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): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 72 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -10/1 -8/1 -7/1 -6/1 -16/3 -21/4 -4/1 -7/2 -8/3 -21/8 -7/3 -2/1 -7/4 -12/7 -7/5 -4/3 -21/16 -7/6 0/1 1/1 7/6 28/23 14/11 21/16 4/3 7/5 3/2 14/9 84/53 28/17 12/7 7/4 2/1 28/13 7/3 196/83 112/47 5/2 28/11 70/27 21/8 8/3 14/5 3/1 42/13 7/2 112/31 56/15 4/1 13/3 84/19 9/2 14/3 19/4 29/6 5/1 31/6 21/4 16/3 11/2 28/5 23/4 6/1 13/2 7/1 15/2 8/1 17/2 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 -1/1 0/1 1/0 -9/1 0/1 1/3 -8/1 -1/1 1/1 -15/2 1/1 1/0 -7/1 -1/1 0/1 1/0 -6/1 -1/1 -1/2 0/1 -23/4 -1/2 -1/3 -17/3 -1/4 0/1 -28/5 0/1 -11/2 0/1 1/0 -16/3 -1/1 -21/4 -1/1 -1/2 0/1 -26/5 -1/1 -2/3 -1/2 -5/1 -1/2 -1/3 -19/4 -1/7 0/1 -14/3 0/1 -9/2 0/1 1/1 -22/5 -3/1 -2/1 1/0 -13/3 -3/2 -1/1 -30/7 -1/1 -4/5 -3/4 -47/11 -5/7 -2/3 -17/4 -2/3 -1/2 -4/1 -1/1 -1/3 -19/5 -1/1 -2/3 -34/9 -1/1 -1/2 0/1 -15/4 -3/5 -1/2 -26/7 -1/2 -4/9 -3/7 -11/3 -1/2 0/1 -7/2 -1/2 -1/3 0/1 -17/5 -1/2 0/1 -27/8 -2/5 -3/8 -10/3 -1/2 -2/5 -1/3 -13/4 -1/3 -1/4 -42/13 -2/7 0/1 -29/9 -1/4 0/1 -16/5 -1/3 -3/1 -1/3 -1/4 -20/7 -1/5 -1/7 -37/13 -1/3 0/1 -17/6 -1/6 0/1 -14/5 0/1 -11/4 -1/2 0/1 -19/7 -2/5 -1/3 -46/17 -1/3 -1/4 0/1 -27/10 -1/2 0/1 -8/3 -1/3 -29/11 -2/7 -1/4 -21/8 -1/3 -2/7 -1/4 -55/21 -2/7 -1/4 -89/34 -1/3 -1/4 -34/13 -2/7 -3/11 -1/4 -13/5 -1/3 -3/10 -31/12 -3/11 -1/4 -18/7 -3/11 -4/15 -1/4 -41/16 -5/19 -1/4 -64/25 -3/11 -5/19 -23/9 -7/27 -1/4 -28/11 -1/4 -5/2 -1/4 -1/5 -17/7 -1/4 -4/17 -29/12 -5/22 -2/9 -12/5 -1/5 -31/13 -1/4 -1/5 -50/21 -1/5 -2/11 -1/6 -19/8 -1/5 0/1 -26/11 -1/4 -2/9 -1/5 -7/3 -1/4 -1/5 0/1 -30/13 -1/4 -2/9 -1/5 -83/36 -1/4 -2/9 -53/23 -1/4 -3/13 -23/10 -1/5 -1/6 -39/17 -1/4 0/1 -55/24 -1/6 0/1 -16/7 -1/3 -1/5 -41/18 -1/3 -1/4 -66/29 -1/4 -1/5 0/1 -25/11 -3/11 -1/4 -84/37 -1/4 -59/26 -1/4 -11/45 -34/15 -1/4 -5/21 -4/17 -9/4 -2/9 -1/5 -20/9 -1/3 -1/5 -11/5 -1/4 -2/9 -13/6 -5/24 -1/5 -28/13 -1/5 -15/7 -1/5 -7/36 -2/1 -1/5 -1/6 0/1 -11/6 -1/6 -2/13 -9/5 -1/7 0/1 -7/4 -1/6 -1/7 0/1 -19/11 -1/7 0/1 -31/18 -1/7 -1/8 -43/25 -1/9 -1/10 -55/32 -1/4 0/1 -12/7 -1/5 -1/7 -41/24 -1/6 -1/7 -70/41 -2/13 0/1 -29/17 -1/6 0/1 -17/10 -2/11 -1/6 -22/13 -1/6 -3/19 -2/13 -27/16 -1/6 -2/13 -5/3 -3/20 -1/7 -28/17 -1/7 -23/14 -1/7 -11/78 -18/11 -1/7 -4/29 -3/22 -13/8 -1/7 -1/8 -34/21 -1/7 -3/22 -2/15 -21/13 -1/7 -2/15 -1/8 -71/44 -3/23 -1/8 -50/31 -1/7 -1/8 0/1 -29/18 -1/8 0/1 -8/5 -1/7 -27/17 -3/22 -2/15 -19/12 -2/15 -3/23 -30/19 -3/23 -4/31 -1/8 -11/7 -1/8 0/1 -36/23 -1/7 -3/23 -61/39 -1/8 -1/9 -86/55 -1/7 -2/15 -1/8 -25/16 -1/7 -1/8 -14/9 -2/15 0/1 -3/2 -1/7 -1/8 -22/15 -1/8 -6/49 -5/41 -19/13 -5/41 -4/33 -54/37 -1/8 -3/25 -2/17 -35/24 -1/8 -4/33 -3/25 -16/11 -3/25 -29/20 -9/76 -2/17 -42/29 -2/17 -55/38 -2/17 -15/128 -13/9 -5/43 -3/26 -36/25 -7/61 -1/9 -59/41 -9/79 -5/44 -23/16 -7/62 -1/9 -10/7 -1/9 -1/10 0/1 -47/33 -1/13 0/1 -84/59 0/1 -37/26 -1/5 0/1 -27/19 -1/8 0/1 -17/12 -1/8 -2/17 -24/17 -1/7 -1/9 -7/5 -1/8 -1/9 0/1 -32/23 -1/7 -1/9 -57/41 -1/8 0/1 -196/141 -1/8 -139/100 -1/8 -2/17 -82/59 -1/8 -2/17 -1/9 -25/18 -1/8 -1/9 -18/13 -1/8 -2/17 -1/9 -65/47 -4/35 -1/9 -112/81 -1/9 -47/34 -1/9 -2/19 -29/21 -1/8 0/1 -40/29 -1/9 -11/8 -1/8 0/1 -26/19 -2/15 -3/23 -1/8 -41/30 -9/71 -1/8 -56/41 -1/8 -15/11 -1/8 -5/41 -19/14 -3/25 -2/17 -23/17 -7/60 -5/43 -27/20 -2/17 -3/26 -4/3 -1/9 -29/22 -2/19 -1/10 -25/19 -3/29 -1/10 -21/16 -1/9 -1/10 0/1 -59/45 -3/29 -1/10 -38/29 -1/10 -1/11 0/1 -55/42 -1/10 0/1 -17/13 -1/8 0/1 -13/10 -1/9 -3/28 -22/17 -1/9 -2/19 -1/10 -53/41 -1/8 -1/9 -84/65 -1/9 -31/24 -1/9 -3/28 -9/7 -1/9 -2/19 -32/25 -1/9 -1/11 -55/43 -1/10 0/1 -23/18 -1/9 -1/10 -14/11 -2/19 0/1 -5/4 -1/9 -1/10 -11/9 -4/39 -1/10 -28/23 -1/10 -17/14 -1/10 -6/61 -6/5 -1/10 -2/21 -1/11 -19/16 -1/11 0/1 -13/11 -1/10 -3/31 -7/6 -1/10 -1/11 0/1 -15/13 -1/10 -3/31 -8/7 -1/9 -1/11 -9/8 -2/21 -1/11 -1/1 -1/12 0/1 0/1 0/1 1/1 0/1 1/12 8/7 1/11 1/9 7/6 0/1 1/11 1/10 20/17 1/11 1/9 13/11 3/31 1/10 6/5 1/11 2/21 1/10 17/14 6/61 1/10 28/23 1/10 11/9 1/10 4/39 5/4 1/10 1/9 14/11 0/1 2/19 23/18 1/10 1/9 9/7 2/19 1/9 22/17 1/10 2/19 1/9 13/10 3/28 1/9 17/13 0/1 1/8 38/29 0/1 1/11 1/10 21/16 0/1 1/10 1/9 25/19 1/10 3/29 4/3 1/9 19/14 2/17 3/25 34/25 3/25 4/33 1/8 15/11 5/41 1/8 11/8 0/1 1/8 29/21 0/1 1/8 47/34 2/19 1/9 18/13 1/9 2/17 1/8 25/18 1/9 1/8 7/5 0/1 1/9 1/8 31/22 1/9 1/8 86/61 1/9 2/17 1/8 55/39 0/1 1/8 24/17 1/9 1/7 17/12 2/17 1/8 27/19 0/1 1/8 10/7 0/1 1/10 1/9 23/16 1/9 7/62 36/25 1/9 7/61 13/9 3/26 5/43 16/11 3/25 19/13 4/33 5/41 3/2 1/8 1/7 14/9 0/1 2/15 25/16 1/8 1/7 11/7 0/1 1/8 30/19 1/8 4/31 3/23 19/12 3/23 2/15 84/53 2/15 65/41 2/15 13/97 46/29 2/15 7/52 5/37 27/17 2/15 3/22 8/5 1/7 29/18 0/1 1/8 50/31 0/1 1/8 1/7 21/13 1/8 2/15 1/7 13/8 1/8 1/7 18/11 3/22 4/29 1/7 23/14 11/78 1/7 28/17 1/7 5/3 1/7 3/20 27/16 2/13 1/6 22/13 2/13 3/19 1/6 17/10 1/6 2/11 29/17 0/1 1/6 70/41 0/1 2/13 41/24 1/7 1/6 12/7 1/7 1/5 7/4 0/1 1/7 1/6 16/9 1/7 1/5 25/14 1/8 1/7 34/19 0/1 1/7 1/6 9/5 0/1 1/7 11/6 2/13 1/6 13/7 7/43 1/6 2/1 0/1 1/6 1/5 15/7 7/36 1/5 28/13 1/5 13/6 1/5 5/24 11/5 2/9 1/4 31/14 1/5 1/4 51/23 3/13 1/4 20/9 1/5 1/3 29/13 0/1 1/6 9/4 1/5 2/9 25/11 1/4 3/11 41/18 1/4 1/3 16/7 1/5 1/3 55/24 0/1 1/6 39/17 0/1 1/4 23/10 1/6 1/5 7/3 0/1 1/5 1/4 33/14 1/6 1/5 59/25 3/13 1/4 85/36 2/9 1/4 196/83 1/4 111/47 0/1 1/4 26/11 1/5 2/9 1/4 19/8 0/1 1/5 50/21 1/6 2/11 1/5 81/34 3/16 1/5 112/47 1/5 31/13 1/5 1/4 12/5 1/5 41/17 7/32 9/41 70/29 2/9 29/12 2/9 5/22 17/7 4/17 1/4 5/2 1/5 1/4 28/11 1/4 23/9 1/4 7/27 41/16 1/4 5/19 59/23 1/4 7/27 77/30 1/4 5/19 4/15 18/7 1/4 4/15 3/11 31/12 1/4 3/11 44/17 3/11 7/25 57/22 9/32 2/7 70/27 2/7 13/5 3/10 1/3 34/13 1/4 3/11 2/7 21/8 1/4 2/7 1/3 50/19 1/4 3/11 2/7 29/11 1/4 2/7 8/3 1/3 27/10 0/1 1/2 19/7 1/3 2/5 11/4 0/1 1/2 14/5 0/1 17/6 0/1 1/6 20/7 1/7 1/5 23/8 1/5 3/14 3/1 1/4 1/3 16/5 1/3 29/9 0/1 1/4 42/13 0/1 2/7 13/4 1/4 1/3 10/3 1/3 2/5 1/2 7/2 0/1 1/3 1/2 18/5 1/3 2/5 1/2 65/18 2/7 1/3 112/31 1/3 47/13 1/3 4/11 29/8 3/8 2/5 11/3 0/1 1/2 26/7 3/7 4/9 1/2 41/11 11/23 1/2 56/15 1/2 15/4 1/2 3/5 34/9 0/1 1/2 1/1 53/14 1/2 7/13 19/5 2/3 1/1 23/6 1/2 1/1 27/7 0/1 1/2 4/1 1/3 1/1 17/4 1/2 2/3 47/11 2/3 5/7 30/7 3/4 4/5 1/1 13/3 1/1 3/2 22/5 2/1 3/1 1/0 53/12 9/1 1/0 84/19 1/0 31/7 -5/1 1/0 9/2 -1/1 0/1 14/3 0/1 19/4 0/1 1/7 24/5 1/5 53/11 1/4 1/3 29/6 0/1 1/4 5/1 1/3 1/2 31/6 1/2 1/1 26/5 1/2 2/3 1/1 21/4 0/1 1/2 1/1 58/11 1/2 2/3 1/1 37/7 0/1 1/3 16/3 1/1 27/5 0/1 1/0 11/2 0/1 1/0 28/5 0/1 17/3 0/1 1/4 23/4 1/3 1/2 29/5 0/1 1/2 6/1 0/1 1/2 1/1 13/2 1/1 1/0 7/1 0/1 1/1 1/0 22/3 1/1 2/1 1/0 15/2 -1/1 1/0 23/3 -3/1 1/0 8/1 -1/1 1/1 17/2 0/1 1/0 9/1 -1/3 0/1 10/1 0/1 1/1 1/0 11/1 -1/2 0/1 1/0 0/1 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(55,588,-42,-449) (-10/1,1/0) -> (-38/29,-55/42) Hyperbolic Matrix(111,1064,70,671) (-10/1,-9/1) -> (65/41,46/29) Hyperbolic Matrix(57,476,-20,-167) (-9/1,-8/1) -> (-20/7,-37/13) Hyperbolic Matrix(169,1288,-66,-503) (-8/1,-15/2) -> (-41/16,-64/25) Hyperbolic Matrix(113,812,-70,-503) (-15/2,-7/1) -> (-21/13,-71/44) Hyperbolic Matrix(55,364,-34,-225) (-7/1,-6/1) -> (-34/21,-21/13) Hyperbolic Matrix(225,1316,-86,-503) (-6/1,-23/4) -> (-89/34,-34/13) Hyperbolic Matrix(225,1288,98,561) (-23/4,-17/3) -> (39/17,23/10) Hyperbolic Matrix(169,952,30,169) (-17/3,-28/5) -> (28/5,17/3) Hyperbolic Matrix(111,616,20,111) (-28/5,-11/2) -> (11/2,28/5) Hyperbolic Matrix(113,616,-82,-447) (-11/2,-16/3) -> (-40/29,-11/8) Hyperbolic Matrix(169,896,-116,-615) (-16/3,-21/4) -> (-35/24,-16/11) Hyperbolic Matrix(391,2044,-268,-1401) (-21/4,-26/5) -> (-54/37,-35/24) Hyperbolic Matrix(391,2016,-250,-1289) (-26/5,-5/1) -> (-61/39,-86/55) Hyperbolic Matrix(111,532,-82,-393) (-5/1,-19/4) -> (-19/14,-23/17) Hyperbolic Matrix(113,532,24,113) (-19/4,-14/3) -> (14/3,19/4) Hyperbolic Matrix(55,252,12,55) (-14/3,-9/2) -> (9/2,14/3) Hyperbolic Matrix(113,504,-50,-223) (-9/2,-22/5) -> (-34/15,-9/4) Hyperbolic Matrix(167,728,64,279) (-22/5,-13/3) -> (13/5,34/13) Hyperbolic Matrix(111,476,52,223) (-13/3,-30/7) -> (2/1,15/7) Hyperbolic Matrix(727,3108,-498,-2129) (-30/7,-47/11) -> (-19/13,-54/37) Hyperbolic Matrix(223,952,26,111) (-47/11,-17/4) -> (17/2,9/1) Hyperbolic Matrix(113,476,80,337) (-17/4,-4/1) -> (24/17,17/12) Hyperbolic Matrix(169,644,-132,-503) (-4/1,-19/5) -> (-9/7,-32/25) Hyperbolic Matrix(281,1064,-192,-727) (-19/5,-34/9) -> (-22/15,-19/13) Hyperbolic Matrix(839,3164,-520,-1961) (-34/9,-15/4) -> (-71/44,-50/31) Hyperbolic Matrix(391,1456,-286,-1065) (-15/4,-26/7) -> (-26/19,-41/30) Hyperbolic Matrix(167,616,106,391) (-26/7,-11/3) -> (11/7,30/19) Hyperbolic Matrix(55,196,-16,-57) (-11/3,-7/2) -> (-7/2,-17/5) Parabolic Matrix(281,952,116,393) (-17/5,-27/8) -> (29/12,17/7) Hyperbolic Matrix(449,1512,-166,-559) (-27/8,-10/3) -> (-46/17,-27/10) Hyperbolic Matrix(111,364,68,223) (-10/3,-13/4) -> (13/8,18/11) Hyperbolic Matrix(337,1092,104,337) (-13/4,-42/13) -> (42/13,13/4) Hyperbolic Matrix(1007,3248,590,1903) (-42/13,-29/9) -> (29/17,70/41) Hyperbolic Matrix(279,896,52,167) (-29/9,-16/5) -> (16/3,27/5) Hyperbolic Matrix(167,532,70,223) (-16/5,-3/1) -> (31/13,12/5) Hyperbolic Matrix(449,1288,-312,-895) (-3/1,-20/7) -> (-36/25,-59/41) Hyperbolic Matrix(503,1428,118,335) (-37/13,-17/6) -> (17/4,47/11) Hyperbolic Matrix(169,476,60,169) (-17/6,-14/5) -> (14/5,17/6) Hyperbolic Matrix(111,308,40,111) (-14/5,-11/4) -> (11/4,14/5) Hyperbolic Matrix(113,308,62,169) (-11/4,-19/7) -> (9/5,11/6) Hyperbolic Matrix(1231,3332,-890,-2409) (-19/7,-46/17) -> (-18/13,-65/47) Hyperbolic Matrix(167,448,104,279) (-27/10,-8/3) -> (8/5,29/18) Hyperbolic Matrix(169,448,106,281) (-8/3,-29/11) -> (27/17,8/5) Hyperbolic Matrix(671,1764,-256,-673) (-29/11,-21/8) -> (-21/8,-55/21) Parabolic Matrix(1401,3668,364,953) (-55/21,-89/34) -> (23/6,27/7) Hyperbolic Matrix(279,728,64,167) (-34/13,-13/5) -> (13/3,22/5) Hyperbolic Matrix(671,1736,-390,-1009) (-13/5,-31/12) -> (-31/18,-43/25) Hyperbolic Matrix(391,1008,282,727) (-31/12,-18/7) -> (18/13,25/18) Hyperbolic Matrix(1343,3444,-590,-1513) (-18/7,-41/16) -> (-41/18,-66/29) Hyperbolic Matrix(1455,3724,656,1679) (-64/25,-23/9) -> (51/23,20/9) Hyperbolic Matrix(505,1288,198,505) (-23/9,-28/11) -> (28/11,23/9) Hyperbolic Matrix(111,280,44,111) (-28/11,-5/2) -> (5/2,28/11) Hyperbolic Matrix(57,140,46,113) (-5/2,-17/7) -> (11/9,5/4) Hyperbolic Matrix(335,812,92,223) (-17/7,-29/12) -> (29/8,11/3) Hyperbolic Matrix(337,812,-232,-559) (-29/12,-12/5) -> (-16/11,-29/20) Hyperbolic Matrix(223,532,70,167) (-12/5,-31/13) -> (3/1,16/5) Hyperbolic Matrix(1399,3332,-1082,-2577) (-31/13,-50/21) -> (-22/17,-53/41) Hyperbolic Matrix(671,1596,494,1175) (-50/21,-19/8) -> (19/14,34/25) Hyperbolic Matrix(449,1064,284,673) (-19/8,-26/11) -> (30/19,19/12) Hyperbolic Matrix(167,392,-72,-169) (-26/11,-7/3) -> (-7/3,-30/13) Parabolic Matrix(4759,10976,-3424,-7897) (-30/13,-83/36) -> (-139/100,-82/59) Hyperbolic Matrix(2575,5936,534,1231) (-83/36,-53/23) -> (53/11,29/6) Hyperbolic Matrix(559,1288,194,447) (-53/23,-23/10) -> (23/8,3/1) Hyperbolic Matrix(561,1288,98,225) (-23/10,-39/17) -> (17/3,23/4) Hyperbolic Matrix(1343,3080,-1026,-2353) (-39/17,-55/24) -> (-55/42,-17/13) Hyperbolic Matrix(1455,3332,562,1287) (-55/24,-16/7) -> (44/17,57/22) Hyperbolic Matrix(503,1148,294,671) (-16/7,-41/18) -> (41/24,12/7) Hyperbolic Matrix(2129,4844,-1624,-3695) (-66/29,-25/11) -> (-59/45,-38/29) Hyperbolic Matrix(2071,4704,468,1063) (-25/11,-84/37) -> (84/19,31/7) Hyperbolic Matrix(4145,9408,938,2129) (-84/37,-59/26) -> (53/12,84/19) Hyperbolic Matrix(1679,3808,444,1007) (-59/26,-34/15) -> (34/9,53/14) Hyperbolic Matrix(113,252,-100,-223) (-9/4,-20/9) -> (-8/7,-9/8) Hyperbolic Matrix(279,616,-178,-393) (-20/9,-11/5) -> (-11/7,-36/23) Hyperbolic Matrix(167,364,128,279) (-11/5,-13/6) -> (13/10,17/13) Hyperbolic Matrix(337,728,156,337) (-13/6,-28/13) -> (28/13,13/6) Hyperbolic Matrix(391,840,182,391) (-28/13,-15/7) -> (15/7,28/13) Hyperbolic Matrix(223,476,52,111) (-15/7,-2/1) -> (30/7,13/3) Hyperbolic Matrix(167,308,-122,-225) (-2/1,-11/6) -> (-11/8,-26/19) Hyperbolic Matrix(169,308,62,113) (-11/6,-9/5) -> (19/7,11/4) Hyperbolic Matrix(111,196,-64,-113) (-9/5,-7/4) -> (-7/4,-19/11) Parabolic Matrix(503,868,-390,-673) (-19/11,-31/18) -> (-31/24,-9/7) Hyperbolic Matrix(1791,3080,-1238,-2129) (-43/25,-55/32) -> (-55/38,-13/9) Hyperbolic Matrix(897,1540,392,673) (-55/32,-12/7) -> (16/7,55/24) Hyperbolic Matrix(671,1148,294,503) (-12/7,-41/24) -> (41/18,16/7) Hyperbolic Matrix(3361,5740,1968,3361) (-41/24,-70/41) -> (70/41,41/24) Hyperbolic Matrix(1903,3248,590,1007) (-70/41,-29/17) -> (29/9,42/13) Hyperbolic Matrix(559,952,394,671) (-29/17,-17/10) -> (17/12,27/19) Hyperbolic Matrix(281,476,232,393) (-17/10,-22/13) -> (6/5,17/14) Hyperbolic Matrix(1177,1988,730,1233) (-22/13,-27/16) -> (29/18,50/31) Hyperbolic Matrix(449,756,-332,-559) (-27/16,-5/3) -> (-23/17,-27/20) Hyperbolic Matrix(169,280,102,169) (-5/3,-28/17) -> (28/17,5/3) Hyperbolic Matrix(783,1288,476,783) (-28/17,-23/14) -> (23/14,28/17) Hyperbolic Matrix(393,644,274,449) (-23/14,-18/11) -> (10/7,23/16) Hyperbolic Matrix(223,364,68,111) (-18/11,-13/8) -> (13/4,10/3) Hyperbolic Matrix(449,728,346,561) (-13/8,-34/21) -> (22/17,13/10) Hyperbolic Matrix(1233,1988,730,1177) (-50/31,-29/18) -> (27/16,22/13) Hyperbolic Matrix(279,448,104,167) (-29/18,-8/5) -> (8/3,27/10) Hyperbolic Matrix(281,448,106,169) (-8/5,-27/17) -> (29/11,8/3) Hyperbolic Matrix(953,1512,-670,-1063) (-27/17,-19/12) -> (-37/26,-27/19) Hyperbolic Matrix(673,1064,284,449) (-19/12,-30/19) -> (26/11,19/8) Hyperbolic Matrix(391,616,106,167) (-30/19,-11/7) -> (11/3,26/7) Hyperbolic Matrix(841,1316,108,169) (-36/23,-61/39) -> (23/3,8/1) Hyperbolic Matrix(3081,4816,2186,3417) (-86/55,-25/16) -> (31/22,86/61) Hyperbolic Matrix(449,700,288,449) (-25/16,-14/9) -> (14/9,25/16) Hyperbolic Matrix(55,84,36,55) (-14/9,-3/2) -> (3/2,14/9) Hyperbolic Matrix(839,1232,190,279) (-3/2,-22/15) -> (22/5,53/12) Hyperbolic Matrix(2241,3248,928,1345) (-29/20,-42/29) -> (70/29,29/12) Hyperbolic Matrix(4313,6244,1664,2409) (-42/29,-55/38) -> (57/22,70/27) Hyperbolic Matrix(505,728,428,617) (-13/9,-36/25) -> (20/17,13/11) Hyperbolic Matrix(2297,3304,974,1401) (-59/41,-23/16) -> (33/14,59/25) Hyperbolic Matrix(449,644,274,393) (-23/16,-10/7) -> (18/11,23/14) Hyperbolic Matrix(393,560,40,57) (-10/7,-47/33) -> (9/1,10/1) Hyperbolic Matrix(6607,9408,4168,5935) (-47/33,-84/59) -> (84/53,65/41) Hyperbolic Matrix(3305,4704,2086,2969) (-84/59,-37/26) -> (19/12,84/53) Hyperbolic Matrix(671,952,394,559) (-27/19,-17/12) -> (17/10,29/17) Hyperbolic Matrix(337,476,80,113) (-17/12,-24/17) -> (4/1,17/4) Hyperbolic Matrix(279,392,-200,-281) (-24/17,-7/5) -> (-7/5,-32/23) Parabolic Matrix(785,1092,202,281) (-32/23,-57/41) -> (27/7,4/1) Hyperbolic Matrix(23687,32928,10030,13943) (-57/41,-196/141) -> (196/83,111/47) Hyperbolic Matrix(31585,43904,13376,18593) (-196/141,-139/100) -> (85/36,196/83) Hyperbolic Matrix(2297,3192,444,617) (-82/59,-25/18) -> (31/6,26/5) Hyperbolic Matrix(727,1008,282,391) (-25/18,-18/13) -> (18/7,31/12) Hyperbolic Matrix(9071,12544,2510,3471) (-65/47,-112/81) -> (112/31,47/13) Hyperbolic Matrix(9073,12544,2512,3473) (-112/81,-47/34) -> (65/18,112/31) Hyperbolic Matrix(1175,1624,526,727) (-47/34,-29/21) -> (29/13,9/4) Hyperbolic Matrix(1177,1624,366,505) (-29/21,-40/29) -> (16/5,29/9) Hyperbolic Matrix(2295,3136,614,839) (-41/30,-56/41) -> (56/15,15/4) Hyperbolic Matrix(2297,3136,616,841) (-56/41,-15/11) -> (41/11,56/15) Hyperbolic Matrix(391,532,-330,-449) (-15/11,-19/14) -> (-19/16,-13/11) Hyperbolic Matrix(167,224,-126,-169) (-27/20,-4/3) -> (-4/3,-29/22) Parabolic Matrix(2913,3836,1234,1625) (-29/22,-25/19) -> (59/25,85/36) Hyperbolic Matrix(1343,1764,-1024,-1345) (-25/19,-21/16) -> (-21/16,-59/45) Parabolic Matrix(279,364,128,167) (-17/13,-13/10) -> (13/6,11/5) Hyperbolic Matrix(281,364,44,57) (-13/10,-22/17) -> (6/1,13/2) Hyperbolic Matrix(6607,8540,2772,3583) (-53/41,-84/65) -> (112/47,31/13) Hyperbolic Matrix(7953,10276,3338,4313) (-84/65,-31/24) -> (81/34,112/47) Hyperbolic Matrix(2407,3080,1706,2183) (-32/25,-55/43) -> (55/39,24/17) Hyperbolic Matrix(1511,1932,262,335) (-55/43,-23/18) -> (23/4,29/5) Hyperbolic Matrix(505,644,396,505) (-23/18,-14/11) -> (14/11,23/18) Hyperbolic Matrix(111,140,88,111) (-14/11,-5/4) -> (5/4,14/11) Hyperbolic Matrix(113,140,46,57) (-5/4,-11/9) -> (17/7,5/2) Hyperbolic Matrix(505,616,414,505) (-11/9,-28/23) -> (28/23,11/9) Hyperbolic Matrix(783,952,644,783) (-28/23,-17/14) -> (17/14,28/23) Hyperbolic Matrix(393,476,232,281) (-17/14,-6/5) -> (22/13,17/10) Hyperbolic Matrix(895,1064,376,447) (-6/5,-19/16) -> (19/8,50/21) Hyperbolic Matrix(167,196,-144,-169) (-13/11,-7/6) -> (-7/6,-15/13) Parabolic Matrix(559,644,388,447) (-15/13,-8/7) -> (36/25,13/9) Hyperbolic Matrix(279,308,202,223) (-9/8,-1/1) -> (29/21,47/34) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(223,-252,100,-113) (1/1,8/7) -> (20/9,29/13) Hyperbolic Matrix(169,-196,144,-167) (8/7,7/6) -> (7/6,20/17) Parabolic Matrix(449,-532,330,-391) (13/11,6/5) -> (34/25,15/11) Hyperbolic Matrix(503,-644,132,-169) (23/18,9/7) -> (19/5,23/6) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(449,-588,42,-55) (17/13,38/29) -> (10/1,11/1) Hyperbolic Matrix(2521,-3304,982,-1287) (38/29,21/16) -> (77/30,18/7) Hyperbolic Matrix(2407,-3164,938,-1233) (21/16,25/19) -> (59/23,77/30) Hyperbolic Matrix(615,-812,128,-169) (25/19,4/3) -> (24/5,53/11) Hyperbolic Matrix(393,-532,82,-111) (4/3,19/14) -> (19/4,24/5) Hyperbolic Matrix(225,-308,122,-167) (15/11,11/8) -> (11/6,13/7) Hyperbolic Matrix(447,-616,82,-113) (11/8,29/21) -> (27/5,11/2) Hyperbolic Matrix(1457,-2016,404,-559) (47/34,18/13) -> (18/5,65/18) Hyperbolic Matrix(281,-392,200,-279) (25/18,7/5) -> (7/5,31/22) Parabolic Matrix(7785,-10976,3296,-4647) (86/61,55/39) -> (111/47,26/11) Hyperbolic Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(895,-1288,312,-449) (23/16,36/25) -> (20/7,23/8) Hyperbolic Matrix(559,-812,232,-337) (13/9,16/11) -> (12/5,41/17) Hyperbolic Matrix(615,-896,116,-169) (16/11,19/13) -> (37/7,16/3) Hyperbolic Matrix(727,-1064,192,-281) (19/13,3/2) -> (53/14,19/5) Hyperbolic Matrix(393,-616,178,-279) (25/16,11/7) -> (11/5,31/14) Hyperbolic Matrix(503,-812,70,-113) (50/31,21/13) -> (7/1,22/3) Hyperbolic Matrix(225,-364,34,-55) (21/13,13/8) -> (13/2,7/1) Hyperbolic Matrix(167,-280,34,-57) (5/3,27/16) -> (29/6,5/1) Hyperbolic Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(895,-1596,346,-617) (16/9,25/14) -> (31/12,44/17) Hyperbolic Matrix(2239,-4004,940,-1681) (25/14,34/19) -> (50/21,81/34) Hyperbolic Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(783,-1736,152,-337) (31/14,51/23) -> (5/1,31/6) Hyperbolic Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(1513,-3444,590,-1343) (25/11,41/18) -> (41/16,59/23) Hyperbolic Matrix(281,-644,24,-55) (55/24,39/17) -> (11/1,1/0) Hyperbolic Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(1567,-3780,604,-1457) (41/17,70/29) -> (70/27,13/5) Hyperbolic Matrix(503,-1288,66,-169) (23/9,41/16) -> (15/2,23/3) Hyperbolic Matrix(673,-1764,256,-671) (34/13,21/8) -> (21/8,50/19) Parabolic Matrix(617,-1624,106,-279) (50/19,29/11) -> (29/5,6/1) Hyperbolic Matrix(673,-1820,186,-503) (27/10,19/7) -> (47/13,29/8) Hyperbolic Matrix(167,-476,20,-57) (17/6,20/7) -> (8/1,17/2) Hyperbolic Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic Matrix(223,-840,30,-113) (15/4,34/9) -> (22/3,15/2) Hyperbolic Matrix(897,-3836,170,-727) (47/11,30/7) -> (58/11,37/7) Hyperbolic Matrix(337,-1764,64,-335) (26/5,21/4) -> (21/4,58/11) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(55,588,-42,-449) -> Matrix(1,0,-10,1) Matrix(111,1064,70,671) -> Matrix(7,2,52,15) Matrix(57,476,-20,-167) -> Matrix(1,0,-6,1) Matrix(169,1288,-66,-503) -> Matrix(1,4,-4,-15) Matrix(113,812,-70,-503) -> Matrix(1,2,-8,-15) Matrix(55,364,-34,-225) -> Matrix(1,2,-8,-15) Matrix(225,1316,-86,-503) -> Matrix(5,2,-18,-7) Matrix(225,1288,98,561) -> Matrix(1,0,8,1) Matrix(169,952,30,169) -> Matrix(1,0,8,1) Matrix(111,616,20,111) -> Matrix(1,0,0,1) Matrix(113,616,-82,-447) -> Matrix(1,0,-8,1) Matrix(169,896,-116,-615) -> Matrix(7,4,-58,-33) Matrix(391,2044,-268,-1401) -> Matrix(7,4,-58,-33) Matrix(391,2016,-250,-1289) -> Matrix(1,0,-6,1) Matrix(111,532,-82,-393) -> Matrix(11,2,-94,-17) Matrix(113,532,24,113) -> Matrix(1,0,14,1) Matrix(55,252,12,55) -> Matrix(1,0,-2,1) Matrix(113,504,-50,-223) -> Matrix(1,-2,-4,9) Matrix(167,728,64,279) -> Matrix(1,0,4,1) Matrix(111,476,52,223) -> Matrix(5,4,26,21) Matrix(727,3108,-498,-2129) -> Matrix(13,10,-108,-83) Matrix(223,952,26,111) -> Matrix(3,2,-2,-1) Matrix(113,476,80,337) -> Matrix(1,0,10,1) Matrix(169,644,-132,-503) -> Matrix(1,0,-8,1) Matrix(281,1064,-192,-727) -> Matrix(11,6,-90,-49) Matrix(839,3164,-520,-1961) -> Matrix(1,0,-6,1) Matrix(391,1456,-286,-1065) -> Matrix(13,6,-102,-47) Matrix(167,616,106,391) -> Matrix(1,0,10,1) Matrix(55,196,-16,-57) -> Matrix(1,0,0,1) Matrix(281,952,116,393) -> Matrix(9,4,38,17) Matrix(449,1512,-166,-559) -> Matrix(5,2,-18,-7) Matrix(111,364,68,223) -> Matrix(7,2,52,15) Matrix(337,1092,104,337) -> Matrix(7,2,24,7) Matrix(1007,3248,590,1903) -> Matrix(1,0,10,1) Matrix(279,896,52,167) -> Matrix(1,0,4,1) Matrix(167,532,70,223) -> Matrix(1,0,8,1) Matrix(449,1288,-312,-895) -> Matrix(21,4,-184,-35) Matrix(503,1428,118,335) -> Matrix(11,2,16,3) Matrix(169,476,60,169) -> Matrix(1,0,12,1) Matrix(111,308,40,111) -> Matrix(1,0,4,1) Matrix(113,308,62,169) -> Matrix(5,2,32,13) Matrix(1231,3332,-890,-2409) -> Matrix(7,2,-60,-17) Matrix(167,448,104,279) -> Matrix(1,0,10,1) Matrix(169,448,106,281) -> Matrix(13,4,94,29) Matrix(671,1764,-256,-673) -> Matrix(1,0,0,1) Matrix(1401,3668,364,953) -> Matrix(7,2,10,3) Matrix(279,728,64,167) -> Matrix(1,0,4,1) Matrix(671,1736,-390,-1009) -> Matrix(7,2,-60,-17) Matrix(391,1008,282,727) -> Matrix(7,2,52,15) Matrix(1343,3444,-590,-1513) -> Matrix(15,4,-64,-17) Matrix(1455,3724,656,1679) -> Matrix(15,4,56,15) Matrix(505,1288,198,505) -> Matrix(55,14,216,55) Matrix(111,280,44,111) -> Matrix(9,2,40,9) Matrix(57,140,46,113) -> Matrix(1,0,14,1) Matrix(335,812,92,223) -> Matrix(17,4,38,9) Matrix(337,812,-232,-559) -> Matrix(37,8,-310,-67) Matrix(223,532,70,167) -> Matrix(1,0,8,1) Matrix(1399,3332,-1082,-2577) -> Matrix(1,0,-4,1) Matrix(671,1596,494,1175) -> Matrix(13,2,110,17) Matrix(449,1064,284,673) -> Matrix(7,2,52,15) Matrix(167,392,-72,-169) -> Matrix(1,0,0,1) Matrix(4759,10976,-3424,-7897) -> Matrix(1,0,-4,1) Matrix(2575,5936,534,1231) -> Matrix(9,2,40,9) Matrix(559,1288,194,447) -> Matrix(9,2,40,9) Matrix(561,1288,98,225) -> Matrix(1,0,8,1) Matrix(1343,3080,-1026,-2353) -> Matrix(1,0,-4,1) Matrix(1455,3332,562,1287) -> Matrix(3,2,10,7) Matrix(503,1148,294,671) -> Matrix(1,0,10,1) Matrix(2129,4844,-1624,-3695) -> Matrix(1,0,-6,1) Matrix(2071,4704,468,1063) -> Matrix(31,8,-4,-1) Matrix(4145,9408,938,2129) -> Matrix(81,20,4,1) Matrix(1679,3808,444,1007) -> Matrix(17,4,38,9) Matrix(113,252,-100,-223) -> Matrix(1,0,-6,1) Matrix(279,616,-178,-393) -> Matrix(9,2,-68,-15) Matrix(167,364,128,279) -> Matrix(9,2,76,17) Matrix(337,728,156,337) -> Matrix(49,10,240,49) Matrix(391,840,182,391) -> Matrix(71,14,360,71) Matrix(223,476,52,111) -> Matrix(21,4,26,5) Matrix(167,308,-122,-225) -> Matrix(13,2,-98,-15) Matrix(169,308,62,113) -> Matrix(13,2,32,5) Matrix(111,196,-64,-113) -> Matrix(1,0,0,1) Matrix(503,868,-390,-673) -> Matrix(13,2,-124,-19) Matrix(1791,3080,-1238,-2129) -> Matrix(23,2,-196,-17) Matrix(897,1540,392,673) -> Matrix(1,0,10,1) Matrix(671,1148,294,503) -> Matrix(1,0,10,1) Matrix(3361,5740,1968,3361) -> Matrix(13,2,84,13) Matrix(1903,3248,590,1007) -> Matrix(1,0,10,1) Matrix(559,952,394,671) -> Matrix(1,0,14,1) Matrix(281,476,232,393) -> Matrix(25,4,256,41) Matrix(1177,1988,730,1233) -> Matrix(13,2,110,17) Matrix(449,756,-332,-559) -> Matrix(51,8,-440,-69) Matrix(169,280,102,169) -> Matrix(41,6,280,41) Matrix(783,1288,476,783) -> Matrix(155,22,1092,155) Matrix(393,644,274,449) -> Matrix(29,4,268,37) Matrix(223,364,68,111) -> Matrix(15,2,52,7) Matrix(449,728,346,561) -> Matrix(29,4,268,37) Matrix(1233,1988,730,1177) -> Matrix(17,2,110,13) Matrix(279,448,104,167) -> Matrix(1,0,10,1) Matrix(281,448,106,169) -> Matrix(29,4,94,13) Matrix(953,1512,-670,-1063) -> Matrix(15,2,-98,-13) Matrix(673,1064,284,449) -> Matrix(15,2,52,7) Matrix(391,616,106,167) -> Matrix(1,0,10,1) Matrix(841,1316,108,169) -> Matrix(15,2,-8,-1) Matrix(3081,4816,2186,3417) -> Matrix(1,0,16,1) Matrix(449,700,288,449) -> Matrix(15,2,112,15) Matrix(55,84,36,55) -> Matrix(15,2,112,15) Matrix(839,1232,190,279) -> Matrix(65,8,8,1) Matrix(2241,3248,928,1345) -> Matrix(237,28,1058,125) Matrix(4313,6244,1664,2409) -> Matrix(409,48,1440,169) Matrix(505,728,428,617) -> Matrix(35,4,376,43) Matrix(2297,3304,974,1401) -> Matrix(53,6,256,29) Matrix(449,644,274,393) -> Matrix(37,4,268,29) Matrix(393,560,40,57) -> Matrix(1,0,10,1) Matrix(6607,9408,4168,5935) -> Matrix(39,2,292,15) Matrix(3305,4704,2086,2969) -> Matrix(7,2,52,15) Matrix(671,952,394,559) -> Matrix(1,0,14,1) Matrix(337,476,80,113) -> Matrix(1,0,10,1) Matrix(279,392,-200,-281) -> Matrix(1,0,0,1) Matrix(785,1092,202,281) -> Matrix(1,0,10,1) Matrix(23687,32928,10030,13943) -> Matrix(1,0,12,1) Matrix(31585,43904,13376,18593) -> Matrix(33,4,140,17) Matrix(2297,3192,444,617) -> Matrix(1,0,10,1) Matrix(727,1008,282,391) -> Matrix(15,2,52,7) Matrix(9071,12544,2510,3471) -> Matrix(71,8,204,23) Matrix(9073,12544,2512,3473) -> Matrix(37,4,120,13) Matrix(1175,1624,526,727) -> Matrix(1,0,14,1) Matrix(1177,1624,366,505) -> Matrix(1,0,12,1) Matrix(2295,3136,614,839) -> Matrix(95,12,182,23) Matrix(2297,3136,616,841) -> Matrix(129,16,266,33) Matrix(391,532,-330,-449) -> Matrix(17,2,-162,-19) Matrix(167,224,-126,-169) -> Matrix(35,4,-324,-37) Matrix(2913,3836,1234,1625) -> Matrix(1,0,14,1) Matrix(1343,1764,-1024,-1345) -> Matrix(1,0,0,1) Matrix(279,364,128,167) -> Matrix(17,2,76,9) Matrix(281,364,44,57) -> Matrix(19,2,28,3) Matrix(6607,8540,2772,3583) -> Matrix(17,2,76,9) Matrix(7953,10276,3338,4313) -> Matrix(55,6,284,31) Matrix(2407,3080,1706,2183) -> Matrix(1,0,18,1) Matrix(1511,1932,262,335) -> Matrix(1,0,12,1) Matrix(505,644,396,505) -> Matrix(19,2,180,19) Matrix(111,140,88,111) -> Matrix(19,2,180,19) Matrix(113,140,46,57) -> Matrix(1,0,14,1) Matrix(505,616,414,505) -> Matrix(79,8,780,79) Matrix(783,952,644,783) -> Matrix(121,12,1220,121) Matrix(393,476,232,281) -> Matrix(41,4,256,25) Matrix(895,1064,376,447) -> Matrix(1,0,16,1) Matrix(167,196,-144,-169) -> Matrix(1,0,0,1) Matrix(559,644,388,447) -> Matrix(43,4,376,35) Matrix(279,308,202,223) -> Matrix(1,0,20,1) Matrix(1,0,2,1) -> Matrix(1,0,24,1) Matrix(223,-252,100,-113) -> Matrix(1,0,-6,1) Matrix(169,-196,144,-167) -> Matrix(1,0,0,1) Matrix(449,-532,330,-391) -> Matrix(19,-2,162,-17) Matrix(503,-644,132,-169) -> Matrix(1,0,-8,1) Matrix(391,-504,218,-281) -> Matrix(19,-2,124,-13) Matrix(449,-588,42,-55) -> Matrix(1,0,-10,1) Matrix(2521,-3304,982,-1287) -> Matrix(41,-4,154,-15) Matrix(2407,-3164,938,-1233) -> Matrix(41,-4,154,-15) Matrix(615,-812,128,-169) -> Matrix(19,-2,86,-9) Matrix(393,-532,82,-111) -> Matrix(17,-2,94,-11) Matrix(225,-308,122,-167) -> Matrix(15,-2,98,-13) Matrix(447,-616,82,-113) -> Matrix(1,0,-8,1) Matrix(1457,-2016,404,-559) -> Matrix(1,0,-6,1) Matrix(281,-392,200,-279) -> Matrix(1,0,0,1) Matrix(7785,-10976,3296,-4647) -> Matrix(1,0,-4,1) Matrix(1063,-1512,670,-953) -> Matrix(13,-2,98,-15) Matrix(895,-1288,312,-449) -> Matrix(35,-4,184,-21) Matrix(559,-812,232,-337) -> Matrix(67,-8,310,-37) Matrix(615,-896,116,-169) -> Matrix(33,-4,58,-7) Matrix(727,-1064,192,-281) -> Matrix(49,-6,90,-11) Matrix(393,-616,178,-279) -> Matrix(15,-2,68,-9) Matrix(503,-812,70,-113) -> Matrix(15,-2,8,-1) Matrix(225,-364,34,-55) -> Matrix(15,-2,8,-1) Matrix(167,-280,34,-57) -> Matrix(13,-2,46,-7) Matrix(113,-196,64,-111) -> Matrix(1,0,0,1) Matrix(895,-1596,346,-617) -> Matrix(17,-2,60,-7) Matrix(2239,-4004,940,-1681) -> Matrix(13,-2,72,-11) Matrix(223,-420,60,-113) -> Matrix(23,-4,52,-9) Matrix(783,-1736,152,-337) -> Matrix(9,-2,14,-3) Matrix(223,-504,50,-113) -> Matrix(9,-2,-4,1) Matrix(1513,-3444,590,-1343) -> Matrix(17,-4,64,-15) Matrix(281,-644,24,-55) -> Matrix(1,0,-6,1) Matrix(169,-392,72,-167) -> Matrix(1,0,0,1) Matrix(1567,-3780,604,-1457) -> Matrix(91,-20,314,-69) Matrix(503,-1288,66,-169) -> Matrix(15,-4,4,-1) Matrix(673,-1764,256,-671) -> Matrix(1,0,0,1) Matrix(617,-1624,106,-279) -> Matrix(7,-2,18,-5) Matrix(673,-1820,186,-503) -> Matrix(7,-2,18,-5) Matrix(167,-476,20,-57) -> Matrix(1,0,-6,1) Matrix(57,-196,16,-55) -> Matrix(1,0,0,1) Matrix(223,-840,30,-113) -> Matrix(3,-2,2,-1) Matrix(897,-3836,170,-727) -> Matrix(3,-2,2,-1) Matrix(337,-1764,64,-335) -> Matrix(1,0,0,1) 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): 48 Degree of the the map X: 48 Degree of the the map Y: 192 ----------------------------------------------------------------------- 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 0/1 0/1 12 1 1/1 (0/1,1/12) 0 28 8/7 0 7 7/6 0 4 20/17 0 7 13/11 (3/31,1/10) 0 28 6/5 0 14 17/14 (6/61,1/10) 0 28 28/23 1/10 10 1 11/9 (1/10,4/39) 0 28 5/4 (1/10,1/9) 0 28 14/11 (1/10,1/9) 0 2 23/18 (1/10,1/9) 0 28 9/7 (2/19,1/9) 0 28 22/17 0 14 13/10 (3/28,1/9) 0 28 17/13 (0/1,1/8) 0 28 38/29 0 14 21/16 0 4 25/19 (1/10,3/29) 0 28 4/3 1/9 2 7 19/14 (2/17,3/25) 0 28 34/25 0 14 15/11 (5/41,1/8) 0 28 11/8 (0/1,1/8) 0 28 29/21 (0/1,1/8) 0 28 47/34 (2/19,1/9) 0 28 18/13 0 14 25/18 (1/9,1/8) 0 28 7/5 0 4 31/22 (1/9,1/8) 0 28 86/61 0 14 55/39 (0/1,1/8) 0 28 24/17 0 7 17/12 (2/17,1/8) 0 28 27/19 (0/1,1/8) 0 28 10/7 0 14 23/16 (1/9,7/62) 0 28 36/25 0 7 13/9 (3/26,5/43) 0 28 16/11 3/25 2 7 19/13 (4/33,5/41) 0 28 3/2 (1/8,1/7) 0 28 14/9 (1/8,1/7) 0 2 25/16 (1/8,1/7) 0 28 11/7 (0/1,1/8) 0 28 30/19 0 14 19/12 (3/23,2/15) 0 28 84/53 2/15 8 1 65/41 (2/15,13/97) 0 28 46/29 0 14 27/17 (2/15,3/22) 0 28 8/5 1/7 2 7 29/18 (0/1,1/8) 0 28 50/31 0 14 21/13 0 4 13/8 (1/8,1/7) 0 28 18/11 0 14 23/14 (11/78,1/7) 0 28 28/17 1/7 14 1 5/3 (1/7,3/20) 0 28 27/16 (2/13,1/6) 0 28 22/13 0 14 17/10 (1/6,2/11) 0 28 29/17 (0/1,1/6) 0 28 70/41 (1/7,1/6) 0 2 41/24 (1/7,1/6) 0 28 12/7 0 7 7/4 0 4 16/9 0 7 25/14 (1/8,1/7) 0 28 34/19 0 14 9/5 (0/1,1/7) 0 28 11/6 (2/13,1/6) 0 28 13/7 (7/43,1/6) 0 28 2/1 0 14 15/7 (7/36,1/5) 0 28 28/13 1/5 12 1 13/6 (1/5,5/24) 0 28 11/5 (2/9,1/4) 0 28 31/14 (1/5,1/4) 0 28 51/23 (3/13,1/4) 0 28 20/9 0 7 29/13 (0/1,1/6) 0 28 9/4 (1/5,2/9) 0 28 25/11 (1/4,3/11) 0 28 41/18 (1/4,1/3) 0 28 16/7 0 7 55/24 (0/1,1/6) 0 28 39/17 (0/1,1/4) 0 28 23/10 (1/6,1/5) 0 28 7/3 0 4 33/14 (1/6,1/5) 0 28 59/25 (3/13,1/4) 0 28 85/36 (2/9,1/4) 0 28 196/83 1/4 2 1 111/47 (0/1,1/4) 0 28 26/11 0 14 19/8 (0/1,1/5) 0 28 50/21 0 14 81/34 (3/16,1/5) 0 28 112/47 1/5 4 1 31/13 (1/5,1/4) 0 28 12/5 1/5 2 7 41/17 (7/32,9/41) 0 28 70/29 2/9 12 2 29/12 (2/9,5/22) 0 28 17/7 (4/17,1/4) 0 28 5/2 (1/5,1/4) 0 28 28/11 1/4 8 1 23/9 (1/4,7/27) 0 28 41/16 (1/4,5/19) 0 28 59/23 (1/4,7/27) 0 28 77/30 0 4 18/7 0 14 31/12 (1/4,3/11) 0 28 44/17 0 7 57/22 (9/32,2/7) 0 28 70/27 2/7 12 2 13/5 (3/10,1/3) 0 28 34/13 0 14 21/8 0 4 50/19 0 14 29/11 (1/4,2/7) 0 28 8/3 1/3 2 7 27/10 (0/1,1/2) 0 28 19/7 (1/3,2/5) 0 28 11/4 (0/1,1/2) 0 28 14/5 0/1 4 2 17/6 (0/1,1/6) 0 28 20/7 0 7 23/8 (1/5,3/14) 0 28 3/1 (1/4,1/3) 0 28 16/5 1/3 2 7 29/9 (0/1,1/4) 0 28 42/13 (1/4,1/3) 0 2 13/4 (1/4,1/3) 0 28 10/3 0 14 7/2 0 4 18/5 0 14 65/18 (2/7,1/3) 0 28 112/31 1/3 6 1 47/13 (1/3,4/11) 0 28 29/8 (3/8,2/5) 0 28 11/3 (0/1,1/2) 0 28 26/7 0 14 41/11 (11/23,1/2) 0 28 56/15 1/2 14 1 15/4 (1/2,3/5) 0 28 34/9 0 14 53/14 (1/2,7/13) 0 28 19/5 (2/3,1/1) 0 28 23/6 (1/2,1/1) 0 28 27/7 (0/1,1/2) 0 28 4/1 0 7 17/4 (1/2,2/3) 0 28 47/11 (2/3,5/7) 0 28 30/7 0 14 13/3 (1/1,3/2) 0 28 22/5 0 14 53/12 (9/1,1/0) 0 28 84/19 1/0 14 1 31/7 (-5/1,1/0) 0 28 9/2 (-1/1,0/1) 0 28 14/3 0/1 8 2 19/4 (0/1,1/7) 0 28 24/5 1/5 2 7 53/11 (1/4,1/3) 0 28 29/6 (0/1,1/4) 0 28 5/1 (1/3,1/2) 0 28 31/6 (1/2,1/1) 0 28 26/5 0 14 21/4 0 4 58/11 0 14 37/7 (0/1,1/3) 0 28 16/3 1/1 2 7 27/5 (0/1,1/0) 0 28 11/2 (0/1,1/0) 0 28 28/5 0/1 4 1 17/3 (0/1,1/4) 0 28 23/4 (1/3,1/2) 0 28 29/5 (0/1,1/2) 0 28 6/1 0 14 13/2 (1/1,1/0) 0 28 7/1 0 4 22/3 0 14 15/2 (-1/1,1/0) 0 28 23/3 (-3/1,1/0) 0 28 8/1 0 7 17/2 (0/1,1/0) 0 28 9/1 (-1/3,0/1) 0 28 10/1 0 14 11/1 (-1/2,0/1) 0 28 1/0 (0/1,1/0) 0 28 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,2,-1) (0/1,1/1) -> (0/1,1/1) Reflection Matrix(223,-252,100,-113) (1/1,8/7) -> (20/9,29/13) Hyperbolic Matrix(169,-196,144,-167) (8/7,7/6) -> (7/6,20/17) Parabolic Matrix(617,-728,428,-505) (20/17,13/11) -> (36/25,13/9) Glide Reflection Matrix(449,-532,330,-391) (13/11,6/5) -> (34/25,15/11) Hyperbolic Matrix(393,-476,232,-281) (6/5,17/14) -> (22/13,17/10) Glide Reflection Matrix(783,-952,644,-783) (17/14,28/23) -> (17/14,28/23) Reflection Matrix(505,-616,414,-505) (28/23,11/9) -> (28/23,11/9) Reflection Matrix(113,-140,46,-57) (11/9,5/4) -> (17/7,5/2) Glide Reflection Matrix(111,-140,88,-111) (5/4,14/11) -> (5/4,14/11) Reflection Matrix(505,-644,396,-505) (14/11,23/18) -> (14/11,23/18) Reflection Matrix(503,-644,132,-169) (23/18,9/7) -> (19/5,23/6) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(281,-364,44,-57) (22/17,13/10) -> (6/1,13/2) Glide Reflection Matrix(279,-364,128,-167) (13/10,17/13) -> (13/6,11/5) Glide Reflection Matrix(449,-588,42,-55) (17/13,38/29) -> (10/1,11/1) Hyperbolic Matrix(2521,-3304,982,-1287) (38/29,21/16) -> (77/30,18/7) Hyperbolic Matrix(2407,-3164,938,-1233) (21/16,25/19) -> (59/23,77/30) Hyperbolic Matrix(615,-812,128,-169) (25/19,4/3) -> (24/5,53/11) Hyperbolic Matrix(393,-532,82,-111) (4/3,19/14) -> (19/4,24/5) Hyperbolic Matrix(1175,-1596,494,-671) (19/14,34/25) -> (19/8,50/21) Glide Reflection Matrix(225,-308,122,-167) (15/11,11/8) -> (11/6,13/7) Hyperbolic Matrix(447,-616,82,-113) (11/8,29/21) -> (27/5,11/2) Hyperbolic Matrix(1175,-1624,526,-727) (29/21,47/34) -> (29/13,9/4) Glide Reflection Matrix(1457,-2016,404,-559) (47/34,18/13) -> (18/5,65/18) Hyperbolic Matrix(727,-1008,282,-391) (18/13,25/18) -> (18/7,31/12) Glide Reflection Matrix(281,-392,200,-279) (25/18,7/5) -> (7/5,31/22) Parabolic Matrix(2463,-3472,476,-671) (31/22,86/61) -> (31/6,26/5) Glide Reflection Matrix(7785,-10976,3296,-4647) (86/61,55/39) -> (111/47,26/11) Hyperbolic Matrix(615,-868,158,-223) (55/39,24/17) -> (27/7,4/1) Glide Reflection Matrix(337,-476,80,-113) (24/17,17/12) -> (4/1,17/4) Glide Reflection Matrix(671,-952,394,-559) (17/12,27/19) -> (17/10,29/17) Glide Reflection Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(449,-644,274,-393) (10/7,23/16) -> (18/11,23/14) Glide Reflection Matrix(895,-1288,312,-449) (23/16,36/25) -> (20/7,23/8) Hyperbolic Matrix(559,-812,232,-337) (13/9,16/11) -> (12/5,41/17) Hyperbolic Matrix(615,-896,116,-169) (16/11,19/13) -> (37/7,16/3) Hyperbolic Matrix(727,-1064,192,-281) (19/13,3/2) -> (53/14,19/5) Hyperbolic Matrix(55,-84,36,-55) (3/2,14/9) -> (3/2,14/9) Reflection Matrix(449,-700,288,-449) (14/9,25/16) -> (14/9,25/16) Reflection Matrix(393,-616,178,-279) (25/16,11/7) -> (11/5,31/14) Hyperbolic Matrix(391,-616,106,-167) (11/7,30/19) -> (11/3,26/7) Glide Reflection Matrix(673,-1064,284,-449) (30/19,19/12) -> (26/11,19/8) Glide Reflection Matrix(2015,-3192,1272,-2015) (19/12,84/53) -> (19/12,84/53) Reflection Matrix(6889,-10920,4346,-6889) (84/53,65/41) -> (84/53,65/41) Reflection Matrix(671,-1064,70,-111) (65/41,46/29) -> (9/1,10/1) Glide Reflection Matrix(281,-448,106,-169) (27/17,8/5) -> (29/11,8/3) Glide Reflection Matrix(279,-448,104,-167) (8/5,29/18) -> (8/3,27/10) Glide Reflection Matrix(1233,-1988,730,-1177) (29/18,50/31) -> (27/16,22/13) Glide Reflection Matrix(503,-812,70,-113) (50/31,21/13) -> (7/1,22/3) Hyperbolic Matrix(225,-364,34,-55) (21/13,13/8) -> (13/2,7/1) Hyperbolic Matrix(223,-364,68,-111) (13/8,18/11) -> (13/4,10/3) Glide Reflection Matrix(783,-1288,476,-783) (23/14,28/17) -> (23/14,28/17) Reflection Matrix(169,-280,102,-169) (28/17,5/3) -> (28/17,5/3) Reflection Matrix(167,-280,34,-57) (5/3,27/16) -> (29/6,5/1) Hyperbolic Matrix(1903,-3248,590,-1007) (29/17,70/41) -> (29/9,42/13) Glide Reflection Matrix(3361,-5740,1968,-3361) (70/41,41/24) -> (70/41,41/24) Reflection Matrix(671,-1148,294,-503) (41/24,12/7) -> (41/18,16/7) Glide Reflection Matrix(113,-196,64,-111) (12/7,7/4) -> (7/4,16/9) Parabolic Matrix(895,-1596,346,-617) (16/9,25/14) -> (31/12,44/17) Hyperbolic Matrix(2239,-4004,940,-1681) (25/14,34/19) -> (50/21,81/34) Hyperbolic Matrix(169,-308,62,-113) (9/5,11/6) -> (19/7,11/4) Glide Reflection Matrix(223,-420,60,-113) (13/7,2/1) -> (26/7,41/11) Hyperbolic Matrix(223,-476,52,-111) (2/1,15/7) -> (30/7,13/3) Glide Reflection Matrix(391,-840,182,-391) (15/7,28/13) -> (15/7,28/13) Reflection Matrix(337,-728,156,-337) (28/13,13/6) -> (28/13,13/6) Reflection Matrix(783,-1736,152,-337) (31/14,51/23) -> (5/1,31/6) Hyperbolic Matrix(391,-868,50,-111) (51/23,20/9) -> (23/3,8/1) Glide Reflection Matrix(223,-504,50,-113) (9/4,25/11) -> (31/7,9/2) Hyperbolic Matrix(1513,-3444,590,-1343) (25/11,41/18) -> (41/16,59/23) Hyperbolic Matrix(1455,-3332,562,-1287) (16/7,55/24) -> (44/17,57/22) Glide Reflection Matrix(281,-644,24,-55) (55/24,39/17) -> (11/1,1/0) Hyperbolic Matrix(561,-1288,98,-225) (39/17,23/10) -> (17/3,23/4) Glide Reflection Matrix(169,-392,72,-167) (23/10,7/3) -> (7/3,33/14) Parabolic Matrix(617,-1456,214,-505) (33/14,59/25) -> (23/8,3/1) Glide Reflection Matrix(2633,-6216,546,-1289) (59/25,85/36) -> (53/11,29/6) Glide Reflection Matrix(14111,-33320,5976,-14111) (85/36,196/83) -> (85/36,196/83) Reflection Matrix(18425,-43512,7802,-18425) (196/83,111/47) -> (196/83,111/47) Reflection Matrix(7615,-18144,3196,-7615) (81/34,112/47) -> (81/34,112/47) Reflection Matrix(2913,-6944,1222,-2913) (112/47,31/13) -> (112/47,31/13) Reflection Matrix(223,-532,70,-167) (31/13,12/5) -> (3/1,16/5) Glide Reflection Matrix(1567,-3780,604,-1457) (41/17,70/29) -> (70/27,13/5) Hyperbolic Matrix(1681,-4060,696,-1681) (70/29,29/12) -> (70/29,29/12) Reflection Matrix(335,-812,92,-223) (29/12,17/7) -> (29/8,11/3) Glide Reflection Matrix(111,-280,44,-111) (5/2,28/11) -> (5/2,28/11) Reflection Matrix(505,-1288,198,-505) (28/11,23/9) -> (28/11,23/9) Reflection Matrix(503,-1288,66,-169) (23/9,41/16) -> (15/2,23/3) Hyperbolic Matrix(3079,-7980,1188,-3079) (57/22,70/27) -> (57/22,70/27) Reflection Matrix(279,-728,64,-167) (13/5,34/13) -> (13/3,22/5) Glide Reflection Matrix(673,-1764,256,-671) (34/13,21/8) -> (21/8,50/19) Parabolic Matrix(617,-1624,106,-279) (50/19,29/11) -> (29/5,6/1) Hyperbolic Matrix(673,-1820,186,-503) (27/10,19/7) -> (47/13,29/8) Hyperbolic Matrix(111,-308,40,-111) (11/4,14/5) -> (11/4,14/5) Reflection Matrix(169,-476,60,-169) (14/5,17/6) -> (14/5,17/6) Reflection Matrix(167,-476,20,-57) (17/6,20/7) -> (8/1,17/2) Hyperbolic Matrix(279,-896,52,-167) (16/5,29/9) -> (16/3,27/5) Glide Reflection Matrix(337,-1092,104,-337) (42/13,13/4) -> (42/13,13/4) Reflection Matrix(57,-196,16,-55) (10/3,7/2) -> (7/2,18/5) Parabolic Matrix(4031,-14560,1116,-4031) (65/18,112/31) -> (65/18,112/31) Reflection Matrix(2913,-10528,806,-2913) (112/31,47/13) -> (112/31,47/13) Reflection Matrix(1231,-4592,330,-1231) (41/11,56/15) -> (41/11,56/15) Reflection Matrix(449,-1680,120,-449) (56/15,15/4) -> (56/15,15/4) Reflection Matrix(223,-840,30,-113) (15/4,34/9) -> (22/3,15/2) Hyperbolic Matrix(785,-2968,178,-673) (34/9,53/14) -> (22/5,53/12) Glide Reflection Matrix(335,-1288,58,-223) (23/6,27/7) -> (23/4,29/5) Glide Reflection Matrix(223,-952,26,-111) (17/4,47/11) -> (17/2,9/1) Glide Reflection Matrix(897,-3836,170,-727) (47/11,30/7) -> (58/11,37/7) Hyperbolic Matrix(2015,-8904,456,-2015) (53/12,84/19) -> (53/12,84/19) Reflection Matrix(1177,-5208,266,-1177) (84/19,31/7) -> (84/19,31/7) Reflection Matrix(55,-252,12,-55) (9/2,14/3) -> (9/2,14/3) Reflection Matrix(113,-532,24,-113) (14/3,19/4) -> (14/3,19/4) Reflection Matrix(337,-1764,64,-335) (26/5,21/4) -> (21/4,58/11) Parabolic Matrix(111,-616,20,-111) (11/2,28/5) -> (11/2,28/5) Reflection Matrix(169,-952,30,-169) (28/5,17/3) -> (28/5,17/3) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,2,-1) -> Matrix(1,0,24,-1) (0/1,1/1) -> (0/1,1/12) Matrix(223,-252,100,-113) -> Matrix(1,0,-6,1) 0/1 Matrix(169,-196,144,-167) -> Matrix(1,0,0,1) Matrix(617,-728,428,-505) -> Matrix(43,-4,376,-35) Matrix(449,-532,330,-391) -> Matrix(19,-2,162,-17) 1/9 Matrix(393,-476,232,-281) -> Matrix(41,-4,256,-25) Matrix(783,-952,644,-783) -> Matrix(121,-12,1220,-121) (17/14,28/23) -> (6/61,1/10) Matrix(505,-616,414,-505) -> Matrix(79,-8,780,-79) (28/23,11/9) -> (1/10,4/39) Matrix(113,-140,46,-57) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(111,-140,88,-111) -> Matrix(19,-2,180,-19) (5/4,14/11) -> (1/10,1/9) Matrix(505,-644,396,-505) -> Matrix(19,-2,180,-19) (14/11,23/18) -> (1/10,1/9) Matrix(503,-644,132,-169) -> Matrix(1,0,-8,1) 0/1 Matrix(391,-504,218,-281) -> Matrix(19,-2,124,-13) Matrix(281,-364,44,-57) -> Matrix(19,-2,28,-3) Matrix(279,-364,128,-167) -> Matrix(17,-2,76,-9) Matrix(449,-588,42,-55) -> Matrix(1,0,-10,1) 0/1 Matrix(2521,-3304,982,-1287) -> Matrix(41,-4,154,-15) Matrix(2407,-3164,938,-1233) -> Matrix(41,-4,154,-15) Matrix(615,-812,128,-169) -> Matrix(19,-2,86,-9) Matrix(393,-532,82,-111) -> Matrix(17,-2,94,-11) Matrix(1175,-1596,494,-671) -> Matrix(17,-2,110,-13) Matrix(225,-308,122,-167) -> Matrix(15,-2,98,-13) 1/7 Matrix(447,-616,82,-113) -> Matrix(1,0,-8,1) 0/1 Matrix(1175,-1624,526,-727) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(1457,-2016,404,-559) -> Matrix(1,0,-6,1) 0/1 Matrix(727,-1008,282,-391) -> Matrix(15,-2,52,-7) Matrix(281,-392,200,-279) -> Matrix(1,0,0,1) Matrix(2463,-3472,476,-671) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(7785,-10976,3296,-4647) -> Matrix(1,0,-4,1) 0/1 Matrix(615,-868,158,-223) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(337,-476,80,-113) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(671,-952,394,-559) -> Matrix(1,0,14,-1) *** -> (0/1,1/7) Matrix(1063,-1512,670,-953) -> Matrix(13,-2,98,-15) 1/7 Matrix(449,-644,274,-393) -> Matrix(37,-4,268,-29) Matrix(895,-1288,312,-449) -> Matrix(35,-4,184,-21) Matrix(559,-812,232,-337) -> Matrix(67,-8,310,-37) Matrix(615,-896,116,-169) -> Matrix(33,-4,58,-7) Matrix(727,-1064,192,-281) -> Matrix(49,-6,90,-11) Matrix(55,-84,36,-55) -> Matrix(15,-2,112,-15) (3/2,14/9) -> (1/8,1/7) Matrix(449,-700,288,-449) -> Matrix(15,-2,112,-15) (14/9,25/16) -> (1/8,1/7) Matrix(393,-616,178,-279) -> Matrix(15,-2,68,-9) Matrix(391,-616,106,-167) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(673,-1064,284,-449) -> Matrix(15,-2,52,-7) Matrix(2015,-3192,1272,-2015) -> Matrix(91,-12,690,-91) (19/12,84/53) -> (3/23,2/15) Matrix(6889,-10920,4346,-6889) -> Matrix(389,-52,2910,-389) (84/53,65/41) -> (2/15,13/97) Matrix(671,-1064,70,-111) -> Matrix(15,-2,52,-7) Matrix(281,-448,106,-169) -> Matrix(29,-4,94,-13) Matrix(279,-448,104,-167) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(1233,-1988,730,-1177) -> Matrix(17,-2,110,-13) Matrix(503,-812,70,-113) -> Matrix(15,-2,8,-1) Matrix(225,-364,34,-55) -> Matrix(15,-2,8,-1) Matrix(223,-364,68,-111) -> Matrix(15,-2,52,-7) Matrix(783,-1288,476,-783) -> Matrix(155,-22,1092,-155) (23/14,28/17) -> (11/78,1/7) Matrix(169,-280,102,-169) -> Matrix(41,-6,280,-41) (28/17,5/3) -> (1/7,3/20) Matrix(167,-280,34,-57) -> Matrix(13,-2,46,-7) Matrix(1903,-3248,590,-1007) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(3361,-5740,1968,-3361) -> Matrix(13,-2,84,-13) (70/41,41/24) -> (1/7,1/6) Matrix(671,-1148,294,-503) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(113,-196,64,-111) -> Matrix(1,0,0,1) Matrix(895,-1596,346,-617) -> Matrix(17,-2,60,-7) Matrix(2239,-4004,940,-1681) -> Matrix(13,-2,72,-11) 1/6 Matrix(169,-308,62,-113) -> Matrix(13,-2,32,-5) Matrix(223,-420,60,-113) -> Matrix(23,-4,52,-9) Matrix(223,-476,52,-111) -> Matrix(21,-4,26,-5) Matrix(391,-840,182,-391) -> Matrix(71,-14,360,-71) (15/7,28/13) -> (7/36,1/5) Matrix(337,-728,156,-337) -> Matrix(49,-10,240,-49) (28/13,13/6) -> (1/5,5/24) Matrix(783,-1736,152,-337) -> Matrix(9,-2,14,-3) Matrix(391,-868,50,-111) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(223,-504,50,-113) -> Matrix(9,-2,-4,1) Matrix(1513,-3444,590,-1343) -> Matrix(17,-4,64,-15) 1/4 Matrix(1455,-3332,562,-1287) -> Matrix(3,-2,10,-7) Matrix(281,-644,24,-55) -> Matrix(1,0,-6,1) 0/1 Matrix(561,-1288,98,-225) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(169,-392,72,-167) -> Matrix(1,0,0,1) Matrix(617,-1456,214,-505) -> Matrix(9,-2,40,-9) *** -> (1/5,1/4) Matrix(2633,-6216,546,-1289) -> Matrix(9,-2,40,-9) *** -> (1/5,1/4) Matrix(14111,-33320,5976,-14111) -> Matrix(17,-4,72,-17) (85/36,196/83) -> (2/9,1/4) Matrix(18425,-43512,7802,-18425) -> Matrix(1,0,8,-1) (196/83,111/47) -> (0/1,1/4) Matrix(7615,-18144,3196,-7615) -> Matrix(31,-6,160,-31) (81/34,112/47) -> (3/16,1/5) Matrix(2913,-6944,1222,-2913) -> Matrix(9,-2,40,-9) (112/47,31/13) -> (1/5,1/4) Matrix(223,-532,70,-167) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(1567,-3780,604,-1457) -> Matrix(91,-20,314,-69) Matrix(1681,-4060,696,-1681) -> Matrix(89,-20,396,-89) (70/29,29/12) -> (2/9,5/22) Matrix(335,-812,92,-223) -> Matrix(17,-4,38,-9) Matrix(111,-280,44,-111) -> Matrix(9,-2,40,-9) (5/2,28/11) -> (1/5,1/4) Matrix(505,-1288,198,-505) -> Matrix(55,-14,216,-55) (28/11,23/9) -> (1/4,7/27) Matrix(503,-1288,66,-169) -> Matrix(15,-4,4,-1) Matrix(3079,-7980,1188,-3079) -> Matrix(127,-36,448,-127) (57/22,70/27) -> (9/32,2/7) Matrix(279,-728,64,-167) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(673,-1764,256,-671) -> Matrix(1,0,0,1) Matrix(617,-1624,106,-279) -> Matrix(7,-2,18,-5) 1/3 Matrix(673,-1820,186,-503) -> Matrix(7,-2,18,-5) 1/3 Matrix(111,-308,40,-111) -> Matrix(1,0,4,-1) (11/4,14/5) -> (0/1,1/2) Matrix(169,-476,60,-169) -> Matrix(1,0,12,-1) (14/5,17/6) -> (0/1,1/6) Matrix(167,-476,20,-57) -> Matrix(1,0,-6,1) 0/1 Matrix(279,-896,52,-167) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(337,-1092,104,-337) -> Matrix(7,-2,24,-7) (42/13,13/4) -> (1/4,1/3) Matrix(57,-196,16,-55) -> Matrix(1,0,0,1) Matrix(4031,-14560,1116,-4031) -> Matrix(13,-4,42,-13) (65/18,112/31) -> (2/7,1/3) Matrix(2913,-10528,806,-2913) -> Matrix(23,-8,66,-23) (112/31,47/13) -> (1/3,4/11) Matrix(1231,-4592,330,-1231) -> Matrix(45,-22,92,-45) (41/11,56/15) -> (11/23,1/2) Matrix(449,-1680,120,-449) -> Matrix(11,-6,20,-11) (56/15,15/4) -> (1/2,3/5) Matrix(223,-840,30,-113) -> Matrix(3,-2,2,-1) 1/1 Matrix(785,-2968,178,-673) -> Matrix(5,-2,2,-1) Matrix(335,-1288,58,-223) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(223,-952,26,-111) -> Matrix(3,-2,-2,1) Matrix(897,-3836,170,-727) -> Matrix(3,-2,2,-1) 1/1 Matrix(2015,-8904,456,-2015) -> Matrix(-1,18,0,1) (53/12,84/19) -> (9/1,1/0) Matrix(1177,-5208,266,-1177) -> Matrix(1,10,0,-1) (84/19,31/7) -> (-5/1,1/0) Matrix(55,-252,12,-55) -> Matrix(-1,0,2,1) (9/2,14/3) -> (-1/1,0/1) Matrix(113,-532,24,-113) -> Matrix(1,0,14,-1) (14/3,19/4) -> (0/1,1/7) Matrix(337,-1764,64,-335) -> Matrix(1,0,0,1) Matrix(111,-616,20,-111) -> Matrix(1,0,0,-1) (11/2,28/5) -> (0/1,1/0) Matrix(169,-952,30,-169) -> Matrix(1,0,8,-1) (28/5,17/3) -> (0/1,1/4) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.