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 -1/1 -7/15 -5/11 -3/7 -2/5 -5/13 -7/19 -1/3 -5/17 -3/11 -1/4 -1/5 -1/7 0/1 1/7 1/5 3/13 5/19 1/3 7/17 1/2 13/23 3/5 7/11 5/7 4/5 11/13 1/1 13/11 11/9 5/4 9/7 7/5 3/2 17/11 73/47 11/7 37/23 89/55 5/3 19/11 23/13 9/5 31/17 13/7 2/1 11/5 25/11 67/29 7/3 17/7 5/2 13/5 35/13 11/4 47/17 3/1 73/23 16/5 49/15 10/3 37/11 17/5 7/2 25/7 11/3 26/7 19/5 4/1 97/23 17/4 13/3 22/5 9/2 14/3 33/7 19/4 5/1 16/3 27/5 11/2 28/5 17/3 23/4 6/1 19/3 13/2 20/3 7/1 15/2 8/1 17/2 43/5 9/1 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/1 1/1 -1/2 1/0 -8/17 -2/1 -1/1 1/0 -7/15 1/0 -6/13 -2/1 1/0 -17/37 -3/1 -1/1 -11/24 -3/2 -5/11 -2/1 0/1 -19/42 1/0 -14/31 -2/1 -1/1 -9/20 -3/2 -13/29 -1/1 -4/9 -2/1 -1/1 -15/34 -3/4 -11/25 0/1 -7/16 1/0 -17/39 -4/3 -10/23 -1/1 -2/3 -3/7 -1/1 -17/40 -1/2 -14/33 -1/2 0/1 -11/26 1/0 -19/45 -2/1 -8/19 -1/1 -2/3 -13/31 0/1 -5/12 1/0 -12/29 -1/1 -2/3 -19/46 -1/2 -7/17 0/1 -23/56 -1/2 -16/39 -1/1 -1/2 -9/22 -1/2 -11/27 -1/1 -2/5 -1/1 0/1 1/0 -11/28 1/0 -9/23 0/1 -7/18 1/0 -12/31 -1/2 0/1 -5/13 0/1 -18/47 0/1 1/0 -13/34 1/0 -47/123 -1/1 1/1 -34/89 0/1 1/0 -21/55 0/1 -29/76 1/0 -8/21 -2/1 -1/1 -11/29 0/1 -3/8 -1/2 -13/35 -2/5 -23/62 -1/4 -10/27 -1/3 0/1 -7/19 0/1 -18/49 0/1 1/3 -11/30 1/2 -15/41 0/1 -4/11 0/1 1/0 -9/25 -1/1 -5/14 -1/2 -16/45 -1/2 0/1 -11/31 -1/3 -6/17 -1/5 0/1 -7/20 1/4 -8/23 0/1 1/1 1/0 -1/3 0/1 -7/22 1/0 -6/19 -1/3 0/1 -5/16 1/4 -9/29 1/3 1/1 -13/42 1/2 -4/13 0/1 1/2 1/1 -7/23 1/1 -3/10 1/0 -11/37 2/1 -8/27 0/1 1/0 -5/17 0/1 -12/41 0/1 1/2 -7/24 1/2 -9/31 0/1 -2/7 0/1 1/1 -7/25 0/1 2/1 -5/18 3/2 -18/65 2/1 1/0 -13/47 2/1 -34/123 2/1 1/0 -21/76 1/0 -8/29 1/1 2/1 1/0 -3/11 1/0 -10/37 -1/1 0/1 1/0 -7/26 1/0 -11/41 0/1 -4/15 1/1 2/1 -5/19 0/1 -11/42 1/2 -6/23 1/1 2/1 -1/4 1/0 -5/21 -1/1 -4/17 0/1 1/1 -7/30 1/0 -10/43 -2/1 -1/1 1/0 -3/13 0/1 -8/35 0/1 1/1 1/0 -5/22 1/0 -2/9 -2/1 1/0 -5/23 -2/1 0/1 -8/37 -2/1 1/0 -3/14 -3/2 -10/47 -1/1 -6/7 -7/33 -2/3 -4/19 -1/1 0/1 1/0 -13/62 1/0 -9/43 -2/1 -5/24 -1/2 -6/29 -1/1 1/0 -1/5 -1/1 1/1 -3/16 -3/2 -8/43 -1/1 -8/9 -5/27 -2/3 -7/38 -1/2 -2/11 -1/1 -1/2 0/1 -3/17 0/1 -10/57 -1/2 0/1 -7/40 -1/2 -4/23 -1/4 0/1 -1/6 1/0 -3/19 -1/1 -2/13 -1/3 0/1 -3/20 -1/2 -4/27 -1/2 -1/3 -1/7 0/1 -2/15 -1/1 0/1 -3/23 1/1 -4/31 -1/1 0/1 1/0 -1/8 1/0 -1/9 0/1 -1/10 1/0 0/1 0/1 1/0 1/9 0/1 2/17 0/1 1/0 1/8 1/0 1/7 0/1 2/13 0/1 1/2 1/1 3/19 2/1 1/6 1/0 3/17 -1/1 2/11 0/1 1/1 3/16 1/0 1/5 0/1 4/19 1/3 1/2 7/33 1/2 10/47 1/2 2/3 1/1 3/14 1/2 2/9 0/1 1/3 7/31 2/3 5/22 1/2 3/13 1/1 4/17 1/1 2/1 1/0 9/38 1/0 5/21 -2/1 1/4 1/0 5/19 0/1 9/34 1/8 4/15 0/1 1/4 3/11 0/1 8/29 1/3 2/5 5/18 1/2 2/7 0/1 1/2 1/1 5/17 2/3 3/10 3/2 7/23 0/1 2/1 4/13 0/1 1/1 1/3 -1/1 1/1 6/17 1/1 1/0 11/31 0/1 5/14 1/2 4/11 0/1 1/1 1/0 7/19 2/3 3/8 3/2 5/13 0/1 2/1 12/31 0/1 1/1 19/49 1/1 7/18 1/0 2/5 2/1 1/0 7/17 1/0 12/29 -6/1 1/0 5/12 1/0 8/19 -1/1 0/1 1/0 19/45 -1/1 11/26 1/0 14/33 0/1 1/0 3/7 0/1 13/30 5/4 10/23 1/1 2/1 1/0 17/39 2/1 7/16 1/0 18/41 5/1 6/1 11/25 1/0 4/9 -1/1 0/1 13/29 0/1 22/49 1/2 1/1 9/20 1/0 5/11 1/1 6/13 2/1 1/0 7/15 4/1 1/2 1/0 7/13 -3/1 -1/1 13/24 -3/2 6/11 -2/1 -1/1 5/9 0/1 9/16 1/0 22/39 4/1 5/1 13/23 1/0 30/53 -8/1 -7/1 17/30 1/0 4/7 -2/1 -1/1 7/12 1/0 3/5 1/0 11/18 1/0 30/49 -2/1 -1/1 49/80 1/0 19/31 -2/1 27/44 1/0 8/13 -2/1 -1/1 1/0 29/47 -3/1 21/34 1/0 13/21 -2/1 18/29 -2/1 1/0 5/8 -3/2 17/27 -1/1 1/1 29/46 1/0 12/19 -1/1 0/1 31/49 -1/1 1/1 19/30 1/0 64/101 -5/1 -4/1 1/0 45/71 -3/1 26/41 -2/1 1/0 7/11 -2/1 0/1 9/14 1/0 11/17 -1/1 24/37 -3/1 -2/1 13/20 -3/2 15/23 -4/3 2/3 -1/1 0/1 13/19 -1/1 11/16 -1/2 20/29 -1/2 0/1 9/13 0/1 16/23 -1/1 -2/3 -1/2 7/10 -1/2 5/7 0/1 13/18 1/0 21/29 0/1 29/40 1/0 8/11 0/1 1/0 19/26 1/0 30/41 7/1 1/0 11/15 -2/1 14/19 -1/1 -1/2 0/1 17/23 0/1 3/4 1/0 10/13 -3/1 1/0 7/9 -1/1 18/23 -2/3 -1/2 11/14 -1/2 15/19 0/1 4/5 -1/1 -1/2 0/1 17/21 0/1 13/16 -1/2 9/11 -1/1 -1/3 5/6 -1/4 11/13 0/1 17/20 1/10 6/7 0/1 1/3 13/15 1/1 7/8 1/0 1/1 0/1 9/8 1/0 8/7 -1/1 0/1 1/0 7/6 -1/4 13/11 0/1 19/16 1/14 6/5 0/1 1/5 17/14 1/4 28/23 0/1 1/4 1/3 11/9 1/3 16/13 0/1 1/2 53/43 1/3 1/1 37/30 1/2 21/17 0/1 26/21 0/1 1/2 5/4 1/2 14/11 1/3 1/2 9/7 1/1 22/17 1/1 2/1 1/0 13/10 1/0 17/13 0/1 2/1 4/3 0/1 1/0 15/11 0/1 56/41 -1/2 0/1 97/71 0/1 41/30 1/0 67/49 -1/1 26/19 -1/1 0/1 1/0 37/27 -1/1 11/8 -1/2 7/5 0/1 17/12 1/4 44/31 0/1 1/4 1/3 27/19 0/1 37/26 1/4 47/33 1/5 1/3 10/7 0/1 1/3 13/9 2/5 42/29 11/23 1/2 71/49 1/2 29/20 1/2 16/11 1/2 2/3 1/1 3/2 1/2 26/17 1/1 8/7 23/15 4/3 20/13 1/1 3/2 2/1 37/24 5/2 17/11 1/1 3/1 31/20 1/0 45/29 6/1 59/38 1/0 73/47 1/0 14/9 -3/1 1/0 25/16 1/0 11/7 0/1 41/26 1/2 71/45 1/3 1/1 30/19 0/1 1/2 49/31 1/3 1/1 68/43 0/1 1/2 1/1 19/12 1/2 46/29 1/2 2/3 1/1 73/46 1/2 27/17 1/1 8/5 1/1 2/1 37/23 1/0 29/18 1/0 21/13 0/1 55/34 1/0 89/55 -1/1 1/1 123/76 1/0 34/21 0/1 1/0 13/8 1/0 5/3 0/1 17/10 1/2 63/37 1/3 1/1 46/27 1/2 1/1 121/71 1/1 75/44 1/0 29/17 0/1 70/41 0/1 1/3 1/2 41/24 1/2 12/7 0/1 1/2 43/25 1/3 74/43 2/5 3/7 1/2 31/18 1/2 112/65 1/2 3/5 2/3 81/47 3/5 1/1 50/29 2/3 1/1 19/11 0/1 2/3 7/4 1/0 30/17 0/1 1/0 23/13 0/1 62/35 0/1 1/4 39/22 1/2 16/9 1/3 1/2 25/14 1/2 9/5 0/1 20/11 2/3 1/1 31/17 1/1 42/23 1/1 4/3 11/6 1/0 24/13 -1/1 0/1 13/7 1/1 15/8 1/0 2/1 0/1 1/1 1/0 17/8 1/0 15/7 0/1 13/6 1/2 24/11 0/1 1/3 11/5 1/1 31/14 1/0 20/9 0/1 1/0 49/22 1/0 29/13 0/1 2/1 9/4 1/2 34/15 0/1 1/0 25/11 0/1 16/7 1/2 1/1 23/10 1/2 53/23 1/1 30/13 4/5 1/1 67/29 1/1 104/45 1/1 14/13 37/16 5/4 7/3 0/1 40/17 0/1 1/3 1/2 33/14 1/2 59/25 1/2 26/11 3/5 2/3 19/8 1/2 69/29 2/3 50/21 1/2 1/1 31/13 3/5 1/1 12/5 2/3 1/1 17/7 1/1 22/9 1/1 4/3 5/2 1/0 23/9 1/1 18/7 3/1 1/0 49/19 -3/1 -1/1 31/12 -1/2 13/5 0/1 34/13 0/1 1/2 55/21 1/3 1/1 21/8 1/2 8/3 2/3 1/1 35/13 1/1 62/23 1/1 16/15 27/10 7/6 19/7 2/1 30/11 2/1 1/0 41/15 1/0 52/19 1/1 1/0 11/4 1/0 58/21 0/1 1/1 47/17 -1/1 1/1 36/13 0/1 1/0 25/9 0/1 14/5 0/1 1/2 17/6 1/2 3/1 1/1 19/6 1/0 73/23 1/1 54/17 1/1 3/2 35/11 2/1 16/5 1/1 2/1 1/0 13/4 1/0 49/15 -1/1 1/1 85/26 1/0 36/11 0/1 1/0 23/7 0/1 10/3 2/3 1/1 37/11 1/1 64/19 1/1 20/19 27/8 9/8 17/5 4/3 24/7 1/1 2/1 55/16 3/2 31/9 2/1 7/2 1/0 25/7 1/1 18/5 -1/1 1/0 47/13 0/1 76/21 0/1 1/2 29/8 1/2 11/3 0/1 37/10 1/2 63/17 3/5 1/1 89/24 1/2 26/7 1/2 2/3 1/1 15/4 3/4 19/5 1/1 23/6 7/6 4/1 1/1 2/1 21/5 2/1 59/14 3/2 97/23 2/1 38/9 2/1 1/0 55/13 1/1 3/1 17/4 1/0 30/7 -1/1 0/1 13/3 1/1 35/8 3/2 22/5 1/1 3/2 2/1 31/7 2/1 40/9 3/2 2/1 9/2 3/2 23/5 1/1 3/1 60/13 7/1 1/0 37/8 1/0 14/3 1/1 2/1 47/10 3/2 33/7 2/1 52/11 2/1 3/1 1/0 19/4 1/0 5/1 0/1 2/1 21/4 1/0 16/3 2/1 1/0 27/5 1/1 11/2 3/2 28/5 2/1 5/2 3/1 45/8 7/2 17/3 1/1 3/1 40/7 2/1 1/0 23/4 1/0 6/1 2/1 1/0 19/3 2/1 13/2 1/0 20/3 3/1 1/0 7/1 1/0 22/3 -1/1 1/0 15/2 1/0 8/1 1/1 2/1 1/0 17/2 1/0 43/5 1/1 3/1 26/3 2/1 1/0 9/1 2/1 10/1 4/1 5/1 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(641,304,272,129) (-1/2,-8/17) -> (40/17,33/14) Hyperbolic Matrix(269,126,1266,593) (-8/17,-7/15) -> (7/33,10/47) Hyperbolic Matrix(983,456,360,167) (-7/15,-6/13) -> (30/11,41/15) Hyperbolic Matrix(1869,860,-4892,-2251) (-6/13,-17/37) -> (-47/123,-34/89) Hyperbolic Matrix(1777,816,1152,529) (-17/37,-11/24) -> (37/24,17/11) Hyperbolic Matrix(795,364,356,163) (-11/24,-5/11) -> (29/13,9/4) Hyperbolic Matrix(1757,796,788,357) (-5/11,-19/42) -> (49/22,29/13) Hyperbolic Matrix(2713,1226,790,357) (-19/42,-14/31) -> (24/7,55/16) Hyperbolic Matrix(523,236,964,435) (-14/31,-9/20) -> (13/24,6/11) Hyperbolic Matrix(699,314,1654,743) (-9/20,-13/29) -> (19/45,11/26) Hyperbolic Matrix(175,78,258,115) (-13/29,-4/9) -> (2/3,13/19) Hyperbolic Matrix(343,152,88,39) (-4/9,-15/34) -> (23/6,4/1) Hyperbolic Matrix(431,190,-2062,-909) (-15/34,-11/25) -> (-9/43,-5/24) Hyperbolic Matrix(769,338,430,189) (-11/25,-7/16) -> (25/14,9/5) Hyperbolic Matrix(1105,482,-2978,-1299) (-7/16,-17/39) -> (-13/35,-23/62) Hyperbolic Matrix(427,186,-2298,-1001) (-17/39,-10/23) -> (-8/43,-5/27) Hyperbolic Matrix(677,294,426,185) (-10/23,-3/7) -> (27/17,8/5) Hyperbolic Matrix(1591,678,1002,427) (-3/7,-17/40) -> (73/46,27/17) Hyperbolic Matrix(2417,1026,1086,461) (-17/40,-14/33) -> (20/9,49/22) Hyperbolic Matrix(335,142,-1918,-813) (-14/33,-11/26) -> (-7/40,-4/23) Hyperbolic Matrix(1079,456,168,71) (-11/26,-19/45) -> (19/3,13/2) Hyperbolic Matrix(583,246,-2742,-1157) (-19/45,-8/19) -> (-10/47,-7/33) Hyperbolic Matrix(333,140,-1244,-523) (-8/19,-13/31) -> (-11/41,-4/15) Hyperbolic Matrix(907,380,580,243) (-13/31,-5/12) -> (25/16,11/7) Hyperbolic Matrix(409,170,166,69) (-5/12,-12/29) -> (22/9,5/2) Hyperbolic Matrix(1393,576,2208,913) (-12/29,-19/46) -> (29/46,12/19) Hyperbolic Matrix(407,168,1800,743) (-19/46,-7/17) -> (7/31,5/22) Hyperbolic Matrix(1061,436,1628,669) (-7/17,-23/56) -> (13/20,15/23) Hyperbolic Matrix(3341,1372,1220,501) (-23/56,-16/39) -> (52/19,11/4) Hyperbolic Matrix(1873,768,1056,433) (-16/39,-9/22) -> (39/22,16/9) Hyperbolic Matrix(891,364,164,67) (-9/22,-11/27) -> (27/5,11/2) Hyperbolic Matrix(887,360,648,263) (-11/27,-2/5) -> (26/19,37/27) Hyperbolic Matrix(869,342,714,281) (-2/5,-11/28) -> (17/14,28/23) Hyperbolic Matrix(393,154,-1498,-587) (-11/28,-9/23) -> (-5/19,-11/42) Hyperbolic Matrix(865,338,238,93) (-9/23,-7/18) -> (29/8,11/3) Hyperbolic Matrix(237,92,-1100,-427) (-7/18,-12/31) -> (-8/37,-3/14) Hyperbolic Matrix(389,150,-1014,-391) (-12/31,-5/13) -> (-5/13,-18/47) Parabolic Matrix(1635,626,2254,863) (-18/47,-13/34) -> (29/40,8/11) Hyperbolic Matrix(3961,1514,934,357) (-13/34,-47/123) -> (55/13,17/4) Hyperbolic Matrix(3027,1156,-10948,-4181) (-34/89,-21/55) -> (-13/47,-34/123) Hyperbolic Matrix(1399,534,-6678,-2549) (-21/55,-29/76) -> (-13/62,-9/43) Hyperbolic Matrix(2637,1006,4658,1777) (-29/76,-8/21) -> (30/53,17/30) Hyperbolic Matrix(773,294,234,89) (-8/21,-11/29) -> (23/7,10/3) Hyperbolic Matrix(1003,380,388,147) (-11/29,-3/8) -> (31/12,13/5) Hyperbolic Matrix(75,28,308,115) (-3/8,-13/35) -> (5/21,1/4) Hyperbolic Matrix(2137,792,456,169) (-23/62,-10/27) -> (14/3,47/10) Hyperbolic Matrix(531,196,-1444,-533) (-10/27,-7/19) -> (-7/19,-18/49) Parabolic Matrix(1439,528,2352,863) (-18/49,-11/30) -> (11/18,30/49) Hyperbolic Matrix(983,360,456,167) (-11/30,-15/41) -> (15/7,13/6) Hyperbolic Matrix(455,166,74,27) (-15/41,-4/11) -> (6/1,19/3) Hyperbolic Matrix(527,190,674,243) (-4/11,-9/25) -> (7/9,18/23) Hyperbolic Matrix(525,188,148,53) (-9/25,-5/14) -> (7/2,25/7) Hyperbolic Matrix(73,26,598,213) (-5/14,-16/45) -> (2/17,1/8) Hyperbolic Matrix(2831,1006,4466,1587) (-16/45,-11/31) -> (45/71,26/41) Hyperbolic Matrix(965,342,522,185) (-11/31,-6/17) -> (24/13,13/7) Hyperbolic Matrix(443,156,372,131) (-6/17,-7/20) -> (19/16,6/5) Hyperbolic Matrix(1251,436,812,283) (-7/20,-8/23) -> (20/13,37/24) Hyperbolic Matrix(877,302,514,177) (-8/23,-1/3) -> (29/17,70/41) Hyperbolic Matrix(565,182,922,297) (-1/3,-7/22) -> (49/80,19/31) Hyperbolic Matrix(775,246,1194,379) (-7/22,-6/19) -> (24/37,13/20) Hyperbolic Matrix(419,132,492,155) (-6/19,-5/16) -> (17/20,6/7) Hyperbolic Matrix(489,152,904,281) (-5/16,-9/29) -> (7/13,13/24) Hyperbolic Matrix(4171,1292,2644,819) (-9/29,-13/42) -> (41/26,71/45) Hyperbolic Matrix(557,172,68,21) (-13/42,-4/13) -> (8/1,17/2) Hyperbolic Matrix(623,190,482,147) (-4/13,-7/23) -> (9/7,22/17) Hyperbolic Matrix(345,104,136,41) (-7/23,-3/10) -> (5/2,23/9) Hyperbolic Matrix(67,20,412,123) (-3/10,-11/37) -> (3/19,1/6) Hyperbolic Matrix(411,122,886,263) (-11/37,-8/27) -> (6/13,7/15) Hyperbolic Matrix(339,100,-1156,-341) (-8/27,-5/17) -> (-5/17,-12/41) Parabolic Matrix(1969,576,1152,337) (-12/41,-7/24) -> (41/24,12/7) Hyperbolic Matrix(337,98,-1826,-531) (-7/24,-9/31) -> (-5/27,-7/38) Hyperbolic Matrix(271,78,66,19) (-9/31,-2/7) -> (4/1,21/5) Hyperbolic Matrix(335,94,866,243) (-2/7,-7/25) -> (5/13,12/31) Hyperbolic Matrix(201,56,664,185) (-7/25,-5/18) -> (3/10,7/23) Hyperbolic Matrix(3651,1012,2060,571) (-5/18,-18/65) -> (62/35,39/22) Hyperbolic Matrix(665,184,-3784,-1047) (-18/65,-13/47) -> (-3/17,-10/57) Hyperbolic Matrix(17713,4896,10944,3025) (-34/123,-21/76) -> (123/76,34/21) Hyperbolic Matrix(333,92,-2588,-715) (-21/76,-8/29) -> (-4/31,-1/8) Hyperbolic Matrix(197,54,-726,-199) (-8/29,-3/11) -> (-3/11,-10/37) Parabolic Matrix(1773,478,1250,337) (-10/37,-7/26) -> (17/12,44/31) Hyperbolic Matrix(1967,528,1248,335) (-7/26,-11/41) -> (11/7,41/26) Hyperbolic Matrix(197,52,716,189) (-4/15,-5/19) -> (3/11,8/29) Hyperbolic Matrix(2017,528,1104,289) (-11/42,-6/23) -> (42/23,11/6) Hyperbolic Matrix(907,236,196,51) (-6/23,-1/4) -> (37/8,14/3) Hyperbolic Matrix(695,166,314,75) (-1/4,-5/21) -> (11/5,31/14) Hyperbolic Matrix(691,164,316,75) (-5/21,-4/17) -> (24/11,11/5) Hyperbolic Matrix(813,190,1442,337) (-4/17,-7/30) -> (9/16,22/39) Hyperbolic Matrix(2377,554,502,117) (-7/30,-10/43) -> (52/11,19/4) Hyperbolic Matrix(1249,290,814,189) (-10/43,-3/13) -> (23/15,20/13) Hyperbolic Matrix(1371,314,310,71) (-3/13,-8/35) -> (22/5,31/7) Hyperbolic Matrix(1677,382,1058,241) (-8/35,-5/22) -> (19/12,46/29) Hyperbolic Matrix(309,70,746,169) (-5/22,-2/9) -> (12/29,5/12) Hyperbolic Matrix(245,54,186,41) (-2/9,-5/23) -> (17/13,4/3) Hyperbolic Matrix(857,186,1350,293) (-5/23,-8/37) -> (26/41,7/11) Hyperbolic Matrix(2137,456,792,169) (-3/14,-10/47) -> (62/23,27/10) Hyperbolic Matrix(123,26,790,167) (-7/33,-4/19) -> (2/13,3/19) Hyperbolic Matrix(7533,1580,4372,917) (-4/19,-13/62) -> (31/18,112/65) Hyperbolic Matrix(789,164,1756,365) (-5/24,-6/29) -> (22/49,9/20) Hyperbolic Matrix(2057,424,1208,249) (-6/29,-1/5) -> (63/37,46/27) Hyperbolic Matrix(297,56,472,89) (-1/5,-3/16) -> (5/8,17/27) Hyperbolic Matrix(2185,408,648,121) (-3/16,-8/43) -> (64/19,27/8) Hyperbolic Matrix(413,76,1940,357) (-7/38,-2/11) -> (10/47,3/14) Hyperbolic Matrix(233,42,294,53) (-2/11,-3/17) -> (15/19,4/5) Hyperbolic Matrix(6285,1102,1922,337) (-10/57,-7/40) -> (85/26,36/11) Hyperbolic Matrix(231,40,872,151) (-4/23,-1/6) -> (9/34,4/15) Hyperbolic Matrix(743,118,170,27) (-1/6,-3/19) -> (13/3,35/8) Hyperbolic Matrix(739,116,172,27) (-3/19,-2/13) -> (30/7,13/3) Hyperbolic Matrix(623,94,338,51) (-2/13,-3/20) -> (11/6,24/13) Hyperbolic Matrix(845,126,114,17) (-3/20,-4/27) -> (22/3,15/2) Hyperbolic Matrix(505,74,1126,165) (-4/27,-1/7) -> (13/29,22/49) Hyperbolic Matrix(223,30,498,67) (-1/7,-2/15) -> (4/9,13/29) Hyperbolic Matrix(717,94,1106,145) (-2/15,-3/23) -> (11/17,24/37) Hyperbolic Matrix(2867,372,4524,587) (-3/23,-4/31) -> (64/101,45/71) Hyperbolic Matrix(163,20,220,27) (-1/8,-1/9) -> (17/23,3/4) Hyperbolic Matrix(753,80,160,17) (-1/9,-1/10) -> (47/10,33/7) Hyperbolic Matrix(265,26,214,21) (-1/10,0/1) -> (26/21,5/4) Hyperbolic Matrix(391,-40,88,-9) (0/1,1/9) -> (31/7,40/9) Hyperbolic Matrix(387,-44,44,-5) (1/9,2/17) -> (26/3,9/1) Hyperbolic Matrix(297,-38,86,-11) (1/8,1/7) -> (31/9,7/2) Hyperbolic Matrix(291,-44,668,-101) (1/7,2/13) -> (10/23,17/39) Hyperbolic Matrix(531,-92,860,-149) (1/6,3/17) -> (29/47,21/34) Hyperbolic Matrix(245,-44,284,-51) (3/17,2/11) -> (6/7,13/15) Hyperbolic Matrix(527,-98,242,-45) (2/11,3/16) -> (13/6,24/11) Hyperbolic Matrix(201,-38,566,-107) (3/16,1/5) -> (11/31,5/14) Hyperbolic Matrix(239,-50,674,-141) (1/5,4/19) -> (6/17,11/31) Hyperbolic Matrix(2495,-528,912,-193) (4/19,7/33) -> (41/15,52/19) Hyperbolic Matrix(237,-52,196,-43) (3/14,2/9) -> (6/5,17/14) Hyperbolic Matrix(391,-88,40,-9) (2/9,7/31) -> (9/1,10/1) Hyperbolic Matrix(429,-98,626,-143) (5/22,3/13) -> (13/19,11/16) Hyperbolic Matrix(427,-100,1012,-237) (3/13,4/17) -> (8/19,19/45) Hyperbolic Matrix(2755,-652,4348,-1029) (4/17,9/38) -> (19/30,64/101) Hyperbolic Matrix(2949,-700,1900,-451) (9/38,5/21) -> (45/29,59/38) Hyperbolic Matrix(191,-50,722,-189) (1/4,5/19) -> (5/19,9/34) Parabolic Matrix(529,-142,190,-51) (4/15,3/11) -> (25/9,14/5) Hyperbolic Matrix(527,-146,1202,-333) (8/29,5/18) -> (7/16,18/41) Hyperbolic Matrix(487,-136,376,-105) (5/18,2/7) -> (22/17,13/10) Hyperbolic Matrix(335,-98,482,-141) (2/7,5/17) -> (9/13,16/23) Hyperbolic Matrix(629,-186,186,-55) (5/17,3/10) -> (27/8,17/5) Hyperbolic Matrix(1397,-426,810,-247) (7/23,4/13) -> (50/29,19/11) Hyperbolic Matrix(439,-136,184,-57) (4/13,1/3) -> (31/13,12/5) Hyperbolic Matrix(677,-236,284,-99) (1/3,6/17) -> (50/21,31/13) Hyperbolic Matrix(529,-190,142,-51) (5/14,4/11) -> (26/7,15/4) Hyperbolic Matrix(387,-142,526,-193) (4/11,7/19) -> (11/15,14/19) Hyperbolic Matrix(665,-246,246,-91) (7/19,3/8) -> (27/10,19/7) Hyperbolic Matrix(243,-92,140,-53) (3/8,5/13) -> (19/11,7/4) Hyperbolic Matrix(3113,-1206,1350,-523) (12/31,19/49) -> (53/23,30/13) Hyperbolic Matrix(3215,-1248,2352,-913) (19/49,7/18) -> (41/30,67/49) Hyperbolic Matrix(379,-148,484,-189) (7/18,2/5) -> (18/23,11/14) Hyperbolic Matrix(239,-98,578,-237) (2/5,7/17) -> (7/17,12/29) Parabolic Matrix(439,-184,136,-57) (5/12,8/19) -> (16/5,13/4) Hyperbolic Matrix(2933,-1242,810,-343) (11/26,14/33) -> (76/21,29/8) Hyperbolic Matrix(875,-372,708,-301) (14/33,3/7) -> (21/17,26/21) Hyperbolic Matrix(469,-202,202,-87) (3/7,13/30) -> (37/16,7/3) Hyperbolic Matrix(1875,-814,334,-145) (13/30,10/23) -> (28/5,45/8) Hyperbolic Matrix(2641,-1152,768,-335) (17/39,7/16) -> (55/16,31/9) Hyperbolic Matrix(3069,-1348,1300,-571) (18/41,11/25) -> (59/25,26/11) Hyperbolic Matrix(533,-236,332,-147) (11/25,4/9) -> (8/5,37/23) Hyperbolic Matrix(861,-388,628,-283) (9/20,5/11) -> (37/27,11/8) Hyperbolic Matrix(527,-242,98,-45) (5/11,6/13) -> (16/3,27/5) Hyperbolic Matrix(555,-262,358,-169) (7/15,1/2) -> (31/20,45/29) Hyperbolic Matrix(437,-234,282,-151) (1/2,7/13) -> (17/11,31/20) Hyperbolic Matrix(279,-154,154,-85) (6/11,5/9) -> (9/5,20/11) Hyperbolic Matrix(339,-190,430,-241) (5/9,9/16) -> (11/14,15/19) Hyperbolic Matrix(1197,-676,2116,-1195) (22/39,13/23) -> (13/23,30/53) Parabolic Matrix(307,-174,30,-17) (17/30,4/7) -> (10/1,1/0) Hyperbolic Matrix(243,-140,92,-53) (4/7,7/12) -> (21/8,8/3) Hyperbolic Matrix(91,-54,150,-89) (7/12,3/5) -> (3/5,11/18) Parabolic Matrix(5179,-3172,1876,-1149) (30/49,49/80) -> (11/4,58/21) Hyperbolic Matrix(3601,-2208,2112,-1295) (19/31,27/44) -> (75/44,29/17) Hyperbolic Matrix(2973,-1826,1874,-1151) (27/44,8/13) -> (46/29,73/46) Hyperbolic Matrix(4037,-2490,2346,-1447) (8/13,29/47) -> (43/25,74/43) Hyperbolic Matrix(1869,-1156,1156,-715) (21/34,13/21) -> (21/13,55/34) Hyperbolic Matrix(1481,-918,534,-331) (13/21,18/29) -> (36/13,25/9) Hyperbolic Matrix(533,-332,236,-147) (18/29,5/8) -> (9/4,34/15) Hyperbolic Matrix(3357,-2116,1972,-1243) (17/27,29/46) -> (17/10,63/37) Hyperbolic Matrix(1383,-874,970,-613) (12/19,31/49) -> (47/33,10/7) Hyperbolic Matrix(3703,-2344,1000,-633) (31/49,19/30) -> (37/10,63/17) Hyperbolic Matrix(381,-244,292,-187) (7/11,9/14) -> (13/10,17/13) Hyperbolic Matrix(437,-282,234,-151) (9/14,11/17) -> (13/7,15/8) Hyperbolic Matrix(667,-436,436,-285) (15/23,2/3) -> (26/17,23/15) Hyperbolic Matrix(1307,-900,228,-157) (11/16,20/29) -> (40/7,23/4) Hyperbolic Matrix(1163,-804,852,-589) (20/29,9/13) -> (15/11,56/41) Hyperbolic Matrix(425,-296,56,-39) (16/23,7/10) -> (15/2,8/1) Hyperbolic Matrix(141,-100,196,-139) (7/10,5/7) -> (5/7,13/18) Parabolic Matrix(279,-202,250,-181) (13/18,21/29) -> (1/1,9/8) Hyperbolic Matrix(3311,-2400,1392,-1009) (21/29,29/40) -> (19/8,69/29) Hyperbolic Matrix(861,-628,388,-283) (8/11,19/26) -> (31/14,20/9) Hyperbolic Matrix(3077,-2250,666,-487) (19/26,30/41) -> (60/13,37/8) Hyperbolic Matrix(1163,-852,804,-589) (30/41,11/15) -> (13/9,42/29) Hyperbolic Matrix(1823,-1346,386,-285) (14/19,17/23) -> (33/7,52/11) Hyperbolic Matrix(381,-292,244,-187) (3/4,10/13) -> (14/9,25/16) Hyperbolic Matrix(487,-376,136,-105) (10/13,7/9) -> (25/7,18/5) Hyperbolic Matrix(875,-708,372,-301) (4/5,17/21) -> (7/3,40/17) Hyperbolic Matrix(1113,-902,902,-731) (17/21,13/16) -> (37/30,21/17) Hyperbolic Matrix(1111,-904,424,-345) (13/16,9/11) -> (55/21,21/8) Hyperbolic Matrix(237,-196,52,-43) (9/11,5/6) -> (9/2,23/5) Hyperbolic Matrix(287,-242,338,-285) (5/6,11/13) -> (11/13,17/20) Parabolic Matrix(769,-670,334,-291) (13/15,7/8) -> (23/10,53/23) Hyperbolic Matrix(253,-226,178,-159) (7/8,1/1) -> (27/19,37/26) Hyperbolic Matrix(677,-764,428,-483) (9/8,8/7) -> (68/43,19/12) Hyperbolic Matrix(245,-284,44,-51) (8/7,7/6) -> (11/2,28/5) Hyperbolic Matrix(287,-338,242,-285) (7/6,13/11) -> (13/11,19/16) Parabolic Matrix(1775,-2162,1298,-1581) (28/23,11/9) -> (67/49,26/19) Hyperbolic Matrix(667,-820,388,-477) (11/9,16/13) -> (12/7,43/25) Hyperbolic Matrix(1677,-2066,194,-239) (16/13,53/43) -> (43/5,26/3) Hyperbolic Matrix(2021,-2492,236,-291) (53/43,37/30) -> (17/2,43/5) Hyperbolic Matrix(339,-430,190,-241) (5/4,14/11) -> (16/9,25/14) Hyperbolic Matrix(379,-484,148,-189) (14/11,9/7) -> (23/9,18/7) Hyperbolic Matrix(387,-526,142,-193) (4/3,15/11) -> (19/7,30/11) Hyperbolic Matrix(6675,-9118,1582,-2161) (56/41,97/71) -> (97/23,38/9) Hyperbolic Matrix(7099,-9700,1684,-2301) (97/71,41/30) -> (59/14,97/23) Hyperbolic Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(1389,-1972,436,-619) (44/31,27/19) -> (35/11,16/5) Hyperbolic Matrix(4079,-5808,1248,-1777) (37/26,47/33) -> (49/15,85/26) Hyperbolic Matrix(335,-482,98,-141) (10/7,13/9) -> (17/5,24/7) Hyperbolic Matrix(2803,-4060,1804,-2613) (42/29,71/49) -> (73/47,14/9) Hyperbolic Matrix(4351,-6306,2802,-4061) (71/49,29/20) -> (59/38,73/47) Hyperbolic Matrix(1821,-2642,1058,-1535) (29/20,16/11) -> (74/43,31/18) Hyperbolic Matrix(429,-626,98,-143) (16/11,3/2) -> (35/8,22/5) Hyperbolic Matrix(837,-1274,362,-551) (3/2,26/17) -> (104/45,37/16) Hyperbolic Matrix(2755,-4348,652,-1029) (71/45,30/19) -> (38/9,55/13) Hyperbolic Matrix(2009,-3174,726,-1147) (30/19,49/31) -> (47/17,36/13) Hyperbolic Matrix(6955,-10996,4036,-6381) (49/31,68/43) -> (112/65,81/47) Hyperbolic Matrix(1821,-2932,772,-1243) (37/23,29/18) -> (33/14,59/25) Hyperbolic Matrix(679,-1096,184,-297) (29/18,21/13) -> (11/3,37/10) Hyperbolic Matrix(9791,-15842,6050,-9789) (55/34,89/55) -> (89/55,123/76) Parabolic Matrix(531,-860,92,-149) (34/21,13/8) -> (23/4,6/1) Hyperbolic Matrix(91,-150,54,-89) (13/8,5/3) -> (5/3,17/10) Parabolic Matrix(5805,-9892,1828,-3115) (46/27,121/71) -> (73/23,54/17) Hyperbolic Matrix(4561,-7774,1438,-2451) (121/71,75/44) -> (19/6,73/23) Hyperbolic Matrix(4273,-7296,1152,-1967) (70/41,41/24) -> (89/24,26/7) Hyperbolic Matrix(4089,-7048,1480,-2551) (81/47,50/29) -> (58/21,47/17) Hyperbolic Matrix(313,-550,70,-123) (7/4,30/17) -> (40/9,9/2) Hyperbolic Matrix(1197,-2116,676,-1195) (30/17,23/13) -> (23/13,62/35) Parabolic Matrix(1055,-1922,578,-1053) (20/11,31/17) -> (31/17,42/23) Parabolic Matrix(33,-64,16,-31) (15/8,2/1) -> (2/1,17/8) Parabolic Matrix(581,-1242,138,-295) (17/8,15/7) -> (21/5,59/14) Hyperbolic Matrix(1541,-3498,426,-967) (34/15,25/11) -> (47/13,76/21) Hyperbolic Matrix(527,-1202,146,-333) (25/11,16/7) -> (18/5,47/13) Hyperbolic Matrix(291,-668,44,-101) (16/7,23/10) -> (13/2,20/3) Hyperbolic Matrix(3887,-8978,1682,-3885) (30/13,67/29) -> (67/29,104/45) Parabolic Matrix(427,-1012,100,-237) (26/11,19/8) -> (17/4,30/7) Hyperbolic Matrix(2301,-5476,724,-1723) (69/29,50/21) -> (54/17,35/11) Hyperbolic Matrix(239,-578,98,-237) (12/5,17/7) -> (17/7,22/9) Parabolic Matrix(1301,-3354,282,-727) (18/7,49/19) -> (23/5,60/13) Hyperbolic Matrix(1059,-2732,188,-485) (49/19,31/12) -> (45/8,17/3) Hyperbolic Matrix(479,-1250,146,-381) (13/5,34/13) -> (36/11,23/7) Hyperbolic Matrix(1061,-2778,186,-487) (34/13,55/21) -> (17/3,40/7) Hyperbolic Matrix(911,-2450,338,-909) (8/3,35/13) -> (35/13,62/23) Parabolic Matrix(201,-566,38,-107) (14/5,17/6) -> (21/4,16/3) Hyperbolic Matrix(37,-108,12,-35) (17/6,3/1) -> (3/1,19/6) Parabolic Matrix(1587,-5180,428,-1397) (13/4,49/15) -> (63/17,89/24) Hyperbolic Matrix(815,-2738,242,-813) (10/3,37/11) -> (37/11,64/19) Parabolic Matrix(191,-722,50,-189) (15/4,19/5) -> (19/5,23/6) Parabolic Matrix(41,-200,8,-39) (19/4,5/1) -> (5/1,21/4) Parabolic Matrix(43,-294,6,-41) (20/3,7/1) -> (7/1,22/3) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,0,1) Matrix(641,304,272,129) -> Matrix(1,2,2,5) Matrix(269,126,1266,593) -> Matrix(1,0,2,1) Matrix(983,456,360,167) -> Matrix(1,4,0,1) Matrix(1869,860,-4892,-2251) -> Matrix(1,2,0,1) Matrix(1777,816,1152,529) -> Matrix(1,4,0,1) Matrix(795,364,356,163) -> Matrix(1,2,0,1) Matrix(1757,796,788,357) -> Matrix(1,2,0,1) Matrix(2713,1226,790,357) -> Matrix(3,4,2,3) Matrix(523,236,964,435) -> Matrix(1,0,0,1) Matrix(699,314,1654,743) -> Matrix(1,2,-2,-3) Matrix(175,78,258,115) -> Matrix(1,2,-2,-3) Matrix(343,152,88,39) -> Matrix(3,4,2,3) Matrix(431,190,-2062,-909) -> Matrix(3,2,-2,-1) Matrix(769,338,430,189) -> Matrix(1,0,2,1) Matrix(1105,482,-2978,-1299) -> Matrix(1,2,-4,-7) Matrix(427,186,-2298,-1001) -> Matrix(5,6,-6,-7) Matrix(677,294,426,185) -> Matrix(1,0,2,1) Matrix(1591,678,1002,427) -> Matrix(3,2,4,3) Matrix(2417,1026,1086,461) -> Matrix(1,0,2,1) Matrix(335,142,-1918,-813) -> Matrix(1,0,-2,1) Matrix(1079,456,168,71) -> Matrix(1,4,0,1) Matrix(583,246,-2742,-1157) -> Matrix(3,4,-4,-5) Matrix(333,140,-1244,-523) -> Matrix(1,0,2,1) Matrix(907,380,580,243) -> Matrix(1,0,0,1) Matrix(409,170,166,69) -> Matrix(1,2,0,1) Matrix(1393,576,2208,913) -> Matrix(3,2,-2,-1) Matrix(407,168,1800,743) -> Matrix(3,2,4,3) Matrix(1061,436,1628,669) -> Matrix(5,4,-4,-3) Matrix(3341,1372,1220,501) -> Matrix(1,0,2,1) Matrix(1873,768,1056,433) -> Matrix(1,0,4,1) Matrix(891,364,164,67) -> Matrix(1,2,0,1) Matrix(887,360,648,263) -> Matrix(1,0,0,1) Matrix(869,342,714,281) -> Matrix(1,0,4,1) Matrix(393,154,-1498,-587) -> Matrix(1,0,2,1) Matrix(865,338,238,93) -> Matrix(1,0,2,1) Matrix(237,92,-1100,-427) -> Matrix(3,2,-2,-1) Matrix(389,150,-1014,-391) -> Matrix(1,0,2,1) Matrix(1635,626,2254,863) -> Matrix(1,0,0,1) Matrix(3961,1514,934,357) -> Matrix(1,2,0,1) Matrix(3027,1156,-10948,-4181) -> Matrix(1,2,0,1) Matrix(1399,534,-6678,-2549) -> Matrix(1,-2,0,1) Matrix(2637,1006,4658,1777) -> Matrix(1,-6,0,1) Matrix(773,294,234,89) -> Matrix(1,0,2,1) Matrix(1003,380,388,147) -> Matrix(1,0,0,1) Matrix(75,28,308,115) -> Matrix(1,0,2,1) Matrix(2137,792,456,169) -> Matrix(5,2,2,1) Matrix(531,196,-1444,-533) -> Matrix(1,0,6,1) Matrix(1439,528,2352,863) -> Matrix(5,-2,-2,1) Matrix(983,360,456,167) -> Matrix(1,0,0,1) Matrix(455,166,74,27) -> Matrix(1,2,0,1) Matrix(527,190,674,243) -> Matrix(1,2,-2,-3) Matrix(525,188,148,53) -> Matrix(1,0,2,1) Matrix(73,26,598,213) -> Matrix(1,0,2,1) Matrix(2831,1006,4466,1587) -> Matrix(3,2,-2,-1) Matrix(965,342,522,185) -> Matrix(1,0,4,1) Matrix(443,156,372,131) -> Matrix(1,0,10,1) Matrix(1251,436,812,283) -> Matrix(3,-2,2,-1) Matrix(877,302,514,177) -> Matrix(1,0,2,1) Matrix(565,182,922,297) -> Matrix(1,-2,0,1) Matrix(775,246,1194,379) -> Matrix(3,2,-2,-1) Matrix(419,132,492,155) -> Matrix(1,0,6,1) Matrix(489,152,904,281) -> Matrix(5,-2,-2,1) Matrix(4171,1292,2644,819) -> Matrix(1,0,0,1) Matrix(557,172,68,21) -> Matrix(3,-2,2,-1) Matrix(623,190,482,147) -> Matrix(3,-2,2,-1) Matrix(345,104,136,41) -> Matrix(1,0,0,1) Matrix(67,20,412,123) -> Matrix(1,0,0,1) Matrix(411,122,886,263) -> Matrix(1,2,0,1) Matrix(339,100,-1156,-341) -> Matrix(1,0,2,1) Matrix(1969,576,1152,337) -> Matrix(1,0,0,1) Matrix(337,98,-1826,-531) -> Matrix(3,-2,-4,3) Matrix(271,78,66,19) -> Matrix(3,-2,2,-1) Matrix(335,94,866,243) -> Matrix(1,0,0,1) Matrix(201,56,664,185) -> Matrix(1,0,0,1) Matrix(3651,1012,2060,571) -> Matrix(1,-2,4,-7) Matrix(665,184,-3784,-1047) -> Matrix(1,-2,-2,5) Matrix(17713,4896,10944,3025) -> Matrix(1,-2,0,1) Matrix(333,92,-2588,-715) -> Matrix(1,-2,0,1) Matrix(197,54,-726,-199) -> Matrix(1,-2,0,1) Matrix(1773,478,1250,337) -> Matrix(1,0,4,1) Matrix(1967,528,1248,335) -> Matrix(1,0,2,1) Matrix(197,52,716,189) -> Matrix(1,0,2,1) Matrix(2017,528,1104,289) -> Matrix(3,-2,2,-1) Matrix(907,236,196,51) -> Matrix(1,0,0,1) Matrix(695,166,314,75) -> Matrix(1,2,0,1) Matrix(691,164,316,75) -> Matrix(1,0,2,1) Matrix(813,190,1442,337) -> Matrix(1,4,0,1) Matrix(2377,554,502,117) -> Matrix(1,4,0,1) Matrix(1249,290,814,189) -> Matrix(3,4,2,3) Matrix(1371,314,310,71) -> Matrix(3,-2,2,-1) Matrix(1677,382,1058,241) -> Matrix(1,-2,2,-3) Matrix(309,70,746,169) -> Matrix(1,-4,0,1) Matrix(245,54,186,41) -> Matrix(1,2,0,1) Matrix(857,186,1350,293) -> Matrix(1,0,0,1) Matrix(2137,456,792,169) -> Matrix(9,10,8,9) Matrix(123,26,790,167) -> Matrix(1,0,2,1) Matrix(7533,1580,4372,917) -> Matrix(1,-2,2,-3) Matrix(789,164,1756,365) -> Matrix(1,0,2,1) Matrix(2057,424,1208,249) -> Matrix(1,0,2,1) Matrix(297,56,472,89) -> Matrix(1,0,0,1) Matrix(2185,408,648,121) -> Matrix(11,12,10,11) Matrix(413,76,1940,357) -> Matrix(3,2,4,3) Matrix(233,42,294,53) -> Matrix(1,0,0,1) Matrix(6285,1102,1922,337) -> Matrix(1,0,2,1) Matrix(231,40,872,151) -> Matrix(1,0,8,1) Matrix(743,118,170,27) -> Matrix(3,4,2,3) Matrix(739,116,172,27) -> Matrix(1,0,2,1) Matrix(623,94,338,51) -> Matrix(1,0,2,1) Matrix(845,126,114,17) -> Matrix(1,0,2,1) Matrix(505,74,1126,165) -> Matrix(1,0,4,1) Matrix(223,30,498,67) -> Matrix(1,0,0,1) Matrix(717,94,1106,145) -> Matrix(1,-2,0,1) Matrix(2867,372,4524,587) -> Matrix(1,-4,0,1) Matrix(163,20,220,27) -> Matrix(1,0,0,1) Matrix(753,80,160,17) -> Matrix(3,-2,2,-1) Matrix(265,26,214,21) -> Matrix(1,0,2,1) Matrix(391,-40,88,-9) -> Matrix(3,-2,2,-1) Matrix(387,-44,44,-5) -> Matrix(1,2,0,1) Matrix(297,-38,86,-11) -> Matrix(1,2,0,1) Matrix(291,-44,668,-101) -> Matrix(3,-2,2,-1) Matrix(531,-92,860,-149) -> Matrix(1,-2,0,1) Matrix(245,-44,284,-51) -> Matrix(1,0,2,1) Matrix(527,-98,242,-45) -> Matrix(1,0,2,1) Matrix(201,-38,566,-107) -> Matrix(1,0,2,1) Matrix(239,-50,674,-141) -> Matrix(1,0,-2,1) Matrix(2495,-528,912,-193) -> Matrix(1,0,-2,1) Matrix(237,-52,196,-43) -> Matrix(1,0,2,1) Matrix(391,-88,40,-9) -> Matrix(7,-4,2,-1) Matrix(429,-98,626,-143) -> Matrix(3,-2,-4,3) Matrix(427,-100,1012,-237) -> Matrix(1,-2,0,1) Matrix(2755,-652,4348,-1029) -> Matrix(1,-6,0,1) Matrix(2949,-700,1900,-451) -> Matrix(1,8,0,1) Matrix(191,-50,722,-189) -> Matrix(1,0,8,1) Matrix(529,-142,190,-51) -> Matrix(1,0,-2,1) Matrix(527,-146,1202,-333) -> Matrix(7,-4,2,-1) Matrix(487,-136,376,-105) -> Matrix(3,-2,2,-1) Matrix(335,-98,482,-141) -> Matrix(3,-2,-4,3) Matrix(629,-186,186,-55) -> Matrix(7,-6,6,-5) Matrix(1397,-426,810,-247) -> Matrix(1,-2,2,-3) Matrix(439,-136,184,-57) -> Matrix(1,-2,2,-3) Matrix(677,-236,284,-99) -> Matrix(1,-2,2,-3) Matrix(529,-190,142,-51) -> Matrix(1,-2,2,-3) Matrix(387,-142,526,-193) -> Matrix(1,0,-2,1) Matrix(665,-246,246,-91) -> Matrix(5,-4,4,-3) Matrix(243,-92,140,-53) -> Matrix(1,-2,2,-3) Matrix(3113,-1206,1350,-523) -> Matrix(3,-4,4,-5) Matrix(3215,-1248,2352,-913) -> Matrix(1,-2,0,1) Matrix(379,-148,484,-189) -> Matrix(1,0,-2,1) Matrix(239,-98,578,-237) -> Matrix(1,-8,0,1) Matrix(439,-184,136,-57) -> Matrix(1,2,0,1) Matrix(2933,-1242,810,-343) -> Matrix(1,0,2,1) Matrix(875,-372,708,-301) -> Matrix(1,0,2,1) Matrix(469,-202,202,-87) -> Matrix(1,0,0,1) Matrix(1875,-814,334,-145) -> Matrix(5,-8,2,-3) Matrix(2641,-1152,768,-335) -> Matrix(3,-8,2,-5) Matrix(3069,-1348,1300,-571) -> Matrix(1,-8,2,-15) Matrix(533,-236,332,-147) -> Matrix(1,2,0,1) Matrix(861,-388,628,-283) -> Matrix(1,0,-2,1) Matrix(527,-242,98,-45) -> Matrix(1,0,0,1) Matrix(555,-262,358,-169) -> Matrix(1,2,0,1) Matrix(437,-234,282,-151) -> Matrix(1,4,0,1) Matrix(279,-154,154,-85) -> Matrix(1,0,2,1) Matrix(339,-190,430,-241) -> Matrix(1,0,-2,1) Matrix(1197,-676,2116,-1195) -> Matrix(1,-12,0,1) Matrix(307,-174,30,-17) -> Matrix(1,6,0,1) Matrix(243,-140,92,-53) -> Matrix(1,0,2,1) Matrix(91,-54,150,-89) -> Matrix(1,-2,0,1) Matrix(5179,-3172,1876,-1149) -> Matrix(1,2,0,1) Matrix(3601,-2208,2112,-1295) -> Matrix(1,2,0,1) Matrix(2973,-1826,1874,-1151) -> Matrix(1,0,2,1) Matrix(4037,-2490,2346,-1447) -> Matrix(1,4,2,9) Matrix(1869,-1156,1156,-715) -> Matrix(1,2,0,1) Matrix(1481,-918,534,-331) -> Matrix(1,2,0,1) Matrix(533,-332,236,-147) -> Matrix(1,2,0,1) Matrix(3357,-2116,1972,-1243) -> Matrix(1,0,2,1) Matrix(1383,-874,970,-613) -> Matrix(1,0,4,1) Matrix(3703,-2344,1000,-633) -> Matrix(1,-2,2,-3) Matrix(381,-244,292,-187) -> Matrix(1,2,0,1) Matrix(437,-282,234,-151) -> Matrix(1,2,0,1) Matrix(667,-436,436,-285) -> Matrix(7,8,6,7) Matrix(1307,-900,228,-157) -> Matrix(5,2,2,1) Matrix(1163,-804,852,-589) -> Matrix(1,0,0,1) Matrix(425,-296,56,-39) -> Matrix(1,0,2,1) Matrix(141,-100,196,-139) -> Matrix(1,0,2,1) Matrix(279,-202,250,-181) -> Matrix(1,0,0,1) Matrix(3311,-2400,1392,-1009) -> Matrix(1,-2,2,-3) Matrix(861,-628,388,-283) -> Matrix(1,0,0,1) Matrix(3077,-2250,666,-487) -> Matrix(1,0,0,1) Matrix(1163,-852,804,-589) -> Matrix(1,4,2,9) Matrix(1823,-1346,386,-285) -> Matrix(5,2,2,1) Matrix(381,-292,244,-187) -> Matrix(1,0,0,1) Matrix(487,-376,136,-105) -> Matrix(1,2,0,1) Matrix(875,-708,372,-301) -> Matrix(1,0,4,1) Matrix(1113,-902,902,-731) -> Matrix(1,0,4,1) Matrix(1111,-904,424,-345) -> Matrix(1,0,4,1) Matrix(237,-196,52,-43) -> Matrix(5,2,2,1) Matrix(287,-242,338,-285) -> Matrix(1,0,14,1) Matrix(769,-670,334,-291) -> Matrix(1,-2,2,-3) Matrix(253,-226,178,-159) -> Matrix(1,0,4,1) Matrix(677,-764,428,-483) -> Matrix(1,0,2,1) Matrix(245,-284,44,-51) -> Matrix(5,2,2,1) Matrix(287,-338,242,-285) -> Matrix(1,0,18,1) Matrix(1775,-2162,1298,-1581) -> Matrix(1,0,-4,1) Matrix(667,-820,388,-477) -> Matrix(1,0,0,1) Matrix(1677,-2066,194,-239) -> Matrix(3,-2,2,-1) Matrix(2021,-2492,236,-291) -> Matrix(3,-2,2,-1) Matrix(339,-430,190,-241) -> Matrix(1,0,0,1) Matrix(379,-484,148,-189) -> Matrix(3,-2,2,-1) Matrix(387,-526,142,-193) -> Matrix(1,2,0,1) Matrix(6675,-9118,1582,-2161) -> Matrix(5,2,2,1) Matrix(7099,-9700,1684,-2301) -> Matrix(3,-2,2,-1) Matrix(141,-196,100,-139) -> Matrix(1,0,6,1) Matrix(1389,-1972,436,-619) -> Matrix(7,-2,4,-1) Matrix(4079,-5808,1248,-1777) -> Matrix(1,0,-4,1) Matrix(335,-482,98,-141) -> Matrix(7,-2,4,-1) Matrix(2803,-4060,1804,-2613) -> Matrix(29,-14,-2,1) Matrix(4351,-6306,2802,-4061) -> Matrix(43,-22,2,-1) Matrix(1821,-2642,1058,-1535) -> Matrix(7,-4,16,-9) Matrix(429,-626,98,-143) -> Matrix(5,-4,4,-3) Matrix(837,-1274,362,-551) -> Matrix(7,-6,6,-5) Matrix(2755,-4348,652,-1029) -> Matrix(3,-2,2,-1) Matrix(2009,-3174,726,-1147) -> Matrix(1,0,-2,1) Matrix(6955,-10996,4036,-6381) -> Matrix(5,-2,8,-3) Matrix(1821,-2932,772,-1243) -> Matrix(1,2,2,5) Matrix(679,-1096,184,-297) -> Matrix(1,0,2,1) Matrix(9791,-15842,6050,-9789) -> Matrix(1,0,0,1) Matrix(531,-860,92,-149) -> Matrix(1,2,0,1) Matrix(91,-150,54,-89) -> Matrix(1,0,2,1) Matrix(5805,-9892,1828,-3115) -> Matrix(5,-4,4,-3) Matrix(4561,-7774,1438,-2451) -> Matrix(1,0,0,1) Matrix(4273,-7296,1152,-1967) -> Matrix(5,-2,8,-3) Matrix(4089,-7048,1480,-2551) -> Matrix(3,-2,2,-1) Matrix(313,-550,70,-123) -> Matrix(3,-2,2,-1) Matrix(1197,-2116,676,-1195) -> Matrix(1,0,4,1) Matrix(1055,-1922,578,-1053) -> Matrix(7,-6,6,-5) Matrix(33,-64,16,-31) -> Matrix(1,0,0,1) Matrix(581,-1242,138,-295) -> Matrix(3,-2,2,-1) Matrix(1541,-3498,426,-967) -> Matrix(1,0,2,1) Matrix(527,-1202,146,-333) -> Matrix(1,0,-2,1) Matrix(291,-668,44,-101) -> Matrix(7,-4,2,-1) Matrix(3887,-8978,1682,-3885) -> Matrix(19,-18,18,-17) Matrix(427,-1012,100,-237) -> Matrix(3,-2,2,-1) Matrix(2301,-5476,724,-1723) -> Matrix(5,-4,4,-3) Matrix(239,-578,98,-237) -> Matrix(7,-6,6,-5) Matrix(1301,-3354,282,-727) -> Matrix(1,4,0,1) Matrix(1059,-2732,188,-485) -> Matrix(1,4,0,1) Matrix(479,-1250,146,-381) -> Matrix(1,0,-2,1) Matrix(1061,-2778,186,-487) -> Matrix(3,-2,2,-1) Matrix(911,-2450,338,-909) -> Matrix(19,-18,18,-17) Matrix(201,-566,38,-107) -> Matrix(3,-2,2,-1) Matrix(37,-108,12,-35) -> Matrix(3,-2,2,-1) Matrix(1587,-5180,428,-1397) -> Matrix(1,-2,2,-3) Matrix(815,-2738,242,-813) -> Matrix(23,-22,22,-21) Matrix(191,-722,50,-189) -> Matrix(11,-10,10,-9) Matrix(41,-200,8,-39) -> Matrix(1,0,0,1) Matrix(43,-294,6,-41) -> Matrix(1,-4,0,1) 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): 56 Degree of the the map X: 56 Degree of the the map Y: 256 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 (0/1,1/0) 0 1 0/1 (0/1,1/0) 0 24 1/9 0/1 1 12 1/8 1/0 1 8 1/7 0/1 2 3 2/13 0 8 1/6 1/0 1 24 3/17 -1/1 1 6 2/11 (0/1,1/1) 0 24 3/16 1/0 1 24 1/5 0/1 2 4 4/19 (1/3,1/2) 0 24 7/33 1/2 2 3 3/14 1/2 1 24 2/9 (0/1,1/3) 0 24 5/22 1/2 1 8 3/13 1/1 2 3 4/17 0 8 1/4 1/0 1 24 5/19 0/1 4 1 4/15 (0/1,1/4) 0 24 3/11 0/1 1 12 5/18 1/2 1 24 2/7 0 8 5/17 2/3 1 12 3/10 3/2 1 24 4/13 (0/1,1/1) 0 24 1/3 0 6 6/17 (1/1,1/0) 0 24 11/31 0/1 2 4 5/14 1/2 1 24 4/11 0 8 7/19 2/3 1 12 3/8 3/2 1 24 5/13 0 4 7/18 1/0 1 24 2/5 (2/1,1/0) 0 24 7/17 1/0 4 1 5/12 1/0 1 24 8/19 0 8 11/26 1/0 1 24 14/33 (0/1,1/0) 0 24 3/7 0/1 1 12 13/30 5/4 1 24 10/23 0 8 17/39 2/1 2 3 7/16 1/0 1 24 11/25 1/0 6 2 4/9 (-1/1,0/1) 0 24 9/20 1/0 1 24 5/11 1/1 1 3 6/13 (2/1,1/0) 0 24 1/2 1/0 1 8 7/13 0 6 6/11 (-2/1,-1/1) 0 24 5/9 0/1 1 12 9/16 1/0 1 24 13/23 1/0 6 2 17/30 1/0 1 24 4/7 (-2/1,-1/1) 0 24 7/12 1/0 1 24 3/5 1/0 1 3 11/18 1/0 1 24 19/31 -2/1 1 12 27/44 1/0 1 24 8/13 0 8 29/47 -3/1 1 6 21/34 1/0 1 24 13/21 -2/1 1 12 18/29 (-2/1,1/0) 0 24 5/8 -3/2 1 24 12/19 (-1/1,0/1) 0 24 31/49 0 3 19/30 1/0 1 24 7/11 0 4 9/14 1/0 1 24 11/17 -1/1 1 6 13/20 -3/2 1 8 2/3 (-1/1,0/1) 0 24 11/16 -1/2 1 8 20/29 (-1/2,0/1) 0 24 9/13 0/1 1 12 16/23 0 8 7/10 -1/2 1 24 5/7 0/1 1 2 13/18 1/0 1 24 21/29 0/1 1 12 8/11 (0/1,1/0) 0 24 19/26 1/0 1 8 30/41 (7/1,1/0) 0 24 11/15 -2/1 1 12 14/19 0 8 3/4 1/0 1 24 10/13 (-3/1,1/0) 0 24 7/9 -1/1 2 3 11/14 -1/2 1 24 4/5 0 8 17/21 0/1 1 12 13/16 -1/2 1 24 9/11 0 6 5/6 -1/4 1 24 11/13 0/1 7 1 6/7 (0/1,1/3) 0 24 13/15 1/1 1 6 7/8 1/0 1 8 1/1 0/1 1 12 9/8 1/0 1 24 8/7 0 8 7/6 -1/4 1 24 13/11 0/1 9 1 6/5 (0/1,1/5) 0 24 17/14 1/4 1 24 11/9 1/3 1 6 16/13 (0/1,1/2) 0 24 53/43 (0/1,1/2) 0 1 37/30 1/2 1 24 21/17 0/1 1 12 5/4 1/2 1 8 14/11 (1/3,1/2) 0 24 9/7 1/1 2 3 13/10 1/0 1 24 4/3 (0/1,1/0) 0 24 15/11 0/1 1 12 56/41 (-1/2,0/1) 0 24 97/71 0/1 2 1 41/30 1/0 1 24 26/19 0 8 11/8 -1/2 1 24 7/5 0/1 3 2 17/12 1/4 1 24 27/19 0/1 1 12 37/26 1/4 1 8 47/33 0 3 10/7 (0/1,1/3) 0 24 13/9 2/5 1 12 42/29 (11/23,1/2) 0 24 71/49 1/2 18 1 29/20 1/2 1 24 16/11 0 8 3/2 1/2 1 24 20/13 0 8 17/11 0 6 31/20 1/0 1 8 14/9 (-3/1,1/0) 0 24 11/7 0/1 2 4 30/19 (0/1,1/2) 0 24 49/31 0 3 68/43 0 8 19/12 1/2 1 24 8/5 (1/1,2/1) 0 24 37/23 1/0 6 2 29/18 1/0 1 24 21/13 0/1 1 12 55/34 1/0 1 24 89/55 (0/1,1/0) 0 1 34/21 (0/1,1/0) 0 24 13/8 1/0 1 8 5/3 0/1 1 3 17/10 1/2 1 8 46/27 (1/2,1/1) 0 24 121/71 1/1 2 1 75/44 1/0 1 24 29/17 0/1 1 12 12/7 (0/1,1/2) 0 24 43/25 1/3 1 6 74/43 0 8 31/18 1/2 1 24 19/11 0 4 7/4 1/0 1 24 30/17 (0/1,1/0) 0 24 23/13 0/1 2 2 16/9 (1/3,1/2) 0 24 9/5 0/1 1 12 20/11 (2/3,1/1) 0 24 31/17 1/1 3 1 11/6 1/0 1 24 13/7 1/1 1 6 15/8 1/0 1 24 2/1 0 8 13/6 1/2 1 24 11/5 1/1 1 3 20/9 (0/1,1/0) 0 24 9/4 1/2 1 24 34/15 (0/1,1/0) 0 24 25/11 0/1 2 2 16/7 (1/2,1/1) 0 24 23/10 1/2 1 8 30/13 (4/5,1/1) 0 24 67/29 1/1 9 1 37/16 5/4 1 24 7/3 0/1 1 12 33/14 1/2 1 24 26/11 (3/5,2/3) 0 24 19/8 1/2 1 8 50/21 (1/2,1/1) 0 24 31/13 0 6 12/5 (2/3,1/1) 0 24 17/7 1/1 3 1 5/2 1/0 1 24 18/7 (3/1,1/0) 0 24 13/5 0/1 2 4 34/13 (0/1,1/2) 0 24 55/21 0 6 21/8 1/2 1 24 8/3 (2/3,1/1) 0 24 35/13 1/1 9 1 27/10 7/6 1 24 19/7 2/1 1 12 30/11 (2/1,1/0) 0 24 11/4 1/0 1 8 47/17 0 3 36/13 (0/1,1/0) 0 24 25/9 0/1 1 12 14/5 (0/1,1/2) 0 24 17/6 1/2 1 24 3/1 1/1 1 6 19/6 1/0 1 24 16/5 0 8 13/4 1/0 1 24 10/3 (2/3,1/1) 0 24 37/11 1/1 11 1 27/8 9/8 1 24 17/5 4/3 1 12 24/7 (1/1,2/1) 0 24 31/9 2/1 2 3 7/2 1/0 1 8 18/5 (-1/1,1/0) 0 24 11/3 0/1 1 12 37/10 1/2 1 24 63/17 0 3 26/7 0 8 15/4 3/4 1 24 19/5 1/1 5 1 4/1 (1/1,2/1) 0 24 17/4 1/0 1 8 13/3 1/1 2 3 22/5 0 8 9/2 3/2 1 24 23/5 0 6 14/3 (1/1,2/1) 0 24 33/7 2/1 2 3 19/4 1/0 1 24 5/1 0 4 21/4 1/0 1 24 16/3 (2/1,1/0) 0 24 11/2 3/2 1 24 28/5 0 8 17/3 0 6 40/7 (2/1,1/0) 0 24 23/4 1/0 1 8 6/1 (2/1,1/0) 0 24 13/2 1/0 1 8 20/3 (3/1,1/0) 0 24 7/1 1/0 2 3 15/2 1/0 1 24 8/1 0 8 9/1 2/1 1 12 1/0 1/0 1 24 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(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(129,-14,304,-33) (0/1,1/9) -> (14/33,3/7) Glide Reflection Matrix(213,-26,172,-21) (1/9,1/8) -> (21/17,5/4) Glide Reflection Matrix(297,-38,86,-11) (1/8,1/7) -> (31/9,7/2) Hyperbolic Matrix(291,-44,668,-101) (1/7,2/13) -> (10/23,17/39) Hyperbolic Matrix(123,-20,166,-27) (2/13,1/6) -> (14/19,3/4) Glide Reflection Matrix(531,-92,860,-149) (1/6,3/17) -> (29/47,21/34) Hyperbolic Matrix(245,-44,284,-51) (3/17,2/11) -> (6/7,13/15) Hyperbolic Matrix(163,-30,364,-67) (2/11,3/16) -> (4/9,9/20) Glide Reflection Matrix(201,-38,566,-107) (3/16,1/5) -> (11/31,5/14) Hyperbolic Matrix(239,-50,674,-141) (1/5,4/19) -> (6/17,11/31) Hyperbolic Matrix(793,-168,118,-25) (4/19,7/33) -> (20/3,7/1) Glide Reflection Matrix(593,-126,80,-17) (7/33,3/14) -> (7/1,15/2) Glide Reflection Matrix(237,-52,196,-43) (3/14,2/9) -> (6/5,17/14) Hyperbolic Matrix(743,-168,314,-71) (2/9,5/22) -> (26/11,19/8) Glide Reflection Matrix(507,-116,118,-27) (5/22,3/13) -> (17/4,13/3) Glide Reflection Matrix(507,-118,116,-27) (3/13,4/17) -> (13/3,22/5) Glide Reflection Matrix(115,-28,78,-19) (4/17,1/4) -> (16/11,3/2) Glide Reflection Matrix(39,-10,152,-39) (1/4,5/19) -> (1/4,5/19) Reflection Matrix(151,-40,570,-151) (5/19,4/15) -> (5/19,4/15) Reflection Matrix(529,-142,190,-51) (4/15,3/11) -> (25/9,14/5) Hyperbolic Matrix(189,-52,338,-93) (3/11,5/18) -> (5/9,9/16) Glide Reflection Matrix(149,-42,188,-53) (5/18,2/7) -> (11/14,4/5) Glide Reflection Matrix(335,-98,482,-141) (2/7,5/17) -> (9/13,16/23) Hyperbolic Matrix(629,-186,186,-55) (5/17,3/10) -> (27/8,17/5) Hyperbolic Matrix(185,-56,294,-89) (3/10,4/13) -> (5/8,12/19) Glide Reflection Matrix(439,-136,184,-57) (4/13,1/3) -> (31/13,12/5) Hyperbolic Matrix(677,-236,284,-99) (1/3,6/17) -> (50/21,31/13) Hyperbolic Matrix(529,-190,142,-51) (5/14,4/11) -> (26/7,15/4) Hyperbolic Matrix(387,-142,526,-193) (4/11,7/19) -> (11/15,14/19) Hyperbolic Matrix(665,-246,246,-91) (7/19,3/8) -> (27/10,19/7) Hyperbolic Matrix(243,-92,140,-53) (3/8,5/13) -> (19/11,7/4) Hyperbolic Matrix(243,-94,380,-147) (5/13,7/18) -> (7/11,9/14) Glide Reflection Matrix(137,-54,104,-41) (7/18,2/5) -> (13/10,4/3) Glide Reflection Matrix(69,-28,170,-69) (2/5,7/17) -> (2/5,7/17) Reflection Matrix(169,-70,408,-169) (7/17,5/12) -> (7/17,5/12) Reflection Matrix(439,-184,136,-57) (5/12,8/19) -> (16/5,13/4) Hyperbolic Matrix(743,-314,168,-71) (8/19,11/26) -> (22/5,9/2) Glide Reflection Matrix(1011,-428,574,-243) (11/26,14/33) -> (7/4,30/17) Glide Reflection Matrix(469,-202,202,-87) (3/7,13/30) -> (37/16,7/3) Hyperbolic Matrix(669,-290,436,-189) (13/30,10/23) -> (3/2,20/13) Glide Reflection Matrix(1269,-554,268,-117) (17/39,7/16) -> (33/7,19/4) Glide Reflection Matrix(433,-190,768,-337) (7/16,11/25) -> (9/16,13/23) Glide Reflection Matrix(533,-236,332,-147) (11/25,4/9) -> (8/5,37/23) Hyperbolic Matrix(363,-164,166,-75) (9/20,5/11) -> (13/6,11/5) Glide Reflection Matrix(363,-166,164,-75) (5/11,6/13) -> (11/5,20/9) Glide Reflection Matrix(263,-122,360,-167) (6/13,1/2) -> (8/11,19/26) Glide Reflection Matrix(437,-234,282,-151) (1/2,7/13) -> (17/11,31/20) Hyperbolic Matrix(435,-236,94,-51) (7/13,6/11) -> (23/5,14/3) Glide Reflection Matrix(279,-154,154,-85) (6/11,5/9) -> (9/5,20/11) Hyperbolic Matrix(1777,-1006,1104,-625) (13/23,17/30) -> (37/23,29/18) Glide Reflection Matrix(1011,-574,428,-243) (17/30,4/7) -> (33/14,26/11) Glide Reflection Matrix(243,-140,92,-53) (4/7,7/12) -> (21/8,8/3) Hyperbolic Matrix(91,-54,150,-89) (7/12,3/5) -> (3/5,11/18) Parabolic Matrix(1013,-620,714,-437) (11/18,19/31) -> (17/12,27/19) Glide Reflection Matrix(3601,-2208,2112,-1295) (19/31,27/44) -> (75/44,29/17) Hyperbolic Matrix(951,-584,298,-183) (27/44,8/13) -> (19/6,16/5) Glide Reflection Matrix(4037,-2490,2346,-1447) (8/13,29/47) -> (43/25,74/43) Hyperbolic Matrix(1869,-1156,1156,-715) (21/34,13/21) -> (21/13,55/34) Hyperbolic Matrix(1481,-918,534,-331) (13/21,18/29) -> (36/13,25/9) Hyperbolic Matrix(533,-332,236,-147) (18/29,5/8) -> (9/4,34/15) Hyperbolic Matrix(1383,-874,970,-613) (12/19,31/49) -> (47/33,10/7) Hyperbolic Matrix(3703,-2344,1000,-633) (31/49,19/30) -> (37/10,63/17) Hyperbolic Matrix(911,-578,528,-335) (19/30,7/11) -> (31/18,19/11) Glide Reflection Matrix(437,-282,234,-151) (9/14,11/17) -> (13/7,15/8) Hyperbolic Matrix(379,-246,436,-283) (11/17,13/20) -> (13/15,7/8) Glide Reflection Matrix(669,-436,290,-189) (13/20,2/3) -> (23/10,30/13) Glide Reflection Matrix(115,-78,28,-19) (2/3,11/16) -> (4/1,17/4) Glide Reflection Matrix(1307,-900,228,-157) (11/16,20/29) -> (40/7,23/4) Hyperbolic Matrix(1163,-804,852,-589) (20/29,9/13) -> (15/11,56/41) Hyperbolic Matrix(425,-296,56,-39) (16/23,7/10) -> (15/2,8/1) Hyperbolic Matrix(141,-100,196,-139) (7/10,5/7) -> (5/7,13/18) Parabolic Matrix(279,-202,250,-181) (13/18,21/29) -> (1/1,9/8) Hyperbolic Matrix(667,-484,390,-283) (21/29,8/11) -> (29/17,12/7) Glide Reflection Matrix(1635,-1196,1054,-771) (19/26,30/41) -> (31/20,14/9) Glide Reflection Matrix(1163,-852,804,-589) (30/41,11/15) -> (13/9,42/29) Hyperbolic Matrix(137,-104,54,-41) (3/4,10/13) -> (5/2,18/7) Glide Reflection Matrix(243,-188,190,-147) (10/13,7/9) -> (14/11,9/7) Glide Reflection Matrix(243,-190,188,-147) (7/9,11/14) -> (9/7,13/10) Glide Reflection Matrix(213,-172,26,-21) (4/5,17/21) -> (8/1,9/1) Glide Reflection Matrix(1113,-902,902,-731) (17/21,13/16) -> (37/30,21/17) Hyperbolic Matrix(1111,-904,424,-345) (13/16,9/11) -> (55/21,21/8) Hyperbolic Matrix(237,-196,52,-43) (9/11,5/6) -> (9/2,23/5) Hyperbolic Matrix(131,-110,156,-131) (5/6,11/13) -> (5/6,11/13) Reflection Matrix(155,-132,182,-155) (11/13,6/7) -> (11/13,6/7) Reflection Matrix(253,-226,178,-159) (7/8,1/1) -> (27/19,37/26) Hyperbolic Matrix(677,-764,428,-483) (9/8,8/7) -> (68/43,19/12) Hyperbolic Matrix(245,-284,44,-51) (8/7,7/6) -> (11/2,28/5) Hyperbolic Matrix(155,-182,132,-155) (7/6,13/11) -> (7/6,13/11) Reflection Matrix(131,-156,110,-131) (13/11,6/5) -> (13/11,6/5) Reflection Matrix(281,-342,152,-185) (17/14,11/9) -> (11/6,13/7) Glide Reflection Matrix(667,-820,388,-477) (11/9,16/13) -> (12/7,43/25) Hyperbolic Matrix(1377,-1696,1118,-1377) (16/13,53/43) -> (16/13,53/43) Reflection Matrix(3181,-3922,2580,-3181) (53/43,37/30) -> (53/43,37/30) Reflection Matrix(149,-188,42,-53) (5/4,14/11) -> (7/2,18/5) Glide Reflection Matrix(387,-526,142,-193) (4/3,15/11) -> (19/7,30/11) Hyperbolic Matrix(7953,-10864,5822,-7953) (56/41,97/71) -> (56/41,97/71) Reflection Matrix(5821,-7954,4260,-5821) (97/71,41/30) -> (97/71,41/30) Reflection Matrix(345,-472,182,-249) (41/30,26/19) -> (15/8,2/1) Glide Reflection Matrix(263,-360,122,-167) (26/19,11/8) -> (2/1,13/6) Glide Reflection Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(1585,-2256,574,-817) (37/26,47/33) -> (11/4,47/17) Glide Reflection Matrix(335,-482,98,-141) (10/7,13/9) -> (17/5,24/7) Hyperbolic Matrix(4117,-5964,2842,-4117) (42/29,71/49) -> (42/29,71/49) Reflection Matrix(2841,-4118,1960,-2841) (71/49,29/20) -> (71/49,29/20) Reflection Matrix(1821,-2642,1058,-1535) (29/20,16/11) -> (74/43,31/18) Hyperbolic Matrix(529,-816,94,-145) (20/13,17/11) -> (28/5,17/3) Glide Reflection Matrix(243,-380,94,-147) (14/9,11/7) -> (18/7,13/5) Glide Reflection Matrix(485,-764,186,-293) (11/7,30/19) -> (13/5,34/13) Glide Reflection Matrix(2009,-3174,726,-1147) (30/19,49/31) -> (47/17,36/13) Hyperbolic Matrix(3515,-5558,948,-1499) (49/31,68/43) -> (63/17,26/7) Glide Reflection Matrix(185,-294,56,-89) (19/12,8/5) -> (13/4,10/3) Glide Reflection Matrix(679,-1096,184,-297) (29/18,21/13) -> (11/3,37/10) Hyperbolic Matrix(6051,-9790,3740,-6051) (55/34,89/55) -> (55/34,89/55) Reflection Matrix(3739,-6052,2310,-3739) (89/55,34/21) -> (89/55,34/21) Reflection Matrix(531,-860,92,-149) (34/21,13/8) -> (23/4,6/1) Hyperbolic Matrix(91,-150,54,-89) (13/8,5/3) -> (5/3,17/10) Parabolic Matrix(1013,-1724,426,-725) (17/10,46/27) -> (19/8,50/21) Glide Reflection Matrix(6533,-11132,3834,-6533) (46/27,121/71) -> (46/27,121/71) Reflection Matrix(10649,-18150,6248,-10649) (121/71,75/44) -> (121/71,75/44) Reflection Matrix(867,-1532,382,-675) (30/17,23/13) -> (34/15,25/11) Glide Reflection Matrix(433,-768,190,-337) (23/13,16/9) -> (25/11,16/7) Glide Reflection Matrix(189,-338,52,-93) (16/9,9/5) -> (18/5,11/3) Glide Reflection Matrix(681,-1240,374,-681) (20/11,31/17) -> (20/11,31/17) Reflection Matrix(373,-682,204,-373) (31/17,11/6) -> (31/17,11/6) Reflection Matrix(163,-364,30,-67) (20/9,9/4) -> (16/3,11/2) Glide Reflection Matrix(291,-668,44,-101) (16/7,23/10) -> (13/2,20/3) Hyperbolic Matrix(1741,-4020,754,-1741) (30/13,67/29) -> (30/13,67/29) Reflection Matrix(2145,-4958,928,-2145) (67/29,37/16) -> (67/29,37/16) Reflection Matrix(129,-304,14,-33) (7/3,33/14) -> (9/1,1/0) Glide Reflection Matrix(169,-408,70,-169) (12/5,17/7) -> (12/5,17/7) Reflection Matrix(69,-170,28,-69) (17/7,5/2) -> (17/7,5/2) Reflection Matrix(1061,-2778,186,-487) (34/13,55/21) -> (17/3,40/7) Hyperbolic Matrix(209,-560,78,-209) (8/3,35/13) -> (8/3,35/13) Reflection Matrix(701,-1890,260,-701) (35/13,27/10) -> (35/13,27/10) Reflection Matrix(167,-456,26,-71) (30/11,11/4) -> (6/1,13/2) Glide Reflection Matrix(201,-566,38,-107) (14/5,17/6) -> (21/4,16/3) Hyperbolic Matrix(37,-108,12,-35) (17/6,3/1) -> (3/1,19/6) Parabolic Matrix(221,-740,66,-221) (10/3,37/11) -> (10/3,37/11) Reflection Matrix(593,-1998,176,-593) (37/11,27/8) -> (37/11,27/8) Reflection Matrix(357,-1226,76,-261) (24/7,31/9) -> (14/3,33/7) Glide Reflection Matrix(151,-570,40,-151) (15/4,19/5) -> (15/4,19/5) Reflection Matrix(39,-152,10,-39) (19/5,4/1) -> (19/5,4/1) Reflection Matrix(41,-200,8,-39) (19/4,5/1) -> (5/1,21/4) Parabolic 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(-1,0,2,1) -> Matrix(1,0,0,-1) (-1/1,0/1) -> (0/1,1/0) Matrix(129,-14,304,-33) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(213,-26,172,-21) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(297,-38,86,-11) -> Matrix(1,2,0,1) 1/0 Matrix(291,-44,668,-101) -> Matrix(3,-2,2,-1) 1/1 Matrix(123,-20,166,-27) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(531,-92,860,-149) -> Matrix(1,-2,0,1) 1/0 Matrix(245,-44,284,-51) -> Matrix(1,0,2,1) 0/1 Matrix(163,-30,364,-67) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(201,-38,566,-107) -> Matrix(1,0,2,1) 0/1 Matrix(239,-50,674,-141) -> Matrix(1,0,-2,1) 0/1 Matrix(793,-168,118,-25) -> Matrix(9,-4,2,-1) Matrix(593,-126,80,-17) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(237,-52,196,-43) -> Matrix(1,0,2,1) 0/1 Matrix(743,-168,314,-71) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(507,-116,118,-27) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(507,-118,116,-27) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(115,-28,78,-19) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(39,-10,152,-39) -> Matrix(1,0,0,-1) (1/4,5/19) -> (0/1,1/0) Matrix(151,-40,570,-151) -> Matrix(1,0,8,-1) (5/19,4/15) -> (0/1,1/4) Matrix(529,-142,190,-51) -> Matrix(1,0,-2,1) 0/1 Matrix(189,-52,338,-93) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(149,-42,188,-53) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(335,-98,482,-141) -> Matrix(3,-2,-4,3) Matrix(629,-186,186,-55) -> Matrix(7,-6,6,-5) 1/1 Matrix(185,-56,294,-89) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(439,-136,184,-57) -> Matrix(1,-2,2,-3) 1/1 Matrix(677,-236,284,-99) -> Matrix(1,-2,2,-3) 1/1 Matrix(529,-190,142,-51) -> Matrix(1,-2,2,-3) 1/1 Matrix(387,-142,526,-193) -> Matrix(1,0,-2,1) 0/1 Matrix(665,-246,246,-91) -> Matrix(5,-4,4,-3) 1/1 Matrix(243,-92,140,-53) -> Matrix(1,-2,2,-3) 1/1 Matrix(243,-94,380,-147) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(137,-54,104,-41) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(69,-28,170,-69) -> Matrix(-1,4,0,1) (2/5,7/17) -> (2/1,1/0) Matrix(169,-70,408,-169) -> Matrix(1,4,0,-1) (7/17,5/12) -> (-2/1,1/0) Matrix(439,-184,136,-57) -> Matrix(1,2,0,1) 1/0 Matrix(743,-314,168,-71) -> Matrix(3,2,2,1) Matrix(1011,-428,574,-243) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(469,-202,202,-87) -> Matrix(1,0,0,1) Matrix(669,-290,436,-189) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(1269,-554,268,-117) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(433,-190,768,-337) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(533,-236,332,-147) -> Matrix(1,2,0,1) 1/0 Matrix(363,-164,166,-75) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(363,-166,164,-75) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(263,-122,360,-167) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(437,-234,282,-151) -> Matrix(1,4,0,1) 1/0 Matrix(435,-236,94,-51) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(279,-154,154,-85) -> Matrix(1,0,2,1) 0/1 Matrix(1777,-1006,1104,-625) -> Matrix(1,6,0,-1) *** -> (-3/1,1/0) Matrix(1011,-574,428,-243) -> Matrix(1,4,2,7) Matrix(243,-140,92,-53) -> Matrix(1,0,2,1) 0/1 Matrix(91,-54,150,-89) -> Matrix(1,-2,0,1) 1/0 Matrix(1013,-620,714,-437) -> Matrix(1,2,4,7) Matrix(3601,-2208,2112,-1295) -> Matrix(1,2,0,1) 1/0 Matrix(951,-584,298,-183) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(4037,-2490,2346,-1447) -> Matrix(1,4,2,9) Matrix(1869,-1156,1156,-715) -> Matrix(1,2,0,1) 1/0 Matrix(1481,-918,534,-331) -> Matrix(1,2,0,1) 1/0 Matrix(533,-332,236,-147) -> Matrix(1,2,0,1) 1/0 Matrix(1383,-874,970,-613) -> Matrix(1,0,4,1) 0/1 Matrix(3703,-2344,1000,-633) -> Matrix(1,-2,2,-3) 1/1 Matrix(911,-578,528,-335) -> Matrix(1,2,2,3) Matrix(437,-282,234,-151) -> Matrix(1,2,0,1) 1/0 Matrix(379,-246,436,-283) -> Matrix(1,2,2,3) Matrix(669,-436,290,-189) -> Matrix(3,4,4,5) Matrix(115,-78,28,-19) -> Matrix(3,2,2,1) Matrix(1307,-900,228,-157) -> Matrix(5,2,2,1) Matrix(1163,-804,852,-589) -> Matrix(1,0,0,1) Matrix(425,-296,56,-39) -> Matrix(1,0,2,1) 0/1 Matrix(141,-100,196,-139) -> Matrix(1,0,2,1) 0/1 Matrix(279,-202,250,-181) -> Matrix(1,0,0,1) Matrix(667,-484,390,-283) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(1635,-1196,1054,-771) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(1163,-852,804,-589) -> Matrix(1,4,2,9) Matrix(137,-104,54,-41) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(243,-188,190,-147) -> Matrix(1,2,2,3) Matrix(243,-190,188,-147) -> Matrix(3,2,2,1) Matrix(213,-172,26,-21) -> Matrix(3,2,2,1) Matrix(1113,-902,902,-731) -> Matrix(1,0,4,1) 0/1 Matrix(1111,-904,424,-345) -> Matrix(1,0,4,1) 0/1 Matrix(237,-196,52,-43) -> Matrix(5,2,2,1) Matrix(131,-110,156,-131) -> Matrix(-1,0,8,1) (5/6,11/13) -> (-1/4,0/1) Matrix(155,-132,182,-155) -> Matrix(1,0,6,-1) (11/13,6/7) -> (0/1,1/3) Matrix(253,-226,178,-159) -> Matrix(1,0,4,1) 0/1 Matrix(677,-764,428,-483) -> Matrix(1,0,2,1) 0/1 Matrix(245,-284,44,-51) -> Matrix(5,2,2,1) Matrix(155,-182,132,-155) -> Matrix(-1,0,8,1) (7/6,13/11) -> (-1/4,0/1) Matrix(131,-156,110,-131) -> Matrix(1,0,10,-1) (13/11,6/5) -> (0/1,1/5) Matrix(281,-342,152,-185) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(667,-820,388,-477) -> Matrix(1,0,0,1) Matrix(1377,-1696,1118,-1377) -> Matrix(1,0,4,-1) (16/13,53/43) -> (0/1,1/2) Matrix(3181,-3922,2580,-3181) -> Matrix(1,0,4,-1) (53/43,37/30) -> (0/1,1/2) Matrix(149,-188,42,-53) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(387,-526,142,-193) -> Matrix(1,2,0,1) 1/0 Matrix(7953,-10864,5822,-7953) -> Matrix(-1,0,4,1) (56/41,97/71) -> (-1/2,0/1) Matrix(5821,-7954,4260,-5821) -> Matrix(1,0,0,-1) (97/71,41/30) -> (0/1,1/0) Matrix(345,-472,182,-249) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(263,-360,122,-167) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(141,-196,100,-139) -> Matrix(1,0,6,1) 0/1 Matrix(1585,-2256,574,-817) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(335,-482,98,-141) -> Matrix(7,-2,4,-1) Matrix(4117,-5964,2842,-4117) -> Matrix(45,-22,92,-45) (42/29,71/49) -> (11/23,1/2) Matrix(2841,-4118,1960,-2841) -> Matrix(27,-14,52,-27) (71/49,29/20) -> (1/2,7/13) Matrix(1821,-2642,1058,-1535) -> Matrix(7,-4,16,-9) 1/2 Matrix(529,-816,94,-145) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(243,-380,94,-147) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(485,-764,186,-293) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(2009,-3174,726,-1147) -> Matrix(1,0,-2,1) 0/1 Matrix(3515,-5558,948,-1499) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(185,-294,56,-89) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(679,-1096,184,-297) -> Matrix(1,0,2,1) 0/1 Matrix(6051,-9790,3740,-6051) -> Matrix(1,0,0,-1) (55/34,89/55) -> (0/1,1/0) Matrix(3739,-6052,2310,-3739) -> Matrix(1,0,0,-1) (89/55,34/21) -> (0/1,1/0) Matrix(531,-860,92,-149) -> Matrix(1,2,0,1) 1/0 Matrix(91,-150,54,-89) -> Matrix(1,0,2,1) 0/1 Matrix(1013,-1724,426,-725) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(6533,-11132,3834,-6533) -> Matrix(3,-2,4,-3) (46/27,121/71) -> (1/2,1/1) Matrix(10649,-18150,6248,-10649) -> Matrix(-1,2,0,1) (121/71,75/44) -> (1/1,1/0) Matrix(867,-1532,382,-675) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(433,-768,190,-337) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(189,-338,52,-93) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(681,-1240,374,-681) -> Matrix(5,-4,6,-5) (20/11,31/17) -> (2/3,1/1) Matrix(373,-682,204,-373) -> Matrix(-1,2,0,1) (31/17,11/6) -> (1/1,1/0) Matrix(163,-364,30,-67) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(291,-668,44,-101) -> Matrix(7,-4,2,-1) Matrix(1741,-4020,754,-1741) -> Matrix(9,-8,10,-9) (30/13,67/29) -> (4/5,1/1) Matrix(2145,-4958,928,-2145) -> Matrix(9,-10,8,-9) (67/29,37/16) -> (1/1,5/4) Matrix(129,-304,14,-33) -> Matrix(5,-2,2,-1) Matrix(169,-408,70,-169) -> Matrix(5,-4,6,-5) (12/5,17/7) -> (2/3,1/1) Matrix(69,-170,28,-69) -> Matrix(-1,2,0,1) (17/7,5/2) -> (1/1,1/0) Matrix(1061,-2778,186,-487) -> Matrix(3,-2,2,-1) 1/1 Matrix(209,-560,78,-209) -> Matrix(5,-4,6,-5) (8/3,35/13) -> (2/3,1/1) Matrix(701,-1890,260,-701) -> Matrix(13,-14,12,-13) (35/13,27/10) -> (1/1,7/6) Matrix(167,-456,26,-71) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(201,-566,38,-107) -> Matrix(3,-2,2,-1) 1/1 Matrix(37,-108,12,-35) -> Matrix(3,-2,2,-1) 1/1 Matrix(221,-740,66,-221) -> Matrix(5,-4,6,-5) (10/3,37/11) -> (2/3,1/1) Matrix(593,-1998,176,-593) -> Matrix(17,-18,16,-17) (37/11,27/8) -> (1/1,9/8) Matrix(357,-1226,76,-261) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(151,-570,40,-151) -> Matrix(7,-6,8,-7) (15/4,19/5) -> (3/4,1/1) Matrix(39,-152,10,-39) -> Matrix(3,-4,2,-3) (19/5,4/1) -> (1/1,2/1) Matrix(41,-200,8,-39) -> Matrix(1,0,0,1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.