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 -1/2 1/0 -1/2 -1/1 0/1 -8/17 -1/1 -7/15 -1/1 -6/13 -1/1 0/1 -17/37 0/1 -11/24 -1/1 0/1 -5/11 -1/1 -19/42 -1/2 -2/5 -14/31 -1/1 -1/2 -9/20 -1/1 0/1 -13/29 -1/2 1/0 -4/9 -1/1 1/0 -15/34 -1/1 -4/5 -11/25 -3/4 -1/2 -7/16 0/1 -17/39 -1/2 1/0 -10/23 -1/1 0/1 -3/7 -1/1 -17/40 -1/2 -4/9 -14/33 -1/3 0/1 -11/26 0/1 -19/45 -1/2 1/0 -8/19 -1/1 0/1 -13/31 0/1 -5/12 -2/1 -1/1 -12/29 -1/1 -5/6 -19/46 -2/3 -7/17 -3/4 -1/2 -23/56 0/1 -16/39 -1/2 -1/3 -9/22 -1/1 0/1 -11/27 -1/2 1/0 -2/5 -1/1 -11/28 -2/3 -1/2 -9/23 -1/2 1/0 -7/18 -1/1 0/1 -12/31 -1/1 0/1 -5/13 -1/1 -18/47 -1/1 -4/5 -13/34 -2/3 -47/123 -2/3 -34/89 -1/1 -2/3 -21/55 -3/4 -1/2 -29/76 -1/1 -2/3 -8/21 -1/1 -2/3 -11/29 -2/3 -3/8 -1/2 0/1 -13/35 -1/2 1/0 -23/62 0/1 -10/27 -1/1 1/0 -7/19 -1/1 -18/49 -1/1 -3/4 -11/30 -1/1 -2/3 -15/41 -3/4 -1/2 -4/11 -1/1 -2/3 -9/25 -1/2 -5/14 0/1 -16/45 -1/1 0/1 -11/31 -1/1 -6/17 -1/1 0/1 -7/20 -1/1 -2/3 -8/23 -1/1 -1/3 -1/2 1/0 -7/22 0/1 -6/19 -1/3 0/1 -5/16 -1/1 0/1 -9/29 0/1 -13/42 -1/1 0/1 -4/13 -1/1 -7/23 -1/2 -3/10 -1/3 0/1 -11/37 -1/2 -1/4 -8/27 -1/3 0/1 -5/17 0/1 -12/41 0/1 1/1 -7/24 0/1 1/0 -9/31 -1/2 1/0 -2/7 -1/1 -1/2 -7/25 -1/3 -5/18 -1/3 0/1 -18/65 -1/3 0/1 -13/47 -1/2 -1/4 -34/123 -1/3 0/1 -21/76 -1/3 0/1 -8/29 -1/3 -3/11 0/1 -10/37 1/1 -7/26 -1/1 0/1 -11/41 0/1 -4/15 -1/1 0/1 -5/19 -1/2 1/0 -11/42 -2/3 -1/2 -6/23 -1/2 -1/3 -1/4 0/1 -5/21 -1/2 1/0 -4/17 -1/1 0/1 -7/30 -2/3 -1/2 -10/43 -1/1 -3/13 -1/2 -1/4 -8/35 -1/3 -5/22 -1/6 0/1 -2/9 0/1 1/1 -5/23 -1/1 -8/37 -1/1 0/1 -3/14 -1/1 0/1 -10/47 -1/1 0/1 -7/33 -1/2 1/0 -4/19 -1/1 -13/62 -1/1 0/1 -9/43 -1/2 1/0 -5/24 -1/1 -2/3 -6/29 -5/9 -1/2 -1/5 0/1 -3/16 -1/1 0/1 -8/43 -1/1 0/1 -5/27 -1/2 1/0 -7/38 0/1 1/0 -2/11 -1/1 -3/17 -1/2 -1/4 -10/57 -1/3 0/1 -7/40 0/1 -4/23 -1/5 0/1 -1/6 0/1 1/0 -3/19 -1/2 1/0 -2/13 -1/1 0/1 -3/20 -1/2 0/1 -4/27 -3/5 -1/2 -1/7 0/1 -2/15 -1/1 0/1 -3/23 -1/1 -4/31 -1/1 -1/8 -1/1 0/1 -1/9 0/1 -1/10 0/1 0/1 -1/1 0/1 1/9 -1/2 1/0 2/17 -1/1 0/1 1/8 0/1 1/7 0/1 2/13 -1/1 3/19 -1/2 1/0 1/6 -1/1 0/1 3/17 -1/1 2/11 -1/1 0/1 3/16 -1/1 0/1 1/5 0/1 4/19 -3/1 1/0 7/33 -1/1 10/47 -1/1 3/14 0/1 1/0 2/9 -1/1 0/1 7/31 -1/2 1/0 5/22 0/1 3/13 -1/2 1/0 4/17 -1/1 9/38 -1/1 0/1 5/21 -1/2 1/0 1/4 -1/2 0/1 5/19 0/1 9/34 0/1 1/8 4/15 0/1 1/3 3/11 1/2 1/0 8/29 0/1 1/1 5/18 0/1 1/0 2/7 -1/1 5/17 -1/2 1/0 3/10 -1/1 0/1 7/23 -1/1 4/13 -1/1 1/0 1/3 0/1 6/17 -5/1 1/0 11/31 -2/1 5/14 -2/1 -1/1 4/11 -1/1 7/19 -1/2 1/0 3/8 -1/1 0/1 5/13 -1/1 12/31 -3/5 -1/2 19/49 -1/1 7/18 -2/3 -1/2 2/5 -1/3 0/1 7/17 0/1 12/29 0/1 1/11 5/12 0/1 1/4 8/19 1/1 19/45 1/2 1/0 11/26 0/1 1/1 14/33 0/1 1/1 3/7 1/2 1/0 13/30 -4/1 1/0 10/23 -1/1 17/39 0/1 7/16 -2/1 1/0 18/41 -2/1 -1/1 11/25 -1/1 4/9 -1/1 0/1 13/29 0/1 22/49 3/1 1/0 9/20 -1/1 0/1 5/11 -1/2 1/0 6/13 -1/1 0/1 7/15 -1/2 1/0 1/2 0/1 7/13 0/1 13/24 0/1 1/1 6/11 1/1 1/0 5/9 -1/2 1/0 9/16 0/1 1/0 22/39 -2/1 -1/1 13/23 -1/1 30/53 -1/1 0/1 17/30 -1/1 0/1 4/7 -1/1 0/1 7/12 -1/1 0/1 3/5 0/1 11/18 0/1 1/3 30/49 1/3 1/2 49/80 2/5 19/31 5/12 1/2 27/44 1/2 8/15 8/13 1/1 29/47 1/1 21/34 0/1 1/1 13/21 1/2 1/0 18/29 0/1 1/1 5/8 0/1 1/1 17/27 0/1 29/46 2/3 12/19 1/1 1/0 31/49 1/2 1/0 19/30 0/1 1/1 64/101 1/1 45/71 1/1 26/41 0/1 1/1 7/11 1/1 9/14 0/1 1/0 11/17 1/1 24/37 1/1 2/1 13/20 2/1 15/23 7/2 1/0 2/3 -1/1 1/0 13/19 -1/2 1/0 11/16 0/1 20/29 -1/1 0/1 9/13 -1/2 1/0 16/23 -1/1 7/10 -1/2 0/1 5/7 0/1 13/18 0/1 1/2 21/29 3/8 1/2 29/40 2/3 8/11 0/1 1/1 19/26 0/1 30/41 1/2 1/1 11/15 1/2 1/0 14/19 1/1 17/23 0/1 3/4 0/1 1/1 10/13 3/1 1/0 7/9 1/0 18/23 -5/1 -4/1 11/14 -2/1 1/0 15/19 -5/2 1/0 4/5 -1/1 17/21 -1/2 1/0 13/16 -1/1 0/1 9/11 0/1 5/6 -1/1 0/1 11/13 0/1 17/20 0/1 1/3 6/7 0/1 1/1 13/15 1/1 7/8 0/1 1/1 -1/2 1/0 9/8 -2/1 1/0 8/7 -1/1 7/6 -2/1 -1/1 13/11 -1/1 19/16 -1/1 -2/3 6/5 -1/1 0/1 17/14 0/1 1/0 28/23 -1/1 11/9 -1/1 16/13 -1/1 0/1 53/43 -1/2 1/0 37/30 -1/1 0/1 21/17 -1/2 1/0 26/21 -1/1 0/1 5/4 0/1 14/11 1/1 1/0 9/7 1/0 22/17 -5/1 13/10 -4/1 1/0 17/13 -3/1 4/3 -2/1 -1/1 15/11 -3/2 1/0 56/41 -2/1 -1/1 97/71 -2/1 41/30 -2/1 -3/2 67/49 -1/1 26/19 -1/1 37/27 -3/2 1/0 11/8 -2/1 -1/1 7/5 -1/1 17/12 -1/1 -2/3 44/31 -3/5 27/19 -1/2 -1/4 37/26 0/1 47/33 -1/2 1/0 10/7 -1/1 -1/2 13/9 -1/2 1/0 42/29 -1/1 1/0 71/49 -1/1 29/20 -1/1 0/1 16/11 -1/1 3/2 0/1 1/0 26/17 -9/1 1/0 23/15 -9/2 1/0 20/13 -3/1 37/24 -3/1 -2/1 17/11 -2/1 31/20 -2/1 45/29 -3/2 1/0 59/38 -2/1 -1/1 73/47 -1/1 14/9 -1/1 1/0 25/16 -4/1 -3/1 11/7 -2/1 41/26 -2/1 -1/1 71/45 -2/1 30/19 -2/1 -1/1 49/31 -3/2 1/0 68/43 -1/1 19/12 -2/1 1/0 46/29 -5/3 73/46 -3/2 -16/11 27/17 -1/1 8/5 -2/1 -1/1 37/23 -1/1 29/18 -2/1 -1/1 21/13 -3/2 1/0 55/34 -2/1 -1/1 89/55 -3/2 1/0 123/76 -2/1 -1/1 34/21 -2/1 -1/1 13/8 -2/1 5/3 -1/1 17/10 -2/3 63/37 -4/7 46/27 -9/17 -1/2 121/71 -1/2 75/44 -1/2 -12/25 29/17 -1/2 -3/8 70/41 -1/3 41/24 -1/2 0/1 12/7 -1/1 0/1 43/25 -1/1 74/43 -1/1 31/18 -1/1 0/1 112/65 -1/1 81/47 -1/2 1/0 50/29 -1/1 1/0 19/11 -1/1 7/4 -1/1 0/1 30/17 -1/1 0/1 23/13 0/1 62/35 0/1 1/1 39/22 0/1 1/1 16/9 -1/1 1/0 25/14 -2/1 9/5 -1/2 1/0 20/11 1/1 1/0 31/17 1/0 42/23 -5/1 1/0 11/6 -2/1 1/0 24/13 -2/1 -1/1 13/7 -1/1 15/8 -2/1 1/0 2/1 -1/1 17/8 -1/2 0/1 15/7 -1/2 1/0 13/6 -1/1 0/1 24/11 -1/1 0/1 11/5 -1/2 1/0 31/14 0/1 20/9 -1/1 0/1 49/22 -4/1 1/0 29/13 -1/1 9/4 -1/1 0/1 34/15 -1/1 0/1 25/11 0/1 16/7 1/1 1/0 23/10 0/1 53/23 1/1 30/13 3/1 1/0 67/29 1/0 104/45 -15/1 1/0 37/16 -6/1 1/0 7/3 -3/2 1/0 40/17 -1/1 33/14 -2/1 -1/1 59/25 -1/1 26/11 -2/1 -1/1 19/8 -2/1 69/29 -25/16 -3/2 50/21 -3/2 -19/13 31/13 -4/3 12/5 -5/4 -1/1 17/7 -1/1 22/9 -1/1 -9/10 5/2 -1/1 -2/3 23/9 -1/2 18/7 -1/2 -1/3 49/19 0/1 31/12 -1/2 -2/5 13/5 0/1 34/13 -1/1 0/1 55/21 0/1 21/8 -1/1 0/1 8/3 -1/1 0/1 35/13 -1/2 1/0 62/23 -1/1 0/1 27/10 -1/1 0/1 19/7 -1/2 1/0 30/11 -1/1 0/1 41/15 -1/1 52/19 -1/2 -1/3 11/4 0/1 58/21 -1/1 1/0 47/17 -1/2 1/0 36/13 -1/1 0/1 25/9 -1/2 1/0 14/5 0/1 1/1 17/6 4/1 1/0 3/1 -1/1 19/6 -6/11 -1/2 73/23 -1/2 54/17 -1/2 -15/31 35/11 -1/2 -9/20 16/5 -1/3 13/4 0/1 1/0 49/15 -1/2 1/0 85/26 0/1 36/11 -1/1 0/1 23/7 0/1 10/3 -1/1 0/1 37/11 -1/2 1/0 64/19 -1/1 0/1 27/8 -1/1 0/1 17/5 -1/2 1/0 24/7 -1/1 -1/2 55/16 -1/2 -2/5 31/9 0/1 7/2 0/1 25/7 1/0 18/5 -1/1 1/0 47/13 -2/1 76/21 -2/1 -1/1 29/8 -2/1 -1/1 11/3 -3/2 1/0 37/10 -2/1 -1/1 63/17 -3/2 1/0 89/24 -2/1 -3/2 26/7 -1/1 15/4 -4/3 -1/1 19/5 -1/1 23/6 -1/1 -6/7 4/1 -1/1 -1/2 21/5 -1/2 1/0 59/14 -1/2 0/1 97/23 0/1 38/9 -1/1 0/1 55/13 0/1 17/4 0/1 30/7 -1/1 0/1 13/3 -1/2 1/0 35/8 0/1 1/0 22/5 -1/1 31/7 -1/2 1/0 40/9 -1/1 0/1 9/2 -1/1 0/1 23/5 0/1 60/13 -1/1 1/0 37/8 0/1 14/3 -1/1 1/0 47/10 0/1 33/7 0/1 52/11 1/1 19/4 2/1 1/0 5/1 -1/1 21/4 -4/7 -1/2 16/3 -1/1 0/1 27/5 -1/2 1/0 11/2 -1/1 0/1 28/5 -1/1 45/8 -1/2 -2/5 17/3 0/1 40/7 -1/1 0/1 23/4 0/1 6/1 -1/1 0/1 19/3 -1/2 1/0 13/2 0/1 20/3 1/1 1/0 7/1 -1/1 22/3 -3/5 -1/2 15/2 -1/2 0/1 8/1 -1/1 17/2 -1/1 0/1 43/5 -1/2 1/0 26/3 -1/1 0/1 9/1 -1/2 1/0 10/1 -1/1 0/1 1/0 -1/1 0/1 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(3,2,-2,-1) Matrix(269,126,1266,593) -> Matrix(1,0,0,1) Matrix(983,456,360,167) -> Matrix(1,0,0,1) Matrix(1869,860,-4892,-2251) -> Matrix(1,2,-2,-3) Matrix(1777,816,1152,529) -> Matrix(1,-2,0,1) Matrix(795,364,356,163) -> Matrix(1,0,0,1) Matrix(1757,796,788,357) -> Matrix(3,2,-2,-1) Matrix(2713,1226,790,357) -> Matrix(1,0,0,1) Matrix(523,236,964,435) -> Matrix(1,0,2,1) Matrix(699,314,1654,743) -> Matrix(1,0,2,1) Matrix(175,78,258,115) -> Matrix(1,0,0,1) Matrix(343,152,88,39) -> Matrix(1,2,-2,-3) Matrix(431,190,-2062,-909) -> Matrix(3,2,-2,-1) Matrix(769,338,430,189) -> Matrix(3,2,-2,-1) Matrix(1105,482,-2978,-1299) -> Matrix(1,0,0,1) Matrix(427,186,-2298,-1001) -> Matrix(1,0,0,1) Matrix(677,294,426,185) -> Matrix(3,2,-2,-1) Matrix(1591,678,1002,427) -> Matrix(5,4,-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(1,0,0,1) Matrix(583,246,-2742,-1157) -> Matrix(1,0,0,1) Matrix(333,140,-1244,-523) -> Matrix(1,0,0,1) Matrix(907,380,580,243) -> Matrix(1,-2,0,1) Matrix(409,170,166,69) -> Matrix(3,4,-4,-5) Matrix(1393,576,2208,913) -> Matrix(5,4,6,5) Matrix(407,168,1800,743) -> Matrix(3,2,-2,-1) Matrix(1061,436,1628,669) -> Matrix(5,2,2,1) Matrix(3341,1372,1220,501) -> Matrix(1,0,0,1) Matrix(1873,768,1056,433) -> Matrix(1,0,2,1) Matrix(891,364,164,67) -> Matrix(1,0,0,1) Matrix(887,360,648,263) -> Matrix(3,2,-2,-1) Matrix(869,342,714,281) -> Matrix(3,2,-2,-1) Matrix(393,154,-1498,-587) -> Matrix(1,0,0,1) Matrix(865,338,238,93) -> Matrix(3,2,-2,-1) Matrix(237,92,-1100,-427) -> Matrix(1,0,0,1) Matrix(389,150,-1014,-391) -> Matrix(3,4,-4,-5) Matrix(1635,626,2254,863) -> Matrix(5,4,6,5) Matrix(3961,1514,934,357) -> Matrix(3,2,-2,-1) Matrix(3027,1156,-10948,-4181) -> Matrix(3,2,-8,-5) Matrix(1399,534,-6678,-2549) -> Matrix(3,2,-2,-1) Matrix(2637,1006,4658,1777) -> Matrix(3,2,-2,-1) Matrix(773,294,234,89) -> Matrix(3,2,-2,-1) Matrix(1003,380,388,147) -> Matrix(3,2,-8,-5) Matrix(75,28,308,115) -> Matrix(1,0,0,1) Matrix(2137,792,456,169) -> Matrix(1,0,0,1) Matrix(531,196,-1444,-533) -> Matrix(3,4,-4,-5) Matrix(1439,528,2352,863) -> Matrix(3,2,10,7) Matrix(983,360,456,167) -> Matrix(3,2,-2,-1) Matrix(455,166,74,27) -> Matrix(3,2,-2,-1) Matrix(527,190,674,243) -> Matrix(11,6,-2,-1) Matrix(525,188,148,53) -> Matrix(1,0,2,1) Matrix(73,26,598,213) -> Matrix(1,0,0,1) Matrix(2831,1006,4466,1587) -> Matrix(1,0,2,1) Matrix(965,342,522,185) -> Matrix(3,2,-2,-1) Matrix(443,156,372,131) -> Matrix(1,0,0,1) Matrix(1251,436,812,283) -> Matrix(7,4,-2,-1) Matrix(877,302,514,177) -> Matrix(3,2,-8,-5) Matrix(565,182,922,297) -> Matrix(5,2,12,5) Matrix(775,246,1194,379) -> Matrix(5,2,2,1) Matrix(419,132,492,155) -> Matrix(1,0,4,1) Matrix(489,152,904,281) -> Matrix(1,0,2,1) Matrix(4171,1292,2644,819) -> Matrix(3,2,-2,-1) Matrix(557,172,68,21) -> Matrix(1,0,0,1) Matrix(623,190,482,147) -> Matrix(11,6,-2,-1) Matrix(345,104,136,41) -> Matrix(5,2,-8,-3) Matrix(67,20,412,123) -> Matrix(1,0,2,1) Matrix(411,122,886,263) -> Matrix(1,0,2,1) Matrix(339,100,-1156,-341) -> Matrix(1,0,4,1) Matrix(1969,576,1152,337) -> Matrix(1,0,-2,1) Matrix(337,98,-1826,-531) -> Matrix(1,0,0,1) Matrix(271,78,66,19) -> Matrix(1,0,0,1) Matrix(335,94,866,243) -> Matrix(5,2,-8,-3) Matrix(201,56,664,185) -> Matrix(1,0,2,1) Matrix(3651,1012,2060,571) -> Matrix(1,0,4,1) Matrix(665,184,-3784,-1047) -> Matrix(1,0,0,1) Matrix(17713,4896,10944,3025) -> Matrix(7,2,-4,-1) Matrix(333,92,-2588,-715) -> Matrix(1,0,2,1) Matrix(197,54,-726,-199) -> Matrix(1,0,4,1) Matrix(1773,478,1250,337) -> Matrix(1,2,-2,-3) Matrix(1967,528,1248,335) -> Matrix(3,2,-2,-1) Matrix(197,52,716,189) -> Matrix(1,0,2,1) Matrix(2017,528,1104,289) -> Matrix(7,4,-2,-1) Matrix(907,236,196,51) -> Matrix(1,0,2,1) Matrix(695,166,314,75) -> Matrix(1,0,0,1) Matrix(691,164,316,75) -> Matrix(1,0,0,1) Matrix(813,190,1442,337) -> Matrix(3,2,-2,-1) Matrix(2377,554,502,117) -> Matrix(1,0,2,1) Matrix(1249,290,814,189) -> Matrix(7,4,-2,-1) Matrix(1371,314,310,71) -> Matrix(1,0,2,1) Matrix(1677,382,1058,241) -> Matrix(11,2,-6,-1) Matrix(309,70,746,169) -> Matrix(1,0,10,1) Matrix(245,54,186,41) -> Matrix(1,-2,0,1) Matrix(857,186,1350,293) -> Matrix(1,0,2,1) Matrix(2137,456,792,169) -> Matrix(1,0,0,1) Matrix(123,26,790,167) -> Matrix(1,0,0,1) Matrix(7533,1580,4372,917) -> Matrix(1,0,0,1) Matrix(789,164,1756,365) -> Matrix(3,2,-2,-1) Matrix(2057,424,1208,249) -> Matrix(9,4,-16,-7) Matrix(297,56,472,89) -> Matrix(1,0,2,1) Matrix(2185,408,648,121) -> Matrix(1,0,0,1) Matrix(413,76,1940,357) -> Matrix(1,0,0,1) Matrix(233,42,294,53) -> Matrix(3,2,-2,-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(1,0,0,1) Matrix(739,116,172,27) -> Matrix(1,0,0,1) Matrix(623,94,338,51) -> Matrix(3,2,-2,-1) Matrix(845,126,114,17) -> Matrix(1,0,0,1) Matrix(505,74,1126,165) -> Matrix(1,0,2,1) 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(1,0,2,1) Matrix(163,20,220,27) -> Matrix(1,0,2,1) Matrix(753,80,160,17) -> Matrix(1,0,0,1) Matrix(265,26,214,21) -> Matrix(1,0,0,1) Matrix(391,-40,88,-9) -> Matrix(1,0,0,1) Matrix(387,-44,44,-5) -> Matrix(1,0,0,1) Matrix(297,-38,86,-11) -> Matrix(1,0,0,1) Matrix(291,-44,668,-101) -> Matrix(1,0,0,1) Matrix(531,-92,860,-149) -> Matrix(1,0,2,1) Matrix(245,-44,284,-51) -> Matrix(1,0,2,1) Matrix(527,-98,242,-45) -> Matrix(1,0,0,1) Matrix(201,-38,566,-107) -> Matrix(3,2,-2,-1) Matrix(239,-50,674,-141) -> Matrix(1,-2,0,1) Matrix(2495,-528,912,-193) -> Matrix(1,2,-2,-3) Matrix(237,-52,196,-43) -> Matrix(1,0,0,1) Matrix(391,-88,40,-9) -> Matrix(1,0,0,1) Matrix(429,-98,626,-143) -> Matrix(1,0,0,1) Matrix(427,-100,1012,-237) -> Matrix(1,0,2,1) Matrix(2755,-652,4348,-1029) -> Matrix(1,0,2,1) Matrix(2949,-700,1900,-451) -> Matrix(3,2,-2,-1) Matrix(191,-50,722,-189) -> Matrix(1,0,10,1) Matrix(529,-142,190,-51) -> Matrix(1,0,-2,1) Matrix(527,-146,1202,-333) -> Matrix(1,-2,0,1) Matrix(487,-136,376,-105) -> Matrix(1,-4,0,1) Matrix(335,-98,482,-141) -> Matrix(1,0,0,1) Matrix(629,-186,186,-55) -> Matrix(1,0,0,1) Matrix(1397,-426,810,-247) -> Matrix(1,0,0,1) Matrix(439,-136,184,-57) -> Matrix(5,4,-4,-3) Matrix(677,-236,284,-99) -> Matrix(3,-4,-2,3) Matrix(529,-190,142,-51) -> Matrix(3,2,-2,-1) Matrix(387,-142,526,-193) -> Matrix(1,0,2,1) Matrix(665,-246,246,-91) -> Matrix(1,0,0,1) Matrix(243,-92,140,-53) -> Matrix(1,0,0,1) Matrix(3113,-1206,1350,-523) -> Matrix(1,0,2,1) Matrix(3215,-1248,2352,-913) -> Matrix(5,4,-4,-3) Matrix(379,-148,484,-189) -> Matrix(7,4,-2,-1) Matrix(239,-98,578,-237) -> Matrix(1,0,14,1) Matrix(439,-184,136,-57) -> Matrix(1,0,-4,1) Matrix(2933,-1242,810,-343) -> Matrix(1,-2,0,1) Matrix(875,-372,708,-301) -> Matrix(1,0,-2,1) Matrix(469,-202,202,-87) -> Matrix(1,-2,0,1) Matrix(1875,-814,334,-145) -> Matrix(1,2,-2,-3) Matrix(2641,-1152,768,-335) -> Matrix(1,0,-2,1) Matrix(3069,-1348,1300,-571) -> Matrix(1,0,0,1) Matrix(533,-236,332,-147) -> Matrix(3,2,-2,-1) Matrix(861,-388,628,-283) -> Matrix(3,2,-2,-1) Matrix(527,-242,98,-45) -> Matrix(1,0,0,1) Matrix(555,-262,358,-169) -> Matrix(3,2,-2,-1) Matrix(437,-234,282,-151) -> Matrix(1,-2,0,1) Matrix(279,-154,154,-85) -> Matrix(1,0,0,1) Matrix(339,-190,430,-241) -> Matrix(1,-2,0,1) Matrix(1197,-676,2116,-1195) -> Matrix(1,2,-2,-3) Matrix(307,-174,30,-17) -> Matrix(1,0,0,1) Matrix(243,-140,92,-53) -> Matrix(1,0,0,1) Matrix(91,-54,150,-89) -> Matrix(1,0,4,1) Matrix(5179,-3172,1876,-1149) -> Matrix(5,-2,-2,1) Matrix(3601,-2208,2112,-1295) -> Matrix(9,-4,-20,9) Matrix(2973,-1826,1874,-1151) -> Matrix(13,-8,-8,5) Matrix(4037,-2490,2346,-1447) -> Matrix(1,0,-2,1) Matrix(1869,-1156,1156,-715) -> Matrix(1,-2,0,1) Matrix(1481,-918,534,-331) -> Matrix(1,0,-2,1) Matrix(533,-332,236,-147) -> Matrix(1,0,-2,1) Matrix(3357,-2116,1972,-1243) -> Matrix(7,-4,-12,7) Matrix(1383,-874,970,-613) -> Matrix(1,0,-2,1) Matrix(3703,-2344,1000,-633) -> Matrix(1,-2,0,1) Matrix(381,-244,292,-187) -> Matrix(1,-4,0,1) Matrix(437,-282,234,-151) -> Matrix(1,-2,0,1) Matrix(667,-436,436,-285) -> Matrix(1,-8,0,1) Matrix(1307,-900,228,-157) -> Matrix(1,0,0,1) Matrix(1163,-804,852,-589) -> Matrix(3,2,-2,-1) Matrix(425,-296,56,-39) -> Matrix(1,0,0,1) Matrix(141,-100,196,-139) -> Matrix(1,0,4,1) Matrix(279,-202,250,-181) -> Matrix(5,-2,-2,1) Matrix(3311,-2400,1392,-1009) -> Matrix(13,-8,-8,5) Matrix(861,-628,388,-283) -> Matrix(1,0,-2,1) Matrix(3077,-2250,666,-487) -> Matrix(1,0,-2,1) Matrix(1163,-852,804,-589) -> Matrix(1,0,-2,1) Matrix(1823,-1346,386,-285) -> Matrix(1,0,0,1) Matrix(381,-292,244,-187) -> Matrix(1,-4,0,1) Matrix(487,-376,136,-105) -> Matrix(1,-4,0,1) Matrix(875,-708,372,-301) -> Matrix(3,2,-2,-1) Matrix(1113,-902,902,-731) -> Matrix(1,0,0,1) Matrix(1111,-904,424,-345) -> Matrix(1,0,0,1) Matrix(237,-196,52,-43) -> Matrix(1,0,0,1) Matrix(287,-242,338,-285) -> Matrix(1,0,4,1) Matrix(769,-670,334,-291) -> Matrix(1,0,0,1) Matrix(253,-226,178,-159) -> Matrix(1,0,-2,1) Matrix(677,-764,428,-483) -> Matrix(1,0,0,1) Matrix(245,-284,44,-51) -> Matrix(1,2,-2,-3) Matrix(287,-338,242,-285) -> Matrix(3,4,-4,-5) Matrix(1775,-2162,1298,-1581) -> Matrix(3,2,-2,-1) Matrix(667,-820,388,-477) -> Matrix(1,0,0,1) Matrix(1677,-2066,194,-239) -> Matrix(1,0,0,1) Matrix(2021,-2492,236,-291) -> Matrix(1,0,0,1) Matrix(339,-430,190,-241) -> Matrix(1,-2,0,1) Matrix(379,-484,148,-189) -> Matrix(1,-2,-2,5) Matrix(387,-526,142,-193) -> Matrix(1,2,-2,-3) Matrix(6675,-9118,1582,-2161) -> Matrix(1,2,-2,-3) Matrix(7099,-9700,1684,-2301) -> Matrix(1,2,-4,-7) Matrix(141,-196,100,-139) -> Matrix(3,4,-4,-5) Matrix(1389,-1972,436,-619) -> Matrix(7,4,-16,-9) Matrix(4079,-5808,1248,-1777) -> Matrix(1,0,0,1) Matrix(335,-482,98,-141) -> Matrix(1,0,0,1) Matrix(2803,-4060,1804,-2613) -> Matrix(1,0,0,1) Matrix(4351,-6306,2802,-4061) -> Matrix(3,2,-2,-1) Matrix(1821,-2642,1058,-1535) -> Matrix(1,0,0,1) Matrix(429,-626,98,-143) -> Matrix(1,0,0,1) Matrix(837,-1274,362,-551) -> Matrix(1,-6,0,1) Matrix(2755,-4348,652,-1029) -> Matrix(1,2,-2,-3) Matrix(2009,-3174,726,-1147) -> Matrix(1,2,-2,-3) Matrix(6955,-10996,4036,-6381) -> Matrix(1,2,-2,-3) Matrix(1821,-2932,772,-1243) -> Matrix(1,0,0,1) Matrix(679,-1096,184,-297) -> Matrix(1,0,0,1) Matrix(9791,-15842,6050,-9789) -> Matrix(1,0,0,1) Matrix(531,-860,92,-149) -> Matrix(1,2,-2,-3) Matrix(91,-150,54,-89) -> Matrix(3,4,-4,-5) Matrix(5805,-9892,1828,-3115) -> Matrix(47,24,-96,-49) Matrix(4561,-7774,1438,-2451) -> Matrix(37,18,-72,-35) Matrix(4273,-7296,1152,-1967) -> Matrix(7,2,-4,-1) Matrix(4089,-7048,1480,-2551) -> Matrix(1,0,0,1) Matrix(313,-550,70,-123) -> Matrix(1,0,0,1) Matrix(1197,-2116,676,-1195) -> Matrix(1,0,2,1) Matrix(1055,-1922,578,-1053) -> Matrix(1,-6,0,1) Matrix(33,-64,16,-31) -> Matrix(1,2,-2,-3) Matrix(581,-1242,138,-295) -> Matrix(1,0,0,1) Matrix(1541,-3498,426,-967) -> Matrix(3,2,-2,-1) Matrix(527,-1202,146,-333) -> Matrix(1,-2,0,1) Matrix(291,-668,44,-101) -> Matrix(1,0,0,1) Matrix(3887,-8978,1682,-3885) -> Matrix(1,-18,0,1) Matrix(427,-1012,100,-237) -> Matrix(1,2,-2,-3) Matrix(2301,-5476,724,-1723) -> Matrix(17,26,-36,-55) Matrix(239,-578,98,-237) -> Matrix(13,14,-14,-15) Matrix(1301,-3354,282,-727) -> Matrix(1,0,2,1) Matrix(1059,-2732,188,-485) -> Matrix(1,0,0,1) Matrix(479,-1250,146,-381) -> Matrix(1,0,0,1) Matrix(1061,-2778,186,-487) -> Matrix(1,0,0,1) Matrix(911,-2450,338,-909) -> Matrix(1,0,0,1) Matrix(201,-566,38,-107) -> Matrix(1,0,-2,1) Matrix(37,-108,12,-35) -> Matrix(1,2,-2,-3) Matrix(1587,-5180,428,-1397) -> Matrix(3,2,-2,-1) Matrix(815,-2738,242,-813) -> Matrix(1,0,0,1) Matrix(191,-722,50,-189) -> Matrix(9,10,-10,-11) Matrix(41,-200,8,-39) -> Matrix(1,2,-2,-3) Matrix(43,-294,6,-41) -> Matrix(1,2,-2,-3) 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): 43 Degree of the the map X: 43 Degree of the the map Y: 256 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 768 Minimal number of generators: 129 Number of equivalence classes of elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 56 Genus: 37 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/7 1/5 3/13 1/3 5/11 1/2 3/5 5/7 7/9 1/1 13/11 11/9 53/43 9/7 7/5 71/49 11/7 89/55 5/3 121/71 23/13 31/17 2/1 11/5 25/11 67/29 17/7 13/5 35/13 11/4 47/17 3/1 37/11 17/5 7/2 11/3 63/17 19/5 4/1 17/4 13/3 9/2 5/1 16/3 11/2 17/3 23/4 6/1 13/2 20/3 7/1 15/2 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/2 1/0 0/1 -1/1 0/1 1/9 -1/2 1/0 1/8 0/1 1/7 0/1 2/13 -1/1 1/6 -1/1 0/1 3/17 -1/1 2/11 -1/1 0/1 3/16 -1/1 0/1 1/5 0/1 4/19 -3/1 1/0 7/33 -1/1 3/14 0/1 1/0 2/9 -1/1 0/1 5/22 0/1 3/13 -1/2 1/0 4/17 -1/1 1/4 -1/2 0/1 5/19 0/1 4/15 0/1 1/3 3/11 1/2 1/0 5/18 0/1 1/0 2/7 -1/1 5/17 -1/2 1/0 3/10 -1/1 0/1 4/13 -1/1 1/0 1/3 0/1 6/17 -5/1 1/0 11/31 -2/1 5/14 -2/1 -1/1 4/11 -1/1 7/19 -1/2 1/0 3/8 -1/1 0/1 5/13 -1/1 7/18 -2/3 -1/2 2/5 -1/3 0/1 7/17 0/1 5/12 0/1 1/4 8/19 1/1 11/26 0/1 1/1 14/33 0/1 1/1 3/7 1/2 1/0 13/30 -4/1 1/0 10/23 -1/1 17/39 0/1 7/16 -2/1 1/0 11/25 -1/1 4/9 -1/1 0/1 9/20 -1/1 0/1 5/11 -1/2 1/0 6/13 -1/1 0/1 1/2 0/1 7/13 0/1 6/11 1/1 1/0 5/9 -1/2 1/0 9/16 0/1 1/0 13/23 -1/1 17/30 -1/1 0/1 4/7 -1/1 0/1 7/12 -1/1 0/1 3/5 0/1 11/18 0/1 1/3 19/31 5/12 1/2 27/44 1/2 8/15 8/13 1/1 29/47 1/1 21/34 0/1 1/1 13/21 1/2 1/0 18/29 0/1 1/1 5/8 0/1 1/1 12/19 1/1 1/0 31/49 1/2 1/0 19/30 0/1 1/1 7/11 1/1 9/14 0/1 1/0 11/17 1/1 13/20 2/1 2/3 -1/1 1/0 11/16 0/1 20/29 -1/1 0/1 9/13 -1/2 1/0 16/23 -1/1 7/10 -1/2 0/1 5/7 0/1 13/18 0/1 1/2 21/29 3/8 1/2 8/11 0/1 1/1 19/26 0/1 30/41 1/2 1/1 11/15 1/2 1/0 14/19 1/1 3/4 0/1 1/1 10/13 3/1 1/0 7/9 1/0 11/14 -2/1 1/0 4/5 -1/1 17/21 -1/2 1/0 13/16 -1/1 0/1 9/11 0/1 5/6 -1/1 0/1 11/13 0/1 6/7 0/1 1/1 13/15 1/1 7/8 0/1 1/1 -1/2 1/0 9/8 -2/1 1/0 8/7 -1/1 7/6 -2/1 -1/1 13/11 -1/1 6/5 -1/1 0/1 17/14 0/1 1/0 11/9 -1/1 16/13 -1/1 0/1 53/43 -1/2 1/0 37/30 -1/1 0/1 21/17 -1/2 1/0 5/4 0/1 14/11 1/1 1/0 9/7 1/0 13/10 -4/1 1/0 4/3 -2/1 -1/1 15/11 -3/2 1/0 56/41 -2/1 -1/1 97/71 -2/1 41/30 -2/1 -3/2 26/19 -1/1 11/8 -2/1 -1/1 7/5 -1/1 17/12 -1/1 -2/3 27/19 -1/2 -1/4 37/26 0/1 47/33 -1/2 1/0 10/7 -1/1 -1/2 13/9 -1/2 1/0 42/29 -1/1 1/0 71/49 -1/1 29/20 -1/1 0/1 16/11 -1/1 3/2 0/1 1/0 20/13 -3/1 17/11 -2/1 31/20 -2/1 14/9 -1/1 1/0 11/7 -2/1 30/19 -2/1 -1/1 49/31 -3/2 1/0 68/43 -1/1 19/12 -2/1 1/0 8/5 -2/1 -1/1 37/23 -1/1 29/18 -2/1 -1/1 21/13 -3/2 1/0 55/34 -2/1 -1/1 89/55 -3/2 1/0 34/21 -2/1 -1/1 13/8 -2/1 5/3 -1/1 17/10 -2/3 46/27 -9/17 -1/2 121/71 -1/2 75/44 -1/2 -12/25 29/17 -1/2 -3/8 12/7 -1/1 0/1 43/25 -1/1 74/43 -1/1 31/18 -1/1 0/1 19/11 -1/1 7/4 -1/1 0/1 30/17 -1/1 0/1 23/13 0/1 16/9 -1/1 1/0 9/5 -1/2 1/0 20/11 1/1 1/0 31/17 1/0 11/6 -2/1 1/0 13/7 -1/1 15/8 -2/1 1/0 2/1 -1/1 13/6 -1/1 0/1 11/5 -1/2 1/0 20/9 -1/1 0/1 9/4 -1/1 0/1 34/15 -1/1 0/1 25/11 0/1 16/7 1/1 1/0 23/10 0/1 30/13 3/1 1/0 67/29 1/0 37/16 -6/1 1/0 7/3 -3/2 1/0 33/14 -2/1 -1/1 26/11 -2/1 -1/1 19/8 -2/1 50/21 -3/2 -19/13 31/13 -4/3 12/5 -5/4 -1/1 17/7 -1/1 5/2 -1/1 -2/3 18/7 -1/2 -1/3 13/5 0/1 34/13 -1/1 0/1 55/21 0/1 21/8 -1/1 0/1 8/3 -1/1 0/1 35/13 -1/2 1/0 27/10 -1/1 0/1 19/7 -1/2 1/0 30/11 -1/1 0/1 11/4 0/1 47/17 -1/2 1/0 36/13 -1/1 0/1 25/9 -1/2 1/0 14/5 0/1 1/1 17/6 4/1 1/0 3/1 -1/1 19/6 -6/11 -1/2 16/5 -1/3 13/4 0/1 1/0 10/3 -1/1 0/1 37/11 -1/2 1/0 27/8 -1/1 0/1 17/5 -1/2 1/0 24/7 -1/1 -1/2 31/9 0/1 7/2 0/1 18/5 -1/1 1/0 11/3 -3/2 1/0 37/10 -2/1 -1/1 63/17 -3/2 1/0 26/7 -1/1 15/4 -4/3 -1/1 19/5 -1/1 4/1 -1/1 -1/2 17/4 0/1 13/3 -1/2 1/0 22/5 -1/1 9/2 -1/1 0/1 23/5 0/1 14/3 -1/1 1/0 33/7 0/1 19/4 2/1 1/0 5/1 -1/1 21/4 -4/7 -1/2 16/3 -1/1 0/1 11/2 -1/1 0/1 28/5 -1/1 17/3 0/1 40/7 -1/1 0/1 23/4 0/1 6/1 -1/1 0/1 13/2 0/1 20/3 1/1 1/0 7/1 -1/1 15/2 -1/2 0/1 8/1 -1/1 9/1 -1/2 1/0 1/0 -1/1 0/1 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(304,-33,129,-14) (0/1,1/9) -> (7/3,33/14) Hyperbolic Matrix(172,-21,213,-26) (1/9,1/8) -> (4/5,17/21) 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(456,-71,167,-26) (2/13,1/6) -> (30/11,11/4) 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(364,-67,163,-30) (2/11,3/16) -> (20/9,9/4) 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(554,-117,1269,-268) (4/19,7/33) -> (17/39,7/16) Hyperbolic Matrix(1226,-261,357,-76) (7/33,3/14) -> (24/7,31/9) Hyperbolic Matrix(237,-52,196,-43) (3/14,2/9) -> (6/5,17/14) Hyperbolic Matrix(314,-71,743,-168) (2/9,5/22) -> (8/19,11/26) Hyperbolic Matrix(118,-27,507,-116) (5/22,3/13) -> (3/13,4/17) Parabolic Matrix(78,-19,115,-28) (4/17,1/4) -> (2/3,11/16) Hyperbolic Matrix(152,-39,39,-10) (1/4,5/19) -> (19/5,4/1) Hyperbolic Matrix(570,-151,151,-40) (5/19,4/15) -> (15/4,19/5) Hyperbolic Matrix(529,-142,190,-51) (4/15,3/11) -> (25/9,14/5) Hyperbolic Matrix(338,-93,189,-52) (3/11,5/18) -> (16/9,9/5) Hyperbolic Matrix(188,-53,149,-42) (5/18,2/7) -> (5/4,14/11) 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(294,-89,185,-56) (3/10,4/13) -> (19/12,8/5) 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(380,-147,243,-94) (5/13,7/18) -> (14/9,11/7) Hyperbolic Matrix(104,-41,137,-54) (7/18,2/5) -> (3/4,10/13) Hyperbolic Matrix(170,-69,69,-28) (2/5,7/17) -> (17/7,5/2) Hyperbolic Matrix(408,-169,169,-70) (7/17,5/12) -> (12/5,17/7) Hyperbolic Matrix(439,-184,136,-57) (5/12,8/19) -> (16/5,13/4) Hyperbolic Matrix(574,-243,1011,-428) (11/26,14/33) -> (17/30,4/7) Hyperbolic Matrix(304,-129,33,-14) (14/33,3/7) -> (9/1,1/0) Hyperbolic Matrix(469,-202,202,-87) (3/7,13/30) -> (37/16,7/3) Hyperbolic Matrix(436,-189,669,-290) (13/30,10/23) -> (13/20,2/3) Hyperbolic Matrix(768,-337,433,-190) (7/16,11/25) -> (23/13,16/9) Hyperbolic Matrix(533,-236,332,-147) (11/25,4/9) -> (8/5,37/23) Hyperbolic Matrix(364,-163,67,-30) (4/9,9/20) -> (16/3,11/2) Hyperbolic Matrix(166,-75,363,-164) (9/20,5/11) -> (5/11,6/13) Parabolic Matrix(360,-167,263,-122) (6/13,1/2) -> (26/19,11/8) Hyperbolic Matrix(437,-234,282,-151) (1/2,7/13) -> (17/11,31/20) Hyperbolic Matrix(342,-185,281,-152) (7/13,6/11) -> (17/14,11/9) Hyperbolic Matrix(279,-154,154,-85) (6/11,5/9) -> (9/5,20/11) Hyperbolic Matrix(338,-189,93,-52) (5/9,9/16) -> (18/5,11/3) Hyperbolic Matrix(768,-433,337,-190) (9/16,13/23) -> (25/11,16/7) Hyperbolic Matrix(1532,-867,675,-382) (13/23,17/30) -> (34/15,25/11) 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(626,-383,863,-528) (11/18,19/31) -> (21/29,8/11) Hyperbolic Matrix(3601,-2208,2112,-1295) (19/31,27/44) -> (75/44,29/17) Hyperbolic Matrix(1486,-913,625,-384) (27/44,8/13) -> (19/8,50/21) 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(294,-185,89,-56) (5/8,12/19) -> (13/4,10/3) 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(764,-485,293,-186) (19/30,7/11) -> (13/5,34/13) Hyperbolic Matrix(380,-243,147,-94) (7/11,9/14) -> (18/7,13/5) Hyperbolic Matrix(437,-282,234,-151) (9/14,11/17) -> (13/7,15/8) Hyperbolic Matrix(816,-529,145,-94) (11/17,13/20) -> (28/5,17/3) 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(360,-263,167,-122) (8/11,19/26) -> (2/1,13/6) Hyperbolic Matrix(472,-345,249,-182) (19/26,30/41) -> (15/8,2/1) Hyperbolic Matrix(1163,-852,804,-589) (30/41,11/15) -> (13/9,42/29) Hyperbolic Matrix(166,-123,27,-20) (14/19,3/4) -> (6/1,13/2) Hyperbolic Matrix(190,-147,243,-188) (10/13,7/9) -> (7/9,11/14) Parabolic Matrix(188,-149,53,-42) (11/14,4/5) -> (7/2,18/5) 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(156,-131,131,-110) (5/6,11/13) -> (13/11,6/5) Hyperbolic Matrix(182,-155,155,-132) (11/13,6/7) -> (7/6,13/11) Hyperbolic Matrix(436,-379,283,-246) (13/15,7/8) -> (20/13,17/11) 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(667,-820,388,-477) (11/9,16/13) -> (12/7,43/25) Hyperbolic Matrix(2280,-2809,1849,-2278) (16/13,53/43) -> (53/43,37/30) Parabolic Matrix(172,-213,21,-26) (21/17,5/4) -> (8/1,9/1) Hyperbolic Matrix(190,-243,147,-188) (14/11,9/7) -> (9/7,13/10) Parabolic Matrix(104,-137,41,-54) (13/10,4/3) -> (5/2,18/7) Hyperbolic Matrix(387,-526,142,-193) (4/3,15/11) -> (19/7,30/11) Hyperbolic Matrix(4970,-6789,3429,-4684) (56/41,97/71) -> (71/49,29/20) Hyperbolic Matrix(5112,-6985,3529,-4822) (97/71,41/30) -> (42/29,71/49) Hyperbolic Matrix(1196,-1635,771,-1054) (41/30,26/19) -> (31/20,14/9) Hyperbolic Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(576,-817,337,-478) (17/12,27/19) -> (29/17,12/7) Hyperbolic Matrix(2496,-3553,673,-958) (37/26,47/33) -> (63/17,26/7) Hyperbolic Matrix(335,-482,98,-141) (10/7,13/9) -> (17/5,24/7) Hyperbolic Matrix(1821,-2642,1058,-1535) (29/20,16/11) -> (74/43,31/18) Hyperbolic Matrix(78,-115,19,-28) (16/11,3/2) -> (4/1,17/4) Hyperbolic Matrix(436,-669,189,-290) (3/2,20/13) -> (23/10,30/13) Hyperbolic Matrix(578,-911,335,-528) (11/7,30/19) -> (31/18,19/11) Hyperbolic Matrix(2009,-3174,726,-1147) (30/19,49/31) -> (47/17,36/13) Hyperbolic Matrix(2362,-3735,855,-1352) (49/31,68/43) -> (11/4,47/17) Hyperbolic Matrix(1104,-1777,625,-1006) (37/23,29/18) -> (30/17,23/13) Hyperbolic Matrix(679,-1096,184,-297) (29/18,21/13) -> (11/3,37/10) Hyperbolic Matrix(4896,-7921,3025,-4894) (55/34,89/55) -> (89/55,34/21) 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(622,-1059,195,-332) (17/10,46/27) -> (19/6,16/5) Hyperbolic Matrix(8592,-14641,5041,-8590) (46/27,121/71) -> (121/71,75/44) Parabolic Matrix(574,-1011,243,-428) (7/4,30/17) -> (33/14,26/11) Hyperbolic Matrix(528,-961,289,-526) (20/11,31/17) -> (31/17,11/6) Parabolic Matrix(236,-435,51,-94) (11/6,13/7) -> (23/5,14/3) Hyperbolic Matrix(166,-363,75,-164) (13/6,11/5) -> (11/5,20/9) Parabolic Matrix(291,-668,44,-101) (16/7,23/10) -> (13/2,20/3) Hyperbolic Matrix(1944,-4489,841,-1942) (30/13,67/29) -> (67/29,37/16) Parabolic Matrix(314,-743,71,-168) (26/11,19/8) -> (22/5,9/2) Hyperbolic Matrix(1061,-2778,186,-487) (34/13,55/21) -> (17/3,40/7) Hyperbolic Matrix(456,-1225,169,-454) (8/3,35/13) -> (35/13,27/10) 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(408,-1369,121,-406) (10/3,37/11) -> (37/11,27/8) Parabolic Matrix(118,-507,27,-116) (17/4,13/3) -> (13/3,22/5) Parabolic Matrix(126,-593,17,-80) (14/3,33/7) -> (7/1,15/2) Hyperbolic Matrix(168,-793,25,-118) (33/7,19/4) -> (20/3,7/1) Hyperbolic Matrix(41,-200,8,-39) (19/4,5/1) -> (5/1,21/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,1,-2,-1) Matrix(304,-33,129,-14) -> Matrix(1,-1,0,1) Matrix(172,-21,213,-26) -> Matrix(1,1,-2,-1) Matrix(297,-38,86,-11) -> Matrix(1,0,0,1) Matrix(291,-44,668,-101) -> Matrix(1,0,0,1) Matrix(456,-71,167,-26) -> Matrix(1,1,-2,-1) Matrix(531,-92,860,-149) -> Matrix(1,0,2,1) Matrix(245,-44,284,-51) -> Matrix(1,0,2,1) Matrix(364,-67,163,-30) -> Matrix(1,1,-2,-1) Matrix(201,-38,566,-107) -> Matrix(3,2,-2,-1) Matrix(239,-50,674,-141) -> Matrix(1,-2,0,1) Matrix(554,-117,1269,-268) -> Matrix(1,1,0,1) Matrix(1226,-261,357,-76) -> Matrix(1,1,-2,-1) Matrix(237,-52,196,-43) -> Matrix(1,0,0,1) Matrix(314,-71,743,-168) -> Matrix(1,1,0,1) Matrix(118,-27,507,-116) -> Matrix(1,1,-2,-1) Matrix(78,-19,115,-28) -> Matrix(1,1,-2,-1) Matrix(152,-39,39,-10) -> Matrix(3,1,-4,-1) Matrix(570,-151,151,-40) -> Matrix(7,-1,-6,1) Matrix(529,-142,190,-51) -> Matrix(1,0,-2,1) Matrix(338,-93,189,-52) -> Matrix(1,-1,0,1) Matrix(188,-53,149,-42) -> Matrix(1,1,0,1) Matrix(335,-98,482,-141) -> Matrix(1,0,0,1) Matrix(629,-186,186,-55) -> Matrix(1,0,0,1) Matrix(294,-89,185,-56) -> Matrix(1,-1,0,1) Matrix(439,-136,184,-57) -> Matrix(5,4,-4,-3) Matrix(677,-236,284,-99) -> Matrix(3,-4,-2,3) Matrix(529,-190,142,-51) -> Matrix(3,2,-2,-1) Matrix(387,-142,526,-193) -> Matrix(1,0,2,1) Matrix(665,-246,246,-91) -> Matrix(1,0,0,1) Matrix(243,-92,140,-53) -> Matrix(1,0,0,1) Matrix(380,-147,243,-94) -> Matrix(5,3,-2,-1) Matrix(104,-41,137,-54) -> Matrix(3,1,2,1) Matrix(170,-69,69,-28) -> Matrix(5,1,-6,-1) Matrix(408,-169,169,-70) -> Matrix(9,-1,-8,1) Matrix(439,-184,136,-57) -> Matrix(1,0,-4,1) Matrix(574,-243,1011,-428) -> Matrix(1,-1,0,1) Matrix(304,-129,33,-14) -> Matrix(1,-1,0,1) Matrix(469,-202,202,-87) -> Matrix(1,-2,0,1) Matrix(436,-189,669,-290) -> Matrix(1,3,0,1) Matrix(768,-337,433,-190) -> Matrix(1,1,0,1) Matrix(533,-236,332,-147) -> Matrix(3,2,-2,-1) Matrix(364,-163,67,-30) -> Matrix(1,1,-2,-1) Matrix(166,-75,363,-164) -> Matrix(1,1,-2,-1) Matrix(360,-167,263,-122) -> Matrix(1,-1,0,1) Matrix(437,-234,282,-151) -> Matrix(1,-2,0,1) Matrix(342,-185,281,-152) -> Matrix(1,-1,0,1) Matrix(279,-154,154,-85) -> Matrix(1,0,0,1) Matrix(338,-189,93,-52) -> Matrix(1,-1,0,1) Matrix(768,-433,337,-190) -> Matrix(1,1,0,1) Matrix(1532,-867,675,-382) -> Matrix(1,1,-2,-1) Matrix(243,-140,92,-53) -> Matrix(1,0,0,1) Matrix(91,-54,150,-89) -> Matrix(1,0,4,1) Matrix(626,-383,863,-528) -> Matrix(3,-1,4,-1) Matrix(3601,-2208,2112,-1295) -> Matrix(9,-4,-20,9) Matrix(1486,-913,625,-384) -> Matrix(7,-5,-4,3) Matrix(4037,-2490,2346,-1447) -> Matrix(1,0,-2,1) Matrix(1869,-1156,1156,-715) -> Matrix(1,-2,0,1) Matrix(1481,-918,534,-331) -> Matrix(1,0,-2,1) Matrix(533,-332,236,-147) -> Matrix(1,0,-2,1) Matrix(294,-185,89,-56) -> Matrix(1,-1,0,1) Matrix(1383,-874,970,-613) -> Matrix(1,0,-2,1) Matrix(3703,-2344,1000,-633) -> Matrix(1,-2,0,1) Matrix(764,-485,293,-186) -> Matrix(1,-1,0,1) Matrix(380,-243,147,-94) -> Matrix(1,-1,-2,3) Matrix(437,-282,234,-151) -> Matrix(1,-2,0,1) Matrix(816,-529,145,-94) -> Matrix(1,-1,-2,3) Matrix(1307,-900,228,-157) -> Matrix(1,0,0,1) Matrix(1163,-804,852,-589) -> Matrix(3,2,-2,-1) Matrix(425,-296,56,-39) -> Matrix(1,0,0,1) Matrix(141,-100,196,-139) -> Matrix(1,0,4,1) Matrix(279,-202,250,-181) -> Matrix(5,-2,-2,1) Matrix(360,-263,167,-122) -> Matrix(1,-1,0,1) Matrix(472,-345,249,-182) -> Matrix(3,-1,-2,1) Matrix(1163,-852,804,-589) -> Matrix(1,0,-2,1) Matrix(166,-123,27,-20) -> Matrix(1,-1,0,1) Matrix(190,-147,243,-188) -> Matrix(1,-5,0,1) Matrix(188,-149,53,-42) -> Matrix(1,1,0,1) Matrix(1113,-902,902,-731) -> Matrix(1,0,0,1) Matrix(1111,-904,424,-345) -> Matrix(1,0,0,1) Matrix(237,-196,52,-43) -> Matrix(1,0,0,1) Matrix(156,-131,131,-110) -> Matrix(1,1,-2,-1) Matrix(182,-155,155,-132) -> Matrix(3,-1,-2,1) Matrix(436,-379,283,-246) -> Matrix(1,-3,0,1) Matrix(253,-226,178,-159) -> Matrix(1,0,-2,1) Matrix(677,-764,428,-483) -> Matrix(1,0,0,1) Matrix(245,-284,44,-51) -> Matrix(1,2,-2,-3) Matrix(667,-820,388,-477) -> Matrix(1,0,0,1) Matrix(2280,-2809,1849,-2278) -> Matrix(1,1,-2,-1) Matrix(172,-213,21,-26) -> Matrix(1,1,-2,-1) Matrix(190,-243,147,-188) -> Matrix(1,-5,0,1) Matrix(104,-137,41,-54) -> Matrix(1,3,-2,-5) Matrix(387,-526,142,-193) -> Matrix(1,2,-2,-3) Matrix(4970,-6789,3429,-4684) -> Matrix(1,1,0,1) Matrix(5112,-6985,3529,-4822) -> Matrix(3,5,-2,-3) Matrix(1196,-1635,771,-1054) -> Matrix(3,5,-2,-3) Matrix(141,-196,100,-139) -> Matrix(3,4,-4,-5) Matrix(576,-817,337,-478) -> Matrix(1,1,-4,-3) Matrix(2496,-3553,673,-958) -> Matrix(1,-1,0,1) Matrix(335,-482,98,-141) -> Matrix(1,0,0,1) Matrix(1821,-2642,1058,-1535) -> Matrix(1,0,0,1) Matrix(78,-115,19,-28) -> Matrix(1,1,-2,-1) Matrix(436,-669,189,-290) -> Matrix(1,3,0,1) Matrix(578,-911,335,-528) -> Matrix(1,1,0,1) Matrix(2009,-3174,726,-1147) -> Matrix(1,2,-2,-3) Matrix(2362,-3735,855,-1352) -> Matrix(1,1,0,1) Matrix(1104,-1777,625,-1006) -> Matrix(1,1,0,1) Matrix(679,-1096,184,-297) -> Matrix(1,0,0,1) Matrix(4896,-7921,3025,-4894) -> Matrix(3,5,-2,-3) Matrix(531,-860,92,-149) -> Matrix(1,2,-2,-3) Matrix(91,-150,54,-89) -> Matrix(3,4,-4,-5) Matrix(622,-1059,195,-332) -> Matrix(5,3,-12,-7) Matrix(8592,-14641,5041,-8590) -> Matrix(41,21,-84,-43) Matrix(574,-1011,243,-428) -> Matrix(1,-1,0,1) Matrix(528,-961,289,-526) -> Matrix(1,-3,0,1) Matrix(236,-435,51,-94) -> Matrix(1,1,0,1) Matrix(166,-363,75,-164) -> Matrix(1,1,-2,-1) Matrix(291,-668,44,-101) -> Matrix(1,0,0,1) Matrix(1944,-4489,841,-1942) -> Matrix(1,-9,0,1) Matrix(314,-743,71,-168) -> Matrix(1,1,0,1) Matrix(1061,-2778,186,-487) -> Matrix(1,0,0,1) Matrix(456,-1225,169,-454) -> Matrix(1,1,-2,-1) Matrix(201,-566,38,-107) -> Matrix(1,0,-2,1) Matrix(37,-108,12,-35) -> Matrix(1,2,-2,-3) Matrix(408,-1369,121,-406) -> Matrix(1,1,-2,-1) Matrix(118,-507,27,-116) -> Matrix(1,1,-2,-1) Matrix(126,-593,17,-80) -> Matrix(1,1,-2,-1) Matrix(168,-793,25,-118) -> Matrix(1,-1,0,1) Matrix(41,-200,8,-39) -> Matrix(1,2,-2,-3) 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): 43 ----------------------------------------------------------------------- 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 (-1/1,0/1).(-1/2,1/0) 0 1 1/1 (-1/2,1/0) 0 12 8/7 -1/1 1 8 7/6 (-2/1,-1/1) 0 24 13/11 -1/1 2 1 6/5 (-1/1,0/1) 0 24 11/9 -1/1 1 6 16/13 (-1/1,0/1) 0 24 53/43 (-1/1,0/1).(-1/2,1/0) 0 1 21/17 (-1/2,1/0) 0 12 5/4 0/1 1 8 14/11 (1/1,1/0) 0 24 9/7 1/0 5 3 13/10 (-4/1,1/0) 0 24 4/3 (-2/1,-1/1) 0 24 15/11 (-3/2,1/0) 0 12 41/30 (-2/1,-3/2) 0 24 26/19 -1/1 1 8 11/8 (-2/1,-1/1) 0 24 7/5 -1/1 2 2 17/12 (-1/1,-2/3) 0 24 27/19 (-1/2,-1/4) 0 12 37/26 0/1 1 8 10/7 (-1/1,-1/2) 0 24 13/9 (-1/2,1/0) 0 12 42/29 (-1/1,1/0) 0 24 71/49 -1/1 1 1 29/20 (-1/1,0/1) 0 24 16/11 -1/1 1 8 3/2 (0/1,1/0) 0 24 20/13 -3/1 1 8 17/11 -2/1 1 6 14/9 (-1/1,1/0) 0 24 11/7 -2/1 1 4 30/19 (-2/1,-1/1) 0 24 49/31 (-2/1,-1/1).(-3/2,1/0) 0 3 68/43 -1/1 1 8 19/12 (-2/1,1/0) 0 24 8/5 (-2/1,-1/1) 0 24 29/18 (-2/1,-1/1) 0 24 21/13 (-3/2,1/0) 0 12 89/55 (-2/1,-1/1).(-3/2,1/0) 0 1 34/21 (-2/1,-1/1) 0 24 13/8 -2/1 1 8 5/3 -1/1 2 3 17/10 -2/3 1 8 46/27 (-9/17,-1/2) 0 24 121/71 -1/2 21 1 29/17 (-1/2,-3/8) 0 12 12/7 (-1/1,0/1) 0 24 7/4 (-1/1,0/1) 0 24 30/17 (-1/1,0/1) 0 24 23/13 0/1 1 2 16/9 (-1/1,1/0) 0 24 9/5 (-1/2,1/0) 0 12 31/17 1/0 3 1 11/6 (-2/1,1/0) 0 24 13/7 -1/1 1 6 15/8 (-2/1,1/0) 0 24 2/1 -1/1 1 8 13/6 (-1/1,0/1) 0 24 11/5 (-1/1,0/1).(-1/2,1/0) 0 3 20/9 (-1/1,0/1) 0 24 9/4 (-1/1,0/1) 0 24 34/15 (-1/1,0/1) 0 24 25/11 0/1 1 2 16/7 (1/1,1/0) 0 24 23/10 0/1 1 8 30/13 (3/1,1/0) 0 24 67/29 1/0 9 1 7/3 (-3/2,1/0) 0 12 33/14 (-2/1,-1/1) 0 24 26/11 (-2/1,-1/1) 0 24 19/8 -2/1 1 8 12/5 (-5/4,-1/1) 0 24 17/7 -1/1 7 1 5/2 (-1/1,-2/3) 0 24 18/7 (-1/2,-1/3) 0 24 13/5 0/1 1 4 34/13 (-1/1,0/1) 0 24 55/21 0/1 1 6 21/8 (-1/1,0/1) 0 24 8/3 (-1/1,0/1) 0 24 35/13 (-1/1,0/1).(-1/2,1/0) 0 1 19/7 (-1/2,1/0) 0 12 30/11 (-1/1,0/1) 0 24 11/4 0/1 1 8 14/5 (0/1,1/1) 0 24 17/6 (4/1,1/0) 0 24 3/1 -1/1 1 6 19/6 (-6/11,-1/2) 0 24 16/5 -1/3 1 8 13/4 (0/1,1/0) 0 24 10/3 (-1/1,0/1) 0 24 37/11 (-1/1,0/1).(-1/2,1/0) 0 1 17/5 (-1/2,1/0) 0 12 24/7 (-1/1,-1/2) 0 24 7/2 0/1 1 8 18/5 (-1/1,1/0) 0 24 11/3 (-3/2,1/0) 0 12 37/10 (-2/1,-1/1) 0 24 63/17 (-2/1,-1/1).(-3/2,1/0) 0 3 26/7 -1/1 1 8 15/4 (-4/3,-1/1) 0 24 19/5 -1/1 5 1 4/1 (-1/1,-1/2) 0 24 17/4 0/1 1 8 13/3 (-1/1,0/1).(-1/2,1/0) 0 3 22/5 -1/1 1 8 9/2 (-1/1,0/1) 0 24 23/5 0/1 1 6 14/3 (-1/1,1/0) 0 24 33/7 0/1 1 3 19/4 (2/1,1/0) 0 24 5/1 -1/1 1 4 21/4 (-4/7,-1/2) 0 24 16/3 (-1/1,0/1) 0 24 11/2 (-1/1,0/1) 0 24 28/5 -1/1 1 8 17/3 0/1 1 6 40/7 (-1/1,0/1) 0 24 23/4 0/1 1 8 6/1 (-1/1,0/1) 0 24 13/2 0/1 1 8 20/3 (1/1,1/0) 0 24 7/1 -1/1 1 3 15/2 (-1/2,0/1) 0 24 8/1 -1/1 1 8 9/1 (-1/2,1/0) 0 12 1/0 (-1/1,0/1) 0 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(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(226,-253,159,-178) (1/1,8/7) -> (27/19,37/26) Glide Reflection 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(196,-237,43,-52) (6/5,11/9) -> (9/2,23/5) Glide Reflection Matrix(904,-1111,345,-424) (11/9,16/13) -> (55/21,21/8) Glide Reflection Matrix(1377,-1696,1118,-1377) (16/13,53/43) -> (16/13,53/43) Reflection Matrix(902,-1113,731,-902) (53/43,21/17) -> (53/43,21/17) Reflection Matrix(172,-213,21,-26) (21/17,5/4) -> (8/1,9/1) Hyperbolic Matrix(149,-188,42,-53) (5/4,14/11) -> (7/2,18/5) Glide Reflection Matrix(190,-243,147,-188) (14/11,9/7) -> (9/7,13/10) Parabolic Matrix(104,-137,41,-54) (13/10,4/3) -> (5/2,18/7) Hyperbolic Matrix(387,-526,142,-193) (4/3,15/11) -> (19/7,30/11) Hyperbolic Matrix(852,-1163,589,-804) (15/11,41/30) -> (13/9,42/29) Glide 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(576,-817,337,-478) (17/12,27/19) -> (29/17,12/7) Hyperbolic Matrix(970,-1383,613,-874) (37/26,10/7) -> (68/43,19/12) 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(900,-1307,157,-228) (29/20,16/11) -> (40/7,23/4) Glide Reflection Matrix(78,-115,19,-28) (16/11,3/2) -> (4/1,17/4) Hyperbolic Matrix(436,-669,189,-290) (3/2,20/13) -> (23/10,30/13) Hyperbolic Matrix(529,-816,94,-145) (20/13,17/11) -> (28/5,17/3) Glide Reflection Matrix(282,-437,151,-234) (17/11,14/9) -> (13/7,15/8) 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(2344,-3703,633,-1000) (30/19,49/31) -> (37/10,63/17) Glide Reflection 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(332,-533,147,-236) (8/5,29/18) -> (9/4,34/15) Glide Reflection Matrix(679,-1096,184,-297) (29/18,21/13) -> (11/3,37/10) Hyperbolic Matrix(1156,-1869,715,-1156) (21/13,89/55) -> (21/13,89/55) 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(622,-1059,195,-332) (17/10,46/27) -> (19/6,16/5) Hyperbolic Matrix(6533,-11132,3834,-6533) (46/27,121/71) -> (46/27,121/71) Reflection Matrix(2058,-3509,1207,-2058) (121/71,29/17) -> (121/71,29/17) Reflection Matrix(140,-243,53,-92) (12/7,7/4) -> (21/8,8/3) Glide Reflection Matrix(574,-1011,243,-428) (7/4,30/17) -> (33/14,26/11) Hyperbolic 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(154,-279,85,-154) (9/5,31/17) -> (9/5,31/17) Reflection Matrix(373,-682,204,-373) (31/17,11/6) -> (31/17,11/6) Reflection Matrix(236,-435,51,-94) (11/6,13/7) -> (23/5,14/3) Hyperbolic Matrix(166,-363,75,-164) (13/6,11/5) -> (11/5,20/9) Parabolic 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(202,-469,87,-202) (67/29,7/3) -> (67/29,7/3) Reflection Matrix(129,-304,14,-33) (7/3,33/14) -> (9/1,1/0) Glide Reflection Matrix(314,-743,71,-168) (26/11,19/8) -> (22/5,9/2) Hyperbolic Matrix(184,-439,57,-136) (19/8,12/5) -> (16/5,13/4) 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(246,-665,91,-246) (35/13,19/7) -> (35/13,19/7) Reflection Matrix(167,-456,26,-71) (30/11,11/4) -> (6/1,13/2) Glide Reflection Matrix(190,-529,51,-142) (11/4,14/5) -> (26/7,15/4) 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(186,-629,55,-186) (37/11,17/5) -> (37/11,17/5) Reflection Matrix(86,-297,11,-38) (24/7,7/2) -> (15/2,8/1) 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(118,-507,27,-116) (17/4,13/3) -> (13/3,22/5) Parabolic Matrix(126,-593,17,-80) (14/3,33/7) -> (7/1,15/2) Hyperbolic Matrix(168,-793,25,-118) (33/7,19/4) -> (20/3,7/1) Hyperbolic 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(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(0,1,1,0) -> Matrix(1,1,0,-1) (-1/1,1/1) -> (-1/2,1/0) Matrix(226,-253,159,-178) -> Matrix(1,1,-2,-3) Matrix(245,-284,44,-51) -> Matrix(1,2,-2,-3) -1/1 Matrix(155,-182,132,-155) -> Matrix(3,4,-2,-3) (7/6,13/11) -> (-2/1,-1/1) Matrix(131,-156,110,-131) -> Matrix(-1,0,2,1) (13/11,6/5) -> (-1/1,0/1) Matrix(196,-237,43,-52) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(904,-1111,345,-424) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(1377,-1696,1118,-1377) -> Matrix(-1,0,2,1) (16/13,53/43) -> (-1/1,0/1) Matrix(902,-1113,731,-902) -> Matrix(1,1,0,-1) (53/43,21/17) -> (-1/2,1/0) Matrix(172,-213,21,-26) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(149,-188,42,-53) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(190,-243,147,-188) -> Matrix(1,-5,0,1) 1/0 Matrix(104,-137,41,-54) -> Matrix(1,3,-2,-5) Matrix(387,-526,142,-193) -> Matrix(1,2,-2,-3) -1/1 Matrix(852,-1163,589,-804) -> Matrix(1,1,-2,-3) Matrix(345,-472,182,-249) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(263,-360,122,-167) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(141,-196,100,-139) -> Matrix(3,4,-4,-5) -1/1 Matrix(576,-817,337,-478) -> Matrix(1,1,-4,-3) -1/2 Matrix(970,-1383,613,-874) -> Matrix(3,1,-2,-1) Matrix(335,-482,98,-141) -> Matrix(1,0,0,1) Matrix(4117,-5964,2842,-4117) -> Matrix(1,2,0,-1) (42/29,71/49) -> (-1/1,1/0) Matrix(2841,-4118,1960,-2841) -> Matrix(-1,0,2,1) (71/49,29/20) -> (-1/1,0/1) Matrix(900,-1307,157,-228) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(78,-115,19,-28) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(436,-669,189,-290) -> Matrix(1,3,0,1) 1/0 Matrix(529,-816,94,-145) -> Matrix(1,2,-2,-5) Matrix(282,-437,151,-234) -> Matrix(1,3,0,-1) *** -> (-3/2,1/0) Matrix(243,-380,94,-147) -> Matrix(1,2,-2,-5) Matrix(485,-764,186,-293) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(2344,-3703,633,-1000) -> Matrix(1,3,0,-1) *** -> (-3/2,1/0) Matrix(3515,-5558,948,-1499) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(185,-294,56,-89) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(332,-533,147,-236) -> Matrix(1,1,-2,-3) Matrix(679,-1096,184,-297) -> Matrix(1,0,0,1) Matrix(1156,-1869,715,-1156) -> Matrix(1,3,0,-1) (21/13,89/55) -> (-3/2,1/0) Matrix(3739,-6052,2310,-3739) -> Matrix(3,4,-2,-3) (89/55,34/21) -> (-2/1,-1/1) Matrix(531,-860,92,-149) -> Matrix(1,2,-2,-3) -1/1 Matrix(91,-150,54,-89) -> Matrix(3,4,-4,-5) -1/1 Matrix(622,-1059,195,-332) -> Matrix(5,3,-12,-7) -1/2 Matrix(6533,-11132,3834,-6533) -> Matrix(35,18,-68,-35) (46/27,121/71) -> (-9/17,-1/2) Matrix(2058,-3509,1207,-2058) -> Matrix(7,3,-16,-7) (121/71,29/17) -> (-1/2,-3/8) Matrix(140,-243,53,-92) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(574,-1011,243,-428) -> Matrix(1,-1,0,1) 1/0 Matrix(867,-1532,382,-675) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(433,-768,190,-337) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(189,-338,52,-93) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(154,-279,85,-154) -> Matrix(1,1,0,-1) (9/5,31/17) -> (-1/2,1/0) Matrix(373,-682,204,-373) -> Matrix(1,4,0,-1) (31/17,11/6) -> (-2/1,1/0) Matrix(236,-435,51,-94) -> Matrix(1,1,0,1) 1/0 Matrix(166,-363,75,-164) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(163,-364,30,-67) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(291,-668,44,-101) -> Matrix(1,0,0,1) Matrix(1741,-4020,754,-1741) -> Matrix(-1,6,0,1) (30/13,67/29) -> (3/1,1/0) Matrix(202,-469,87,-202) -> Matrix(1,3,0,-1) (67/29,7/3) -> (-3/2,1/0) Matrix(129,-304,14,-33) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(314,-743,71,-168) -> Matrix(1,1,0,1) 1/0 Matrix(184,-439,57,-136) -> Matrix(1,1,-4,-5) Matrix(169,-408,70,-169) -> Matrix(9,10,-8,-9) (12/5,17/7) -> (-5/4,-1/1) Matrix(69,-170,28,-69) -> Matrix(5,4,-6,-5) (17/7,5/2) -> (-1/1,-2/3) Matrix(1061,-2778,186,-487) -> Matrix(1,0,0,1) Matrix(209,-560,78,-209) -> Matrix(-1,0,2,1) (8/3,35/13) -> (-1/1,0/1) Matrix(246,-665,91,-246) -> Matrix(1,1,0,-1) (35/13,19/7) -> (-1/2,1/0) Matrix(167,-456,26,-71) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(190,-529,51,-142) -> Matrix(3,1,-2,-1) Matrix(201,-566,38,-107) -> Matrix(1,0,-2,1) 0/1 Matrix(37,-108,12,-35) -> Matrix(1,2,-2,-3) -1/1 Matrix(221,-740,66,-221) -> Matrix(-1,0,2,1) (10/3,37/11) -> (-1/1,0/1) Matrix(186,-629,55,-186) -> Matrix(1,1,0,-1) (37/11,17/5) -> (-1/2,1/0) Matrix(86,-297,11,-38) -> Matrix(1,1,0,-1) *** -> (-1/2,1/0) Matrix(151,-570,40,-151) -> Matrix(7,8,-6,-7) (15/4,19/5) -> (-4/3,-1/1) Matrix(39,-152,10,-39) -> Matrix(3,2,-4,-3) (19/5,4/1) -> (-1/1,-1/2) Matrix(118,-507,27,-116) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(126,-593,17,-80) -> Matrix(1,1,-2,-1) (-1/1,0/1).(-1/2,1/0) Matrix(168,-793,25,-118) -> Matrix(1,-1,0,1) 1/0 Matrix(41,-200,8,-39) -> Matrix(1,2,-2,-3) -1/1 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.