/23 2/3 23/16 3/4 13/9 4/5 16/11 1/1 3/2 1/0 20/13 1/1 17/11 6/1 31/20 1/0 14/9 -1/1 11/7 0/1 19/12 1/2 8/5 3/5 29/18 7/8 50/31 1/1 21/13 4/3 55/34 1/0 89/55 0/1 34/21 1/1 47/29 2/1 13/8 1/0 31/19 0/1 49/30 -1/8 67/41 0/1 18/11 1/5 23/14 1/2 5/3 2/3 17/10 1/1 12/7 1/1 31/18 5/4 50/29 13/9 19/11 2/1 26/15 9/5 7/4 1/0 16/9 1/1 57/32 1/2 41/23 2/3 25/14 3/4 34/19 1/1 43/24 15/16 52/29 1/1 9/5 4/3 11/6 1/0 35/19 0/1 24/13 1/3 13/7 2/3 15/8 1/2 2/1 1/1 13/6 3/2 37/17 2/1 24/11 3/1 11/5 2/1 20/9 -1/1 9/4 5/4 16/7 1/1 55/24 1/0 94/41 1/1 39/17 2/1 23/10 1/0 53/23 2/1 83/36 7/4 113/49 2/1 30/13 3/1 7/3 0/1 19/8 1/1 12/5 1/1 29/12 13/10 17/7 4/3 56/23 19/13 39/16 3/2 22/9 5/3 5/2 1/0 28/11 1/1 23/9 2/1 41/16 3/2 59/23 28/19 136/53 3/2 77/30 3/2 18/7 5/3 13/5 2/1 21/8 1/0 8/3 1/1 27/10 3/2 46/17 3/2 19/7 12/7 49/18 27/14 79/29 2/1 30/11 15/7 11/4 1/0 47/17 2/1 83/30 15/8 119/43 2/1 36/13 7/3 25/9 4/1 39/14 1/0 53/19 0/1 67/24 1/0 14/5 1/1 17/6 1/0 20/7 1/1 3/1 2/1 16/5 3/1 29/9 4/1 42/13 3/1 55/17 4/1 13/4 1/0 23/7 2/1 10/3 7/3 27/8 1/0 44/13 3/1 17/5 4/1 7/2 1/0 25/7 2/1 43/12 1/0 18/5 1/1 29/8 1/0 11/3 4/3 48/13 17/9 85/23 2/1 37/10 13/6 26/7 3/1 41/11 2/1 56/15 3/1 71/19 2/1 15/4 1/0 19/5 0/1 42/11 1/1 107/28 1/1 65/17 16/15 23/6 5/4 4/1 3/1 21/5 16/5 17/4 1/0 30/7 5/1 73/17 6/1 43/10 1/0 13/3 6/1 22/5 1/0 9/2 1/0 23/5 2/5 37/8 1/1 14/3 1/1 19/4 1/0 43/9 2/1 67/14 1/0 24/5 1/1 5/1 2/1 21/4 1/0 37/7 2/1 16/3 3/1 11/2 9/2 17/3 10/1 23/4 1/0 6/1 -1/1 19/3 0/1 13/2 1/0 20/3 5/3 47/7 2/1 27/4 9/4 7/1 2/1 15/2 1/0 8/1 1/0 9/1 0/1 10/1 3/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(345,-32,248,-23) (0/1,1/9) -> (57/41,32/23) Hyperbolic Matrix(530,-63,387,-46) (1/9,1/8) -> (26/19,37/27) Hyperbolic Matrix(475,-64,334,-45) (1/8,1/7) -> (27/19,37/26) Hyperbolic Matrix(609,-92,470,-71) (1/7,2/13) -> (22/17,35/27) Hyperbolic Matrix(233,-38,92,-15) (2/13,1/6) -> (5/2,28/11) Hyperbolic Matrix(367,-66,228,-41) (1/6,2/11) -> (8/5,29/18) Hyperbolic Matrix(136,-25,457,-84) (2/11,3/16) -> (8/27,3/10) Hyperbolic Matrix(1453,-276,816,-155) (3/16,4/21) -> (16/9,57/32) Hyperbolic Matrix(46,-9,225,-44) (4/21,1/5) -> (1/5,5/24) Parabolic Matrix(1429,-300,624,-131) (5/24,4/19) -> (16/7,55/24) Hyperbolic Matrix(268,-57,489,-104) (4/19,3/14) -> (6/11,11/20) Hyperbolic Matrix(355,-78,132,-29) (3/14,2/9) -> (8/3,27/10) Hyperbolic Matrix(396,-89,89,-20) (2/9,5/22) -> (22/5,9/2) Hyperbolic Matrix(572,-131,131,-30) (5/22,3/13) -> (13/3,22/5) Hyperbolic Matrix(701,-164,218,-51) (3/13,4/17) -> (16/5,29/9) Hyperbolic Matrix(131,-32,86,-21) (4/17,1/4) -> (3/2,20/13) Hyperbolic Matrix(513,-136,298,-79) (1/4,4/15) -> (12/7,31/18) Hyperbolic Matrix(425,-114,384,-103) (4/15,11/41) -> (1/1,10/9) Hyperbolic Matrix(852,-229,1957,-526) (11/41,7/26) -> (10/23,17/39) Hyperbolic Matrix(807,-218,596,-161) (7/26,3/11) -> (23/17,19/14) Hyperbolic Matrix(211,-58,382,-105) (3/11,5/18) -> (11/20,5/9) Hyperbolic Matrix(85,-24,294,-83) (5/18,2/7) -> (2/7,7/24) Parabolic Matrix(1838,-537,753,-220) (7/24,12/41) -> (39/16,22/9) Hyperbolic Matrix(1546,-453,2505,-734) (12/41,5/17) -> (29/47,21/34) Hyperbolic Matrix(291,-86,626,-185) (5/17,8/27) -> (6/13,7/15) Hyperbolic Matrix(497,-152,206,-63) (3/10,4/13) -> (12/5,29/12) Hyperbolic Matrix(701,-218,164,-51) (4/13,5/16) -> (17/4,30/7) Hyperbolic Matrix(328,-103,535,-168) (5/16,1/3) -> (19/31,8/13) Hyperbolic Matrix(439,-156,318,-113) (1/3,5/14) -> (11/8,29/21) Hyperbolic Matrix(1669,-600,1032,-371) (5/14,9/25) -> (21/13,55/34) Hyperbolic Matrix(874,-315,1071,-386) (9/25,13/36) -> (22/27,9/11) Hyperbolic Matrix(911,-330,1626,-589) (13/36,4/11) -> (14/25,37/66) Hyperbolic Matrix(276,-101,317,-116) (4/11,11/30) -> (6/7,7/8) Hyperbolic Matrix(1501,-552,552,-203) (11/30,7/19) -> (19/7,49/18) Hyperbolic Matrix(355,-132,78,-29) (7/19,3/8) -> (9/2,23/5) Hyperbolic Matrix(156,-59,275,-104) (3/8,8/21) -> (9/16,4/7) Hyperbolic Matrix(196,-75,507,-194) (8/21,5/13) -> (5/13,7/18) Parabolic Matrix(1631,-636,2526,-985) (7/18,16/41) -> (20/31,31/48) Hyperbolic Matrix(310,-121,661,-258) (16/41,9/23) -> (7/15,1/2) Hyperbolic Matrix(233,-92,38,-15) (9/23,2/5) -> (6/1,19/3) Hyperbolic Matrix(153,-62,116,-47) (2/5,7/17) -> (17/13,4/3) Hyperbolic Matrix(497,-206,152,-63) (7/17,5/12) -> (13/4,23/7) Hyperbolic Matrix(456,-191,191,-80) (5/12,8/19) -> (19/8,12/5) Hyperbolic Matrix(266,-113,113,-48) (8/19,3/7) -> (7/3,19/8) Hyperbolic Matrix(1885,-816,1356,-587) (3/7,13/30) -> (25/18,57/41) Hyperbolic Matrix(1091,-474,1770,-769) (13/30,10/23) -> (8/13,37/60) Hyperbolic Matrix(1429,-624,300,-131) (17/39,7/16) -> (19/4,43/9) Hyperbolic Matrix(188,-83,299,-132) (7/16,4/9) -> (5/8,12/19) Hyperbolic Matrix(261,-118,334,-151) (4/9,5/11) -> (7/9,18/23) Hyperbolic Matrix(407,-186,186,-85) (5/11,6/13) -> (24/11,11/5) Hyperbolic Matrix(317,-170,386,-207) (1/2,7/13) -> (9/11,23/28) Hyperbolic Matrix(455,-246,246,-133) (7/13,6/11) -> (24/13,13/7) Hyperbolic Matrix(2149,-1200,1524,-851) (5/9,19/34) -> (31/22,55/39) Hyperbolic Matrix(1178,-659,1523,-852) (19/34,14/25) -> (17/22,24/31) Hyperbolic Matrix(6505,-3648,2352,-1319) (37/66,23/41) -> (47/17,83/30) Hyperbolic Matrix(1453,-816,276,-155) (23/41,9/16) -> (21/4,37/7) Hyperbolic Matrix(205,-118,172,-99) (4/7,11/19) -> (13/11,6/5) Hyperbolic Matrix(513,-298,136,-79) (11/19,7/12) -> (15/4,19/5) Hyperbolic Matrix(408,-239,239,-140) (7/12,10/17) -> (17/10,12/7) Hyperbolic Matrix(170,-101,101,-60) (10/17,3/5) -> (5/3,17/10) Hyperbolic Matrix(571,-348,402,-245) (3/5,11/18) -> (17/12,27/19) Hyperbolic Matrix(2077,-1272,1272,-779) (11/18,19/31) -> (31/19,49/30) Hyperbolic Matrix(7081,-4368,3072,-1895) (37/60,29/47) -> (53/23,83/36) Hyperbolic Matrix(1669,-1032,600,-371) (21/34,13/21) -> (25/9,39/14) Hyperbolic Matrix(367,-228,66,-41) (13/21,5/8) -> (11/2,17/3) Hyperbolic Matrix(232,-147,363,-230) (12/19,7/11) -> (7/11,9/14) Parabolic Matrix(756,-487,919,-592) (9/14,20/31) -> (23/28,14/17) Hyperbolic Matrix(3511,-2268,918,-593) (31/48,11/17) -> (65/17,23/6) Hyperbolic Matrix(131,-86,32,-21) (11/17,2/3) -> (4/1,21/5) Hyperbolic Matrix(96,-65,65,-44) (2/3,11/16) -> (16/11,3/2) Hyperbolic Matrix(416,-287,287,-198) (11/16,9/13) -> (13/9,16/11) Hyperbolic Matrix(893,-620,350,-243) (9/13,16/23) -> (28/11,23/9) Hyperbolic Matrix(287,-200,254,-177) (16/23,7/10) -> (9/8,8/7) Hyperbolic Matrix(571,-402,348,-245) (7/10,12/17) -> (18/11,23/14) Hyperbolic Matrix(570,-403,727,-514) (12/17,17/24) -> (18/23,11/14) Hyperbolic Matrix(2149,-1524,1200,-851) (17/24,22/31) -> (34/19,43/24) Hyperbolic Matrix(316,-225,441,-314) (22/31,5/7) -> (5/7,23/32) Parabolic Matrix(345,-248,32,-23) (23/32,18/25) -> (10/1,1/0) Hyperbolic Matrix(440,-317,533,-384) (18/25,13/18) -> (14/17,5/6) Hyperbolic Matrix(439,-318,156,-113) (13/18,8/11) -> (14/5,17/6) Hyperbolic Matrix(999,-728,188,-137) (8/11,27/37) -> (37/7,16/3) Hyperbolic Matrix(530,-387,63,-46) (27/37,19/26) -> (8/1,9/1) Hyperbolic Matrix(1153,-844,250,-183) (19/26,11/15) -> (23/5,37/8) Hyperbolic Matrix(623,-458,404,-297) (11/15,14/19) -> (20/13,17/11) Hyperbolic Matrix(807,-596,218,-161) (14/19,3/4) -> (37/10,26/7) Hyperbolic Matrix(153,-116,62,-47) (3/4,10/13) -> (22/9,5/2) Hyperbolic Matrix(609,-470,92,-71) (10/13,17/22) -> (13/2,20/3) Hyperbolic Matrix(1277,-990,396,-307) (24/31,7/9) -> (29/9,42/13) Hyperbolic Matrix(121,-96,150,-119) (11/14,4/5) -> (4/5,13/16) Parabolic Matrix(1846,-1503,1071,-872) (13/16,22/27) -> (31/18,50/29) Hyperbolic Matrix(205,-172,118,-99) (5/6,6/7) -> (26/15,7/4) Hyperbolic Matrix(287,-254,200,-177) (7/8,1/1) -> (33/23,23/16) Hyperbolic Matrix(715,-796,256,-285) (10/9,9/8) -> (67/24,14/5) Hyperbolic Matrix(276,-317,101,-116) (8/7,7/6) -> (30/11,11/4) Hyperbolic Matrix(248,-291,75,-88) (7/6,13/11) -> (23/7,10/3) Hyperbolic Matrix(440,-533,317,-384) (6/5,17/14) -> (18/13,25/18) Hyperbolic Matrix(317,-386,170,-207) (17/14,11/9) -> (13/7,15/8) Hyperbolic Matrix(121,-150,96,-119) (11/9,5/4) -> (5/4,19/15) Parabolic Matrix(1190,-1509,429,-544) (19/15,33/26) -> (36/13,25/9) Hyperbolic Matrix(642,-815,167,-212) (33/26,14/11) -> (23/6,4/1) Hyperbolic Matrix(261,-334,118,-151) (14/11,9/7) -> (11/5,20/9) Hyperbolic Matrix(613,-790,142,-183) (9/7,31/24) -> (43/10,13/3) Hyperbolic Matrix(1178,-1523,659,-852) (31/24,22/17) -> (25/14,34/19) Hyperbolic Matrix(799,-1036,118,-153) (35/27,13/10) -> (27/4,7/1) Hyperbolic Matrix(844,-1099,235,-306) (13/10,30/23) -> (43/12,18/5) Hyperbolic Matrix(983,-1284,258,-337) (30/23,17/13) -> (19/5,42/11) Hyperbolic Matrix(849,-1148,230,-311) (4/3,23/17) -> (11/3,48/13) Hyperbolic Matrix(481,-654,114,-155) (19/14,15/11) -> (21/5,17/4) Hyperbolic Matrix(867,-1184,320,-437) (15/11,26/19) -> (46/17,19/7) Hyperbolic Matrix(1867,-2560,1048,-1437) (37/27,11/8) -> (57/32,41/23) Hyperbolic Matrix(522,-721,181,-250) (29/21,47/34) -> (20/7,3/1) Hyperbolic Matrix(838,-1159,295,-408) (47/34,18/13) -> (17/6,20/7) Hyperbolic Matrix(316,-441,225,-314) (32/23,7/5) -> (7/5,31/22) Parabolic Matrix(2532,-3571,1411,-1990) (55/39,79/56) -> (52/29,9/5) Hyperbolic Matrix(3292,-4645,1837,-2592) (79/56,24/17) -> (43/24,52/29) Hyperbolic Matrix(448,-633,201,-284) (24/17,17/12) -> (20/9,9/4) Hyperbolic Matrix(1024,-1459,379,-540) (37/26,10/7) -> (27/10,46/17) Hyperbolic Matrix(1575,-2258,422,-605) (10/7,33/23) -> (41/11,56/15) Hyperbolic Matrix(421,-606,66,-95) (23/16,13/9) -> (19/3,13/2) Hyperbolic Matrix(1631,-2526,636,-985) (17/11,31/20) -> (41/16,59/23) Hyperbolic Matrix(318,-493,169,-262) (31/20,14/9) -> (15/8,2/1) Hyperbolic Matrix(232,-363,147,-230) (14/9,11/7) -> (11/7,19/12) Parabolic Matrix(188,-299,83,-132) (19/12,8/5) -> (9/4,16/7) Hyperbolic Matrix(600,-967,103,-166) (29/18,50/31) -> (23/4,6/1) Hyperbolic Matrix(826,-1333,145,-234) (50/31,21/13) -> (17/3,23/4) Hyperbolic Matrix(3239,-5240,866,-1401) (55/34,89/55) -> (71/19,15/4) Hyperbolic Matrix(3465,-5608,1072,-1735) (89/55,34/21) -> (42/13,55/17) Hyperbolic Matrix(1772,-2871,495,-802) (34/21,47/29) -> (25/7,43/12) Hyperbolic Matrix(1091,-1770,474,-769) (47/29,13/8) -> (23/10,53/23) Hyperbolic Matrix(328,-535,103,-168) (13/8,31/19) -> (3/1,16/5) Hyperbolic Matrix(2748,-4489,1681,-2746) (49/30,67/41) -> (67/41,18/11) Parabolic Matrix(143,-236,20,-33) (23/14,5/3) -> (7/1,15/2) Hyperbolic Matrix(1109,-1914,456,-787) (50/29,19/11) -> (17/7,56/23) Hyperbolic Matrix(574,-993,237,-410) (19/11,26/15) -> (29/12,17/7) Hyperbolic Matrix(156,-275,59,-104) (7/4,16/9) -> (21/8,8/3) Hyperbolic Matrix(911,-1626,330,-589) (41/23,25/14) -> (11/4,47/17) Hyperbolic Matrix(211,-382,58,-105) (9/5,11/6) -> (29/8,11/3) Hyperbolic Matrix(666,-1225,361,-664) (11/6,35/19) -> (35/19,24/13) Parabolic Matrix(291,-626,86,-185) (2/1,13/6) -> (27/8,44/13) Hyperbolic Matrix(630,-1369,289,-628) (13/6,37/17) -> (37/17,24/11) Parabolic Matrix(2592,-5941,541,-1240) (55/24,94/41) -> (67/14,24/5) Hyperbolic Matrix(2902,-6655,607,-1392) (94/41,39/17) -> (43/9,67/14) Hyperbolic Matrix(852,-1957,229,-526) (39/17,23/10) -> (26/7,41/11) Hyperbolic Matrix(5538,-12769,2401,-5536) (83/36,113/49) -> (113/49,30/13) Parabolic Matrix(147,-340,16,-37) (30/13,7/3) -> (9/1,10/1) Hyperbolic Matrix(2059,-5014,802,-1953) (56/23,39/16) -> (77/30,18/7) Hyperbolic Matrix(668,-1709,197,-504) (23/9,41/16) -> (44/13,17/5) Hyperbolic Matrix(5906,-15153,1545,-3964) (59/23,136/53) -> (107/28,65/17) Hyperbolic Matrix(5436,-13951,1423,-3652) (136/53,77/30) -> (42/11,107/28) Hyperbolic Matrix(196,-507,75,-194) (18/7,13/5) -> (13/5,21/8) Parabolic Matrix(2292,-6241,841,-2290) (49/18,79/29) -> (79/29,30/11) Parabolic Matrix(5118,-14161,1849,-5116) (83/30,119/43) -> (119/43,36/13) Parabolic Matrix(1839,-5126,428,-1193) (39/14,53/19) -> (73/17,43/10) Hyperbolic Matrix(2322,-6481,541,-1510) (53/19,67/24) -> (30/7,73/17) Hyperbolic Matrix(1236,-4003,331,-1072) (55/17,13/4) -> (56/15,71/19) Hyperbolic Matrix(136,-457,25,-84) (10/3,27/8) -> (16/3,11/2) Hyperbolic Matrix(85,-294,24,-83) (17/5,7/2) -> (7/2,25/7) Parabolic Matrix(222,-803,47,-170) (18/5,29/8) -> (14/3,19/4) Hyperbolic Matrix(1956,-7225,529,-1954) (48/13,85/23) -> (85/23,37/10) Parabolic Matrix(144,-667,19,-88) (37/8,14/3) -> (15/2,8/1) Hyperbolic Matrix(46,-225,9,-44) (24/5,5/1) -> (5/1,21/4) Parabolic Matrix(330,-2209,49,-328) (20/3,47/7) -> (47/7,27/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,1,1) Matrix(345,-32,248,-23) -> Matrix(3,-4,4,-5) Matrix(530,-63,387,-46) -> Matrix(3,-2,5,-3) Matrix(475,-64,334,-45) -> Matrix(5,-6,6,-7) Matrix(609,-92,470,-71) -> Matrix(1,-2,0,1) Matrix(233,-38,92,-15) -> Matrix(3,-2,2,-1) Matrix(367,-66,228,-41) -> Matrix(5,-6,6,-7) Matrix(136,-25,457,-84) -> Matrix(7,-10,5,-7) Matrix(1453,-276,816,-155) -> Matrix(3,-4,4,-5) Matrix(46,-9,225,-44) -> Matrix(3,-4,1,-1) Matrix(1429,-300,624,-131) -> Matrix(1,0,0,1) Matrix(268,-57,489,-104) -> Matrix(1,-2,1,-1) Matrix(355,-78,132,-29) -> Matrix(3,-2,2,-1) Matrix(396,-89,89,-20) -> Matrix(3,-2,-1,1) Matrix(572,-131,131,-30) -> Matrix(11,-12,1,-1) Matrix(701,-164,218,-51) -> Matrix(11,-14,4,-5) Matrix(131,-32,86,-21) -> Matrix(1,-2,2,-3) Matrix(513,-136,298,-79) -> Matrix(3,-2,2,-1) Matrix(425,-114,384,-103) -> Matrix(1,-2,2,-3) Matrix(852,-229,1957,-526) -> Matrix(3,-4,1,-1) Matrix(807,-218,596,-161) -> Matrix(1,-2,6,-11) Matrix(211,-58,382,-105) -> Matrix(1,0,0,1) Matrix(85,-24,294,-83) -> Matrix(3,-2,2,-1) Matrix(1838,-537,753,-220) -> Matrix(1,-4,1,-3) Matrix(1546,-453,2505,-734) -> Matrix(5,-6,1,-1) Matrix(291,-86,626,-185) -> Matrix(5,-8,2,-3) Matrix(497,-152,206,-63) -> Matrix(3,-2,2,-1) Matrix(701,-218,164,-51) -> Matrix(9,-14,2,-3) Matrix(328,-103,535,-168) -> Matrix(1,-2,3,-5) Matrix(439,-156,318,-113) -> Matrix(1,-2,2,-3) Matrix(1669,-600,1032,-371) -> Matrix(1,0,0,1) Matrix(874,-315,1071,-386) -> Matrix(1,-2,1,-1) Matrix(911,-330,1626,-589) -> Matrix(1,-4,0,1) Matrix(276,-101,317,-116) -> Matrix(1,-2,3,-5) Matrix(1501,-552,552,-203) -> Matrix(11,-24,6,-13) Matrix(355,-132,78,-29) -> Matrix(1,-2,0,1) Matrix(156,-59,275,-104) -> Matrix(1,-2,1,-1) Matrix(196,-75,507,-194) -> Matrix(7,-12,3,-5) Matrix(1631,-636,2526,-985) -> Matrix(3,-10,4,-13) Matrix(310,-121,661,-258) -> Matrix(3,-10,1,-3) Matrix(233,-92,38,-15) -> Matrix(1,-2,0,1) Matrix(153,-62,116,-47) -> Matrix(1,-2,0,1) Matrix(497,-206,152,-63) -> Matrix(1,-2,0,1) Matrix(456,-191,191,-80) -> Matrix(1,-10,1,-9) Matrix(266,-113,113,-48) -> Matrix(1,0,1,1) Matrix(1885,-816,1356,-587) -> Matrix(3,-4,4,-5) Matrix(1091,-474,1770,-769) -> Matrix(1,0,0,1) Matrix(1429,-624,300,-131) -> Matrix(1,0,0,1) Matrix(188,-83,299,-132) -> Matrix(1,-2,-1,3) Matrix(261,-118,334,-151) -> Matrix(1,0,0,1) Matrix(407,-186,186,-85) -> Matrix(1,0,0,1) Matrix(317,-170,386,-207) -> Matrix(1,0,0,1) Matrix(455,-246,246,-133) -> Matrix(1,0,2,1) Matrix(2149,-1200,1524,-851) -> Matrix(1,8,2,17) Matrix(1178,-659,1523,-852) -> Matrix(1,4,1,5) Matrix(6505,-3648,2352,-1319) -> Matrix(7,12,4,7) Matrix(1453,-816,276,-155) -> Matrix(1,4,0,1) Matrix(205,-118,172,-99) -> Matrix(1,-2,2,-3) Matrix(513,-298,136,-79) -> Matrix(1,-2,0,1) Matrix(408,-239,239,-140) -> Matrix(1,-10,1,-9) Matrix(170,-101,101,-60) -> Matrix(1,4,1,5) Matrix(571,-348,402,-245) -> Matrix(3,2,4,3) Matrix(2077,-1272,1272,-779) -> Matrix(1,0,-4,1) Matrix(7081,-4368,3072,-1895) -> Matrix(3,-8,2,-5) Matrix(1669,-1032,600,-371) -> Matrix(1,0,0,1) Matrix(367,-228,66,-41) -> Matrix(1,6,0,1) Matrix(232,-147,363,-230) -> Matrix(1,0,3,1) Matrix(756,-487,919,-592) -> Matrix(3,-2,-1,1) Matrix(3511,-2268,918,-593) -> Matrix(11,-10,10,-9) Matrix(131,-86,32,-21) -> Matrix(1,2,0,1) Matrix(96,-65,65,-44) -> Matrix(1,-2,1,-1) Matrix(416,-287,287,-198) -> Matrix(1,8,1,9) Matrix(893,-620,350,-243) -> Matrix(3,10,2,7) Matrix(287,-200,254,-177) -> Matrix(1,2,0,1) Matrix(571,-402,348,-245) -> Matrix(1,2,2,5) Matrix(570,-403,727,-514) -> Matrix(1,2,-1,-1) Matrix(2149,-1524,1200,-851) -> Matrix(9,8,10,9) Matrix(316,-225,441,-314) -> Matrix(1,0,1,1) Matrix(345,-248,32,-23) -> Matrix(1,4,0,1) Matrix(440,-317,533,-384) -> Matrix(1,2,-1,-1) Matrix(439,-318,156,-113) -> Matrix(1,2,0,1) Matrix(999,-728,188,-137) -> Matrix(1,4,0,1) Matrix(530,-387,63,-46) -> Matrix(1,2,-1,-1) Matrix(1153,-844,250,-183) -> Matrix(3,2,4,3) Matrix(623,-458,404,-297) -> Matrix(5,2,2,1) Matrix(807,-596,218,-161) -> Matrix(9,2,4,1) Matrix(153,-116,62,-47) -> Matrix(3,-2,2,-1) Matrix(609,-470,92,-71) -> Matrix(3,-2,2,-1) Matrix(1277,-990,396,-307) -> Matrix(1,2,0,1) Matrix(121,-96,150,-119) -> Matrix(1,-2,0,1) Matrix(1846,-1503,1071,-872) -> Matrix(7,4,5,3) Matrix(205,-172,118,-99) -> Matrix(1,2,0,1) Matrix(287,-254,200,-177) -> Matrix(1,-2,2,-3) Matrix(715,-796,256,-285) -> Matrix(1,0,0,1) Matrix(276,-317,101,-116) -> Matrix(3,2,1,1) Matrix(248,-291,75,-88) -> Matrix(5,-2,3,-1) Matrix(440,-533,317,-384) -> Matrix(3,-2,5,-3) Matrix(317,-386,170,-207) -> Matrix(1,0,0,1) Matrix(121,-150,96,-119) -> Matrix(3,-2,2,-1) Matrix(1190,-1509,429,-544) -> Matrix(3,-4,1,-1) Matrix(642,-815,167,-212) -> Matrix(1,-4,1,-3) Matrix(261,-334,118,-151) -> Matrix(1,0,0,1) Matrix(613,-790,142,-183) -> Matrix(1,4,0,1) Matrix(1178,-1523,659,-852) -> Matrix(1,4,1,5) Matrix(799,-1036,118,-153) -> Matrix(5,2,2,1) Matrix(844,-1099,235,-306) -> Matrix(1,0,-1,1) Matrix(983,-1284,258,-337) -> Matrix(1,-2,2,-3) Matrix(849,-1148,230,-311) -> Matrix(15,-2,8,-1) Matrix(481,-654,114,-155) -> Matrix(15,-4,4,-1) Matrix(867,-1184,320,-437) -> Matrix(19,-8,12,-5) Matrix(1867,-2560,1048,-1437) -> Matrix(1,0,0,1) Matrix(522,-721,181,-250) -> Matrix(5,-2,3,-1) Matrix(838,-1159,295,-408) -> Matrix(1,0,-1,1) Matrix(316,-441,225,-314) -> Matrix(1,0,1,1) Matrix(2532,-3571,1411,-1990) -> Matrix(33,-16,31,-15) Matrix(3292,-4645,1837,-2592) -> Matrix(43,-22,45,-23) Matrix(448,-633,201,-284) -> Matrix(3,-2,5,-3) Matrix(1024,-1459,379,-540) -> Matrix(5,-2,3,-1) Matrix(1575,-2258,422,-605) -> Matrix(7,-4,2,-1) Matrix(421,-606,66,-95) -> Matrix(5,-4,4,-3) Matrix(1631,-2526,636,-985) -> Matrix(3,10,2,7) Matrix(318,-493,169,-262) -> Matrix(1,2,1,3) Matrix(232,-363,147,-230) -> Matrix(1,0,3,1) Matrix(188,-299,83,-132) -> Matrix(5,-2,3,-1) Matrix(600,-967,103,-166) -> Matrix(9,-8,-1,1) Matrix(826,-1333,145,-234) -> Matrix(13,-14,1,-1) Matrix(3239,-5240,866,-1401) -> Matrix(1,2,0,1) Matrix(3465,-5608,1072,-1735) -> Matrix(7,-4,2,-1) Matrix(1772,-2871,495,-802) -> Matrix(3,-4,1,-1) Matrix(1091,-1770,474,-769) -> Matrix(1,0,0,1) Matrix(328,-535,103,-168) -> Matrix(3,2,1,1) Matrix(2748,-4489,1681,-2746) -> Matrix(1,0,13,1) Matrix(143,-236,20,-33) -> Matrix(7,-4,2,-1) Matrix(1109,-1914,456,-787) -> Matrix(11,-18,8,-13) Matrix(574,-993,237,-410) -> Matrix(7,-10,5,-7) Matrix(156,-275,59,-104) -> Matrix(1,-2,1,-1) Matrix(911,-1626,330,-589) -> Matrix(5,-4,4,-3) Matrix(211,-382,58,-105) -> Matrix(1,0,0,1) Matrix(666,-1225,361,-664) -> Matrix(1,0,3,1) Matrix(291,-626,86,-185) -> Matrix(5,-8,2,-3) Matrix(630,-1369,289,-628) -> Matrix(7,-12,3,-5) Matrix(2592,-5941,541,-1240) -> Matrix(1,-2,1,-1) Matrix(2902,-6655,607,-1392) -> Matrix(3,-4,1,-1) Matrix(852,-1957,229,-526) -> Matrix(3,-4,1,-1) Matrix(5538,-12769,2401,-5536) -> Matrix(11,-20,5,-9) Matrix(147,-340,16,-37) -> Matrix(1,0,0,1) Matrix(2059,-5014,802,-1953) -> Matrix(49,-72,32,-47) Matrix(668,-1709,197,-504) -> Matrix(5,-6,1,-1) Matrix(5906,-15153,1545,-3964) -> Matrix(51,-76,49,-73) Matrix(5436,-13951,1423,-3652) -> Matrix(41,-62,43,-65) Matrix(196,-507,75,-194) -> Matrix(7,-12,3,-5) Matrix(2292,-6241,841,-2290) -> Matrix(43,-84,21,-41) Matrix(5118,-14161,1849,-5116) -> Matrix(23,-44,11,-21) Matrix(1839,-5126,428,-1193) -> Matrix(1,6,0,1) Matrix(2322,-6481,541,-1510) -> Matrix(5,-6,1,-1) Matrix(1236,-4003,331,-1072) -> Matrix(3,-10,1,-3) Matrix(136,-457,25,-84) -> Matrix(3,-10,1,-3) Matrix(85,-294,24,-83) -> Matrix(1,-2,0,1) Matrix(222,-803,47,-170) -> Matrix(1,-2,1,-1) Matrix(1956,-7225,529,-1954) -> Matrix(31,-60,15,-29) Matrix(144,-667,19,-88) -> Matrix(5,-6,1,-1) Matrix(46,-225,9,-44) -> Matrix(3,-4,1,-1) Matrix(330,-2209,49,-328) -> Matrix(15,-28,7,-13) 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): 108 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 0/1 1 1 1/1 0/1 1 27 8/7 -1/1 1 9 7/6 1/6 1 27 6/5 1/1 1 27 17/14 1/2 1 27 11/9 2/3 1 27 5/4 1/1 1 3 19/15 0/1 1 27 33/26 5/2 1 27 14/11 -1/1 1 27 9/7 2/1 1 27 31/24 1/0 1 27 22/17 -1/1 1 9 13/10 1/2 1 27 4/3 -1/1 1 27 19/14 1/4 1 9 15/11 4/11 1 27 26/19 1/2 5 3 37/27 2/3 1 27 11/8 1/2 1 27 18/13 1/1 1 27 25/18 1/2 1 27 32/23 1/1 1 27 7/5 0/1 1 9 31/22 1/2 1 27 24/17 7/13 1 27 17/12 5/8 1 27 10/7 1/1 1 27 33/23 2/3 1 27 23/16 3/4 1 9 13/9 4/5 1 27 16/11 1/1 5 1 3/2 1/0 1 27 17/11 6/1 1 27 31/20 1/0 1 9 14/9 -1/1 1 27 11/7 0/1 3 3 19/12 1/2 1 27 8/5 3/5 1 27 21/13 4/3 1 27 34/21 1/1 1 27 47/29 2/1 1 27 13/8 1/0 1 9 31/19 0/1 1 27 67/41 0/1 13 1 18/11 1/5 1 27 23/14 1/2 1 27 5/3 2/3 1 27 17/10 1/1 7 1 12/7 1/1 1 27 19/11 2/1 1 9 26/15 9/5 1 27 7/4 1/0 1 27 16/9 1/1 1 27 41/23 2/3 1 27 25/14 3/4 1 9 34/19 1/1 1 27 43/24 15/16 1 27 52/29 1/1 19 1 9/5 4/3 1 27 11/6 1/0 1 27 35/19 0/1 3 1 13/7 2/3 1 27 15/8 1/2 1 27 2/1 1/1 1 9 13/6 3/2 1 27 37/17 2/1 3 1 11/5 2/1 1 27 20/9 -1/1 1 27 9/4 5/4 1 27 16/7 1/1 1 27 39/17 2/1 1 27 23/10 1/0 1 9 53/23 2/1 1 27 113/49 2/1 5 1 30/13 3/1 1 27 7/3 0/1 1 27 19/8 1/1 5 1 12/5 1/1 1 27 17/7 4/3 1 9 39/16 3/2 1 27 22/9 5/3 1 27 5/2 1/0 1 27 23/9 2/1 1 27 41/16 3/2 1 9 59/23 28/19 1 27 18/7 5/3 1 27 13/5 2/1 3 3 21/8 1/0 1 27 8/3 1/1 1 27 19/7 12/7 1 27 79/29 2/1 21 1 30/11 15/7 1 27 11/4 1/0 1 9 47/17 2/1 1 27 119/43 2/1 11 1 36/13 7/3 1 27 25/9 4/1 1 27 39/14 1/0 1 27 53/19 0/1 1 3 14/5 1/1 1 27 17/6 1/0 1 27 20/7 1/1 1 1 3/1 2/1 1 27 16/5 3/1 1 9 13/4 1/0 1 27 23/7 2/1 1 9 10/3 7/3 1 27 27/8 1/0 1 27 44/13 3/1 1 9 17/5 4/1 1 27 7/2 1/0 1 3 25/7 2/1 1 27 43/12 1/0 1 27 18/5 1/1 1 27 29/8 1/0 1 27 11/3 4/3 1 27 85/23 2/1 15 1 37/10 13/6 1 27 26/7 3/1 1 9 41/11 2/1 1 27 56/15 3/1 1 27 71/19 2/1 1 3 15/4 1/0 1 27 19/5 0/1 1 9 42/11 1/1 1 27 107/28 1/1 23 1 65/17 16/15 1 27 23/6 5/4 1 27 4/1 3/1 1 27 21/5 16/5 1 27 17/4 1/0 1 9 30/7 5/1 1 27 73/17 6/1 1 3 43/10 1/0 1 27 13/3 6/1 1 27 22/5 1/0 7 1 9/2 1/0 1 27 23/5 2/5 1 27 37/8 1/1 5 3 14/3 1/1 1 27 19/4 1/0 1 27 43/9 2/1 1 27 67/14 1/0 1 1 24/5 1/1 1 27 5/1 2/1 1 9 21/4 1/0 1 27 37/7 2/1 1 27 16/3 3/1 1 27 11/2 9/2 1 27 17/3 10/1 1 27 23/4 1/0 11 1 6/1 -1/1 1 27 19/3 0/1 1 27 13/2 1/0 1 9 20/3 5/3 1 27 47/7 2/1 7 1 7/1 2/1 1 27 15/2 1/0 1 27 8/1 1/0 5 3 9/1 0/1 1 27 10/1 3/1 1 27 1/0 1/0 1 27 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(254,-287,177,-200) (1/1,8/7) -> (33/23,23/16) Glide Reflection Matrix(276,-317,101,-116) (8/7,7/6) -> (30/11,11/4) Hyperbolic Matrix(172,-205,99,-118) (7/6,6/5) -> (26/15,7/4) Glide Reflection Matrix(440,-533,317,-384) (6/5,17/14) -> (18/13,25/18) Hyperbolic Matrix(317,-386,170,-207) (17/14,11/9) -> (13/7,15/8) Hyperbolic Matrix(121,-150,96,-119) (11/9,5/4) -> (5/4,19/15) Parabolic Matrix(1190,-1509,429,-544) (19/15,33/26) -> (36/13,25/9) Hyperbolic Matrix(642,-815,167,-212) (33/26,14/11) -> (23/6,4/1) Hyperbolic Matrix(261,-334,118,-151) (14/11,9/7) -> (11/5,20/9) Hyperbolic Matrix(613,-790,142,-183) (9/7,31/24) -> (43/10,13/3) Hyperbolic Matrix(1178,-1523,659,-852) (31/24,22/17) -> (25/14,34/19) Hyperbolic Matrix(470,-609,71,-92) (22/17,13/10) -> (13/2,20/3) Glide Reflection Matrix(116,-153,47,-62) (13/10,4/3) -> (22/9,5/2) Glide Reflection Matrix(596,-807,161,-218) (4/3,19/14) -> (37/10,26/7) Glide Reflection Matrix(481,-654,114,-155) (19/14,15/11) -> (21/5,17/4) Hyperbolic Matrix(844,-1153,183,-250) (15/11,26/19) -> (23/5,37/8) Glide Reflection Matrix(387,-530,46,-63) (26/19,37/27) -> (8/1,9/1) Glide Reflection Matrix(728,-999,137,-188) (37/27,11/8) -> (37/7,16/3) Glide Reflection Matrix(318,-439,113,-156) (11/8,18/13) -> (14/5,17/6) Glide Reflection Matrix(248,-345,23,-32) (25/18,32/23) -> (10/1,1/0) Glide Reflection Matrix(316,-441,225,-314) (32/23,7/5) -> (7/5,31/22) Parabolic Matrix(1524,-2149,851,-1200) (31/22,24/17) -> (34/19,43/24) Glide Reflection Matrix(448,-633,201,-284) (24/17,17/12) -> (20/9,9/4) Hyperbolic Matrix(402,-571,245,-348) (17/12,10/7) -> (18/11,23/14) Glide Reflection Matrix(1575,-2258,422,-605) (10/7,33/23) -> (41/11,56/15) Hyperbolic Matrix(421,-606,66,-95) (23/16,13/9) -> (19/3,13/2) 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(86,-131,21,-32) (3/2,17/11) -> (4/1,21/5) Glide Reflection Matrix(1631,-2526,636,-985) (17/11,31/20) -> (41/16,59/23) Hyperbolic Matrix(318,-493,169,-262) (31/20,14/9) -> (15/8,2/1) Hyperbolic Matrix(232,-363,147,-230) (14/9,11/7) -> (11/7,19/12) Parabolic Matrix(188,-299,83,-132) (19/12,8/5) -> (9/4,16/7) Hyperbolic Matrix(228,-367,41,-66) (8/5,21/13) -> (11/2,17/3) Glide Reflection Matrix(1032,-1669,371,-600) (21/13,34/21) -> (25/9,39/14) Glide Reflection Matrix(1772,-2871,495,-802) (34/21,47/29) -> (25/7,43/12) Hyperbolic Matrix(1091,-1770,474,-769) (47/29,13/8) -> (23/10,53/23) Hyperbolic Matrix(328,-535,103,-168) (13/8,31/19) -> (3/1,16/5) Hyperbolic Matrix(1272,-2077,779,-1272) (31/19,67/41) -> (31/19,67/41) Reflection Matrix(1475,-2412,902,-1475) (67/41,18/11) -> (67/41,18/11) Reflection Matrix(143,-236,20,-33) (23/14,5/3) -> (7/1,15/2) Hyperbolic Matrix(101,-170,60,-101) (5/3,17/10) -> (5/3,17/10) Reflection Matrix(239,-408,140,-239) (17/10,12/7) -> (17/10,12/7) Reflection Matrix(298,-513,79,-136) (12/7,19/11) -> (15/4,19/5) Glide Reflection Matrix(455,-788,138,-239) (19/11,26/15) -> (23/7,10/3) Glide Reflection Matrix(156,-275,59,-104) (7/4,16/9) -> (21/8,8/3) Hyperbolic Matrix(816,-1453,155,-276) (16/9,41/23) -> (21/4,37/7) Glide Reflection Matrix(911,-1626,330,-589) (41/23,25/14) -> (11/4,47/17) Hyperbolic Matrix(2495,-4472,1392,-2495) (43/24,52/29) -> (43/24,52/29) Reflection Matrix(521,-936,290,-521) (52/29,9/5) -> (52/29,9/5) Reflection Matrix(211,-382,58,-105) (9/5,11/6) -> (29/8,11/3) Hyperbolic Matrix(419,-770,228,-419) (11/6,35/19) -> (11/6,35/19) Reflection Matrix(246,-455,133,-246) (35/19,13/7) -> (35/19,13/7) Reflection Matrix(291,-626,86,-185) (2/1,13/6) -> (27/8,44/13) Hyperbolic Matrix(443,-962,204,-443) (13/6,37/17) -> (13/6,37/17) Reflection Matrix(186,-407,85,-186) (37/17,11/5) -> (37/17,11/5) Reflection Matrix(624,-1429,131,-300) (16/7,39/17) -> (19/4,43/9) Glide Reflection Matrix(852,-1957,229,-526) (39/17,23/10) -> (26/7,41/11) Hyperbolic Matrix(2598,-5989,1127,-2598) (53/23,113/49) -> (53/23,113/49) Reflection Matrix(2939,-6780,1274,-2939) (113/49,30/13) -> (113/49,30/13) Reflection Matrix(147,-340,16,-37) (30/13,7/3) -> (9/1,10/1) Hyperbolic Matrix(113,-266,48,-113) (7/3,19/8) -> (7/3,19/8) Reflection Matrix(191,-456,80,-191) (19/8,12/5) -> (19/8,12/5) Reflection Matrix(206,-497,63,-152) (12/5,17/7) -> (13/4,23/7) Glide Reflection Matrix(598,-1455,157,-382) (17/7,39/16) -> (19/5,42/11) Glide Reflection Matrix(675,-1648,188,-459) (39/16,22/9) -> (43/12,18/5) Glide Reflection Matrix(92,-233,15,-38) (5/2,23/9) -> (6/1,19/3) Glide Reflection Matrix(668,-1709,197,-504) (23/9,41/16) -> (44/13,17/5) Hyperbolic Matrix(984,-2527,257,-660) (59/23,18/7) -> (65/17,23/6) Glide Reflection Matrix(196,-507,75,-194) (18/7,13/5) -> (13/5,21/8) Parabolic Matrix(132,-355,29,-78) (8/3,19/7) -> (9/2,23/5) Glide Reflection Matrix(552,-1501,203,-552) (19/7,79/29) -> (19/7,79/29) Reflection Matrix(1739,-4740,638,-1739) (79/29,30/11) -> (79/29,30/11) Reflection Matrix(2022,-5593,731,-2022) (47/17,119/43) -> (47/17,119/43) Reflection Matrix(3095,-8568,1118,-3095) (119/43,36/13) -> (119/43,36/13) Reflection Matrix(1839,-5126,428,-1193) (39/14,53/19) -> (73/17,43/10) Hyperbolic Matrix(640,-1789,171,-478) (53/19,14/5) -> (71/19,15/4) Glide Reflection Matrix(239,-680,84,-239) (17/6,20/7) -> (17/6,20/7) Reflection Matrix(41,-120,14,-41) (20/7,3/1) -> (20/7,3/1) Reflection Matrix(218,-701,51,-164) (16/5,13/4) -> (17/4,30/7) Glide Reflection Matrix(136,-457,25,-84) (10/3,27/8) -> (16/3,11/2) Hyperbolic Matrix(85,-294,24,-83) (17/5,7/2) -> (7/2,25/7) Parabolic Matrix(222,-803,47,-170) (18/5,29/8) -> (14/3,19/4) Hyperbolic Matrix(254,-935,69,-254) (11/3,85/23) -> (11/3,85/23) Reflection Matrix(1701,-6290,460,-1701) (85/23,37/10) -> (85/23,37/10) Reflection Matrix(1665,-6218,388,-1449) (56/15,71/19) -> (30/7,73/17) Glide Reflection Matrix(2353,-8988,616,-2353) (42/11,107/28) -> (42/11,107/28) Reflection Matrix(3639,-13910,952,-3639) (107/28,65/17) -> (107/28,65/17) Reflection Matrix(131,-572,30,-131) (13/3,22/5) -> (13/3,22/5) Reflection Matrix(89,-396,20,-89) (22/5,9/2) -> (22/5,9/2) Reflection Matrix(144,-667,19,-88) (37/8,14/3) -> (15/2,8/1) Hyperbolic Matrix(1205,-5762,252,-1205) (43/9,67/14) -> (43/9,67/14) Reflection Matrix(671,-3216,140,-671) (67/14,24/5) -> (67/14,24/5) Reflection Matrix(46,-225,9,-44) (24/5,5/1) -> (5/1,21/4) Parabolic Matrix(137,-782,24,-137) (17/3,23/4) -> (17/3,23/4) Reflection Matrix(47,-276,8,-47) (23/4,6/1) -> (23/4,6/1) Reflection Matrix(281,-1880,42,-281) (20/3,47/7) -> (20/3,47/7) Reflection Matrix(48,-329,7,-48) (47/7,7/1) -> (47/7,7/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(1,0,0,-1) (-1/1,1/0) -> (0/1,1/0) Matrix(0,1,1,0) -> Matrix(1,0,1,-1) (-1/1,1/1) -> (0/1,2/1) Matrix(254,-287,177,-200) -> Matrix(1,-2,1,-3) Matrix(276,-317,101,-116) -> Matrix(3,2,1,1) Matrix(172,-205,99,-118) -> Matrix(3,-2,1,-1) Matrix(440,-533,317,-384) -> Matrix(3,-2,5,-3) (0/1,2/3).(1/2,1/1) Matrix(317,-386,170,-207) -> Matrix(1,0,0,1) Matrix(121,-150,96,-119) -> Matrix(3,-2,2,-1) 1/1 Matrix(1190,-1509,429,-544) -> Matrix(3,-4,1,-1) 2/1 Matrix(642,-815,167,-212) -> Matrix(1,-4,1,-3) 2/1 Matrix(261,-334,118,-151) -> Matrix(1,0,0,1) Matrix(613,-790,142,-183) -> Matrix(1,4,0,1) 1/0 Matrix(1178,-1523,659,-852) -> Matrix(1,4,1,5) Matrix(470,-609,71,-92) -> Matrix(1,2,1,1) Matrix(116,-153,47,-62) -> Matrix(1,2,1,1) Matrix(596,-807,161,-218) -> Matrix(11,-2,5,-1) Matrix(481,-654,114,-155) -> Matrix(15,-4,4,-1) Matrix(844,-1153,183,-250) -> Matrix(5,-2,7,-3) Matrix(387,-530,46,-63) -> Matrix(3,-2,-2,1) Matrix(728,-999,137,-188) -> Matrix(5,-4,1,-1) Matrix(318,-439,113,-156) -> Matrix(3,-2,1,-1) Matrix(248,-345,23,-32) -> Matrix(5,-4,1,-1) Matrix(316,-441,225,-314) -> Matrix(1,0,1,1) 0/1 Matrix(1524,-2149,851,-1200) -> Matrix(17,-8,19,-9) Matrix(448,-633,201,-284) -> Matrix(3,-2,5,-3) (0/1,2/3).(1/2,1/1) Matrix(402,-571,245,-348) -> Matrix(3,-2,7,-5) Matrix(1575,-2258,422,-605) -> Matrix(7,-4,2,-1) Matrix(421,-606,66,-95) -> Matrix(5,-4,4,-3) 1/1 Matrix(287,-416,198,-287) -> Matrix(9,-8,10,-9) (13/9,16/11) -> (4/5,1/1) Matrix(65,-96,44,-65) -> Matrix(-1,2,0,1) (16/11,3/2) -> (1/1,1/0) Matrix(86,-131,21,-32) -> Matrix(3,-2,1,-1) Matrix(1631,-2526,636,-985) -> Matrix(3,10,2,7) Matrix(318,-493,169,-262) -> Matrix(1,2,1,3) Matrix(232,-363,147,-230) -> Matrix(1,0,3,1) 0/1 Matrix(188,-299,83,-132) -> Matrix(5,-2,3,-1) Matrix(228,-367,41,-66) -> Matrix(7,-6,1,-1) Matrix(1032,-1669,371,-600) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(1772,-2871,495,-802) -> Matrix(3,-4,1,-1) 2/1 Matrix(1091,-1770,474,-769) -> Matrix(1,0,0,1) Matrix(328,-535,103,-168) -> Matrix(3,2,1,1) Matrix(1272,-2077,779,-1272) -> Matrix(-1,0,3,1) (31/19,67/41) -> (-2/3,0/1) Matrix(1475,-2412,902,-1475) -> Matrix(1,0,10,-1) (67/41,18/11) -> (0/1,1/5) Matrix(143,-236,20,-33) -> Matrix(7,-4,2,-1) Matrix(101,-170,60,-101) -> Matrix(5,-4,6,-5) (5/3,17/10) -> (2/3,1/1) Matrix(239,-408,140,-239) -> Matrix(9,-10,8,-9) (17/10,12/7) -> (1/1,5/4) Matrix(298,-513,79,-136) -> Matrix(1,-2,-1,1) Matrix(455,-788,138,-239) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(156,-275,59,-104) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(816,-1453,155,-276) -> Matrix(5,-4,1,-1) Matrix(911,-1626,330,-589) -> Matrix(5,-4,4,-3) 1/1 Matrix(2495,-4472,1392,-2495) -> Matrix(31,-30,32,-31) (43/24,52/29) -> (15/16,1/1) Matrix(521,-936,290,-521) -> Matrix(7,-8,6,-7) (52/29,9/5) -> (1/1,4/3) Matrix(211,-382,58,-105) -> Matrix(1,0,0,1) Matrix(419,-770,228,-419) -> Matrix(1,0,0,-1) (11/6,35/19) -> (0/1,1/0) Matrix(246,-455,133,-246) -> Matrix(1,0,3,-1) (35/19,13/7) -> (0/1,2/3) Matrix(291,-626,86,-185) -> Matrix(5,-8,2,-3) 2/1 Matrix(443,-962,204,-443) -> Matrix(7,-12,4,-7) (13/6,37/17) -> (3/2,2/1) Matrix(186,-407,85,-186) -> Matrix(1,0,1,-1) (37/17,11/5) -> (0/1,2/1) Matrix(624,-1429,131,-300) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(852,-1957,229,-526) -> Matrix(3,-4,1,-1) 2/1 Matrix(2598,-5989,1127,-2598) -> Matrix(5,-8,3,-5) (53/23,113/49) -> (4/3,2/1) Matrix(2939,-6780,1274,-2939) -> Matrix(5,-12,2,-5) (113/49,30/13) -> (2/1,3/1) Matrix(147,-340,16,-37) -> Matrix(1,0,0,1) Matrix(113,-266,48,-113) -> Matrix(1,0,2,-1) (7/3,19/8) -> (0/1,1/1) Matrix(191,-456,80,-191) -> Matrix(9,-10,8,-9) (19/8,12/5) -> (1/1,5/4) Matrix(206,-497,63,-152) -> Matrix(1,-2,-1,1) Matrix(598,-1455,157,-382) -> Matrix(3,-4,5,-7) Matrix(675,-1648,188,-459) -> Matrix(1,-2,-2,3) Matrix(92,-233,15,-38) -> Matrix(1,-2,-1,1) Matrix(668,-1709,197,-504) -> Matrix(5,-6,1,-1) Matrix(984,-2527,257,-660) -> Matrix(13,-20,11,-17) Matrix(196,-507,75,-194) -> Matrix(7,-12,3,-5) 2/1 Matrix(132,-355,29,-78) -> Matrix(1,-2,-1,1) Matrix(552,-1501,203,-552) -> Matrix(13,-24,7,-13) (19/7,79/29) -> (12/7,2/1) Matrix(1739,-4740,638,-1739) -> Matrix(29,-60,14,-29) (79/29,30/11) -> (2/1,15/7) Matrix(2022,-5593,731,-2022) -> Matrix(9,-16,5,-9) (47/17,119/43) -> (8/5,2/1) Matrix(3095,-8568,1118,-3095) -> Matrix(13,-28,6,-13) (119/43,36/13) -> (2/1,7/3) Matrix(1839,-5126,428,-1193) -> Matrix(1,6,0,1) 1/0 Matrix(640,-1789,171,-478) -> Matrix(3,-2,1,-1) Matrix(239,-680,84,-239) -> Matrix(-1,2,0,1) (17/6,20/7) -> (1/1,1/0) Matrix(41,-120,14,-41) -> Matrix(3,-4,2,-3) (20/7,3/1) -> (1/1,2/1) Matrix(218,-701,51,-164) -> Matrix(5,-14,1,-3) Matrix(136,-457,25,-84) -> Matrix(3,-10,1,-3) (2/1,4/1).(3/1,1/0) Matrix(85,-294,24,-83) -> Matrix(1,-2,0,1) 1/0 Matrix(222,-803,47,-170) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(254,-935,69,-254) -> Matrix(5,-8,3,-5) (11/3,85/23) -> (4/3,2/1) Matrix(1701,-6290,460,-1701) -> Matrix(25,-52,12,-25) (85/23,37/10) -> (2/1,13/6) Matrix(1665,-6218,388,-1449) -> Matrix(-1,8,0,1) *** -> (4/1,1/0) Matrix(2353,-8988,616,-2353) -> Matrix(15,-14,16,-15) (42/11,107/28) -> (7/8,1/1) Matrix(3639,-13910,952,-3639) -> Matrix(31,-32,30,-31) (107/28,65/17) -> (1/1,16/15) Matrix(131,-572,30,-131) -> Matrix(-1,12,0,1) (13/3,22/5) -> (6/1,1/0) Matrix(89,-396,20,-89) -> Matrix(1,2,0,-1) (22/5,9/2) -> (-1/1,1/0) Matrix(144,-667,19,-88) -> Matrix(5,-6,1,-1) Matrix(1205,-5762,252,-1205) -> Matrix(-1,4,0,1) (43/9,67/14) -> (2/1,1/0) Matrix(671,-3216,140,-671) -> Matrix(-1,2,0,1) (67/14,24/5) -> (1/1,1/0) Matrix(46,-225,9,-44) -> Matrix(3,-4,1,-1) 2/1 Matrix(137,-782,24,-137) -> Matrix(-1,20,0,1) (17/3,23/4) -> (10/1,1/0) Matrix(47,-276,8,-47) -> Matrix(1,2,0,-1) (23/4,6/1) -> (-1/1,1/0) Matrix(281,-1880,42,-281) -> Matrix(11,-20,6,-11) (20/3,47/7) -> (5/3,2/1) Matrix(48,-329,7,-48) -> Matrix(3,-8,1,-3) (47/7,7/1) -> (2/1,4/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.