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 -8/1 -7/1 -6/1 -21/5 -4/1 -7/2 -10/3 -16/5 -8/3 -12/5 -7/3 -2/1 -7/4 -21/13 -7/5 -4/3 -21/17 -7/6 0/1 1/1 7/6 28/23 14/11 4/3 15/11 7/5 42/29 3/2 14/9 21/13 28/17 7/4 84/47 28/15 2/1 7/3 12/5 5/2 28/11 8/3 14/5 3/1 35/11 16/5 42/13 10/3 84/25 7/2 196/55 25/7 112/31 11/3 56/15 27/7 4/1 21/5 13/3 84/19 9/2 23/5 14/3 5/1 11/2 28/5 17/3 6/1 19/3 13/2 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -8/1 2/3 -7/1 1/1 -20/3 0/1 -13/2 1/2 1/1 -6/1 0/1 -17/3 1/3 1/2 -28/5 1/2 -11/2 1/2 2/3 -5/1 1/2 1/1 -14/3 1/1 -23/5 1/1 4/3 -9/2 2/1 1/0 -22/5 0/1 -13/3 2/3 1/1 -17/4 3/2 2/1 -38/9 2/1 -21/5 1/0 -25/6 2/1 1/0 -4/1 0/1 -19/5 1/2 2/3 -34/9 2/3 -15/4 3/4 1/1 -11/3 0/1 1/0 -29/8 0/1 1/2 -47/13 5/11 1/2 -18/5 2/3 -25/7 0/1 1/2 -7/2 1/1 -31/9 2/1 1/0 -86/25 6/1 -55/16 -6/1 1/0 -24/7 0/1 -17/5 1/1 1/0 -27/8 2/1 1/0 -10/3 0/1 -23/7 1/1 2/1 -36/11 0/1 -13/4 1/1 1/0 -16/5 0/1 -19/6 0/1 1/2 -3/1 0/1 1/1 -14/5 0/1 -25/9 0/1 1/2 -11/4 0/1 1/2 -30/11 2/1 -19/7 0/1 1/0 -84/31 0/1 -65/24 0/1 1/6 -46/17 0/1 -27/10 2/5 1/2 -8/3 0/1 -29/11 1/3 1/2 -50/19 2/3 -21/8 1/2 -13/5 0/1 1/1 -18/7 2/3 -23/9 4/5 1/1 -28/11 1/1 -5/2 1/1 1/0 -27/11 -3/1 1/0 -22/9 0/1 -17/7 -1/1 1/0 -29/12 -2/1 1/0 -70/29 -1/1 -41/17 -1/1 0/1 -12/5 0/1 -7/3 0/1 -16/7 0/1 -25/11 0/1 1/2 -34/15 0/1 -9/4 2/5 1/2 -11/5 1/2 2/3 -13/6 5/6 1/1 -2/1 0/1 -15/8 7/8 1/1 -28/15 1/1 -13/7 1/1 6/5 -11/6 2/1 1/0 -31/17 2/1 1/0 -51/28 1/2 1/1 -20/11 2/1 -29/16 4/1 1/0 -9/5 -1/1 1/0 -25/14 0/1 1/0 -41/23 -1/1 0/1 -16/9 0/1 -55/31 0/1 1/0 -39/22 -1/2 0/1 -23/13 0/1 1/1 -7/4 0/1 -33/19 0/1 1/3 -59/34 2/5 1/2 -85/49 9/19 1/2 -196/113 1/2 -111/64 1/2 14/27 -26/15 2/3 -19/11 0/1 1/2 -50/29 0/1 -81/47 0/1 1/0 -112/65 0/1 -31/18 0/1 1/2 -12/7 0/1 -41/24 1/3 1/2 -70/41 1/2 -29/17 1/3 1/2 -17/10 0/1 1/2 -5/3 1/2 1/1 -28/17 1/1 -23/14 1/1 9/8 -41/25 1/1 6/5 -59/36 6/5 5/4 -77/47 5/4 -18/11 4/3 -31/19 3/2 2/1 -44/27 2/1 -57/35 2/1 1/0 -70/43 1/0 -13/8 1/1 1/0 -34/21 2/1 -21/13 1/1 -50/31 4/3 -29/18 3/2 8/5 -8/5 2/1 -27/17 1/1 1/0 -19/12 -2/1 1/0 -11/7 2/1 1/0 -14/9 1/0 -17/11 -1/1 1/0 -20/13 0/1 -23/15 1/1 2/1 -3/2 0/1 1/0 -16/11 0/1 -29/20 0/1 1/2 -42/29 1/1 -13/9 0/1 1/1 -10/7 2/1 -7/5 1/0 -18/13 0/1 -65/47 7/1 1/0 -112/81 1/0 -47/34 -6/1 1/0 -29/21 -3/1 1/0 -11/8 -2/1 1/0 -26/19 -4/3 -41/30 -9/8 -1/1 -56/41 -1/1 -15/11 -1/1 -2/3 -34/25 0/1 -53/39 -1/1 0/1 -19/14 0/1 1/0 -23/17 -1/1 -2/3 -27/20 -6/11 -1/2 -4/3 0/1 -17/13 1/2 1/1 -47/36 2/3 3/4 -30/23 4/5 -13/10 1/1 3/2 -22/17 2/1 -53/41 1/1 2/1 -84/65 2/1 -31/24 2/1 1/0 -9/7 1/1 1/0 -14/11 1/0 -19/15 -2/1 1/0 -24/19 0/1 -53/42 2/1 1/0 -29/23 -5/1 1/0 -5/4 -1/1 1/0 -31/25 -2/3 -1/2 -26/21 -2/5 -21/17 0/1 -58/47 -2/1 -37/30 0/1 1/0 -16/13 0/1 -27/22 -1/2 0/1 -11/9 -1/4 0/1 -28/23 0/1 -17/14 0/1 1/6 -23/19 0/1 1/3 -29/24 1/2 4/7 -6/5 0/1 -13/11 1/1 2/1 -7/6 1/0 -22/19 -2/1 -15/13 -1/1 0/1 -23/20 -1/1 -3/4 -8/7 0/1 -17/15 -1/1 1/0 -9/8 -1/2 0/1 -10/9 0/1 -11/10 -1/2 0/1 -1/1 0/1 1/0 0/1 0/1 1/1 0/1 1/4 10/9 0/1 9/8 0/1 1/6 8/7 0/1 15/13 0/1 1/5 7/6 1/4 6/5 0/1 23/19 0/1 1/1 17/14 -1/2 0/1 28/23 0/1 11/9 0/1 1/8 16/13 0/1 21/17 0/1 26/21 2/13 5/4 1/5 1/4 19/15 2/9 1/4 14/11 1/4 9/7 1/4 1/3 22/17 2/7 13/10 3/10 1/3 30/23 4/11 47/36 3/8 2/5 17/13 1/3 1/2 4/3 0/1 19/14 0/1 1/4 34/25 0/1 15/11 2/11 1/5 26/19 4/19 11/8 2/9 1/4 7/5 1/4 17/12 0/1 1/4 27/19 1/5 1/4 10/7 2/7 13/9 0/1 1/3 42/29 1/3 29/20 0/1 1/2 16/11 0/1 3/2 0/1 1/4 20/13 0/1 37/24 0/1 1/6 17/11 1/5 1/4 14/9 1/4 11/7 1/4 2/7 19/12 2/9 1/4 46/29 4/15 27/17 1/4 1/3 8/5 2/7 29/18 8/27 3/10 21/13 1/3 55/34 2/9 1/4 89/55 3/11 2/7 34/21 2/7 13/8 1/4 1/3 31/19 2/7 3/10 18/11 4/13 41/25 6/19 1/3 64/39 6/19 23/14 9/28 1/3 28/17 1/3 5/3 1/3 1/2 17/10 0/1 1/2 29/17 1/2 1/1 12/7 0/1 31/18 0/1 1/2 50/29 0/1 19/11 0/1 1/2 26/15 2/5 7/4 0/1 30/17 2/9 83/47 1/4 9/35 53/30 1/4 2/7 23/13 0/1 1/3 39/22 0/1 1/6 55/31 0/1 1/4 16/9 0/1 41/23 0/1 1/5 66/37 2/9 25/14 0/1 1/4 84/47 0/1 59/33 0/1 1/5 34/19 0/1 9/5 1/5 1/4 20/11 2/7 11/6 1/4 2/7 13/7 6/19 1/3 28/15 1/3 15/8 1/3 7/20 2/1 0/1 11/5 2/5 1/2 9/4 1/2 2/3 7/3 0/1 19/8 1/4 2/7 31/13 0/1 1/4 43/18 1/3 1/2 55/23 0/1 1/2 12/5 0/1 41/17 0/1 1/5 70/29 1/5 29/12 2/9 1/4 17/7 1/5 1/4 22/9 0/1 27/11 3/13 1/4 5/2 1/4 1/3 28/11 1/3 23/9 1/3 4/11 18/7 2/5 13/5 0/1 1/3 34/13 2/5 21/8 1/2 71/27 0/1 1/3 50/19 2/5 29/11 1/2 1/1 8/3 0/1 27/10 1/2 2/3 19/7 0/1 1/4 30/11 2/7 11/4 0/1 1/2 36/13 0/1 61/22 1/3 3/8 86/31 4/9 25/9 0/1 1/2 14/5 0/1 3/1 0/1 1/3 22/7 0/1 19/6 0/1 1/2 54/17 2/5 35/11 0/1 16/5 0/1 29/9 1/4 1/3 42/13 1/4 55/17 1/4 2/7 13/4 1/4 1/3 36/11 0/1 59/18 0/1 1/4 23/7 2/7 1/3 10/3 0/1 47/14 0/1 1/0 84/25 0/1 37/11 0/1 1/6 27/8 1/4 2/7 17/5 1/4 1/3 24/7 0/1 7/2 1/3 32/9 2/5 57/16 8/17 1/2 196/55 1/2 139/39 1/2 15/29 82/23 4/7 25/7 0/1 1/2 18/5 2/5 65/18 8/17 1/2 112/31 1/2 47/13 1/2 5/9 29/8 0/1 1/2 40/11 0/1 11/3 0/1 1/4 26/7 2/7 41/11 8/25 1/3 56/15 1/3 15/4 1/3 3/8 19/5 2/5 1/2 23/6 1/3 1/2 27/7 5/11 1/2 4/1 0/1 29/7 5/21 1/4 25/6 1/4 2/7 21/5 1/4 59/14 1/4 4/15 38/9 2/7 55/13 1/4 2/7 17/4 2/7 3/10 13/3 1/3 2/5 22/5 0/1 53/12 0/1 1/2 84/19 0/1 31/7 0/1 1/4 9/2 1/4 2/7 32/7 2/7 55/12 3/10 16/53 23/5 4/13 1/3 14/3 1/3 5/1 1/3 1/2 11/2 2/5 1/2 28/5 1/2 17/3 1/2 1/1 6/1 0/1 19/3 0/1 1/4 13/2 1/3 1/2 7/1 1/3 15/2 1/3 3/8 8/1 2/5 9/1 5/11 1/2 1/0 0/1 1/2 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(29,252,-16,-139) (-8/1,1/0) -> (-20/11,-29/16) Hyperbolic Matrix(27,196,-4,-29) (-8/1,-7/1) -> (-7/1,-20/3) Parabolic Matrix(111,728,34,223) (-20/3,-13/2) -> (13/4,36/11) Hyperbolic Matrix(83,532,-22,-141) (-13/2,-6/1) -> (-34/9,-15/4) Hyperbolic Matrix(83,476,34,195) (-6/1,-17/3) -> (17/7,22/9) 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(27,140,16,83) (-11/2,-5/1) -> (5/3,17/10) Hyperbolic Matrix(29,140,6,29) (-5/1,-14/3) -> (14/3,5/1) Hyperbolic Matrix(139,644,30,139) (-14/3,-23/5) -> (23/5,14/3) Hyperbolic Matrix(141,644,-104,-475) (-23/5,-9/2) -> (-19/14,-23/17) 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(85,364,46,197) (-13/3,-17/4) -> (11/6,13/7) Hyperbolic Matrix(139,588,-126,-533) (-17/4,-38/9) -> (-10/9,-11/10) Hyperbolic Matrix(783,3304,-478,-2017) (-38/9,-21/5) -> (-77/47,-18/11) Hyperbolic Matrix(757,3164,-462,-1931) (-21/5,-25/6) -> (-59/36,-77/47) Hyperbolic Matrix(197,812,-156,-643) (-25/6,-4/1) -> (-24/19,-53/42) Hyperbolic Matrix(139,532,-110,-421) (-4/1,-19/5) -> (-19/15,-24/19) Hyperbolic Matrix(421,1596,244,925) (-19/5,-34/9) -> (50/29,19/11) Hyperbolic Matrix(83,308,-38,-141) (-15/4,-11/3) -> (-11/5,-13/6) Hyperbolic Matrix(169,616,-138,-503) (-11/3,-29/8) -> (-27/22,-11/9) Hyperbolic Matrix(85,308,8,29) (-29/8,-47/13) -> (9/1,1/0) Hyperbolic Matrix(559,2016,-404,-1457) (-47/13,-18/5) -> (-18/13,-65/47) Hyperbolic Matrix(281,1008,172,617) (-18/5,-25/7) -> (31/19,18/11) Hyperbolic Matrix(111,392,-32,-113) (-25/7,-7/2) -> (-7/2,-31/9) Parabolic Matrix(1399,4816,504,1735) (-31/9,-86/25) -> (86/31,25/9) Hyperbolic Matrix(3191,10976,-1840,-6329) (-86/25,-55/16) -> (-111/64,-26/15) Hyperbolic Matrix(897,3080,196,673) (-55/16,-24/7) -> (32/7,55/12) Hyperbolic Matrix(139,476,106,363) (-24/7,-17/5) -> (17/13,4/3) Hyperbolic 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(195,644,76,251) (-10/3,-23/7) -> (23/9,18/7) Hyperbolic Matrix(393,1288,-256,-839) (-23/7,-36/11) -> (-20/13,-23/15) Hyperbolic Matrix(197,644,26,85) (-36/11,-13/4) -> (15/2,8/1) Hyperbolic Matrix(253,812,-148,-475) (-13/4,-16/5) -> (-12/7,-41/24) Hyperbolic Matrix(281,896,-228,-727) (-16/5,-19/6) -> (-37/30,-16/13) Hyperbolic Matrix(337,1064,-248,-783) (-19/6,-3/1) -> (-53/39,-19/14) Hyperbolic Matrix(29,84,10,29) (-3/1,-14/5) -> (14/5,3/1) Hyperbolic Matrix(251,700,90,251) (-14/5,-25/9) -> (25/9,14/5) Hyperbolic Matrix(223,616,-122,-337) (-25/9,-11/4) -> (-11/6,-31/17) Hyperbolic Matrix(225,616,164,449) (-11/4,-30/11) -> (26/19,11/8) Hyperbolic Matrix(391,1064,226,615) (-30/11,-19/7) -> (19/11,26/15) Hyperbolic Matrix(1735,4704,516,1399) (-19/7,-84/31) -> (84/25,37/11) Hyperbolic Matrix(3473,9408,1034,2801) (-84/31,-65/24) -> (47/14,84/25) Hyperbolic Matrix(393,1064,352,953) (-65/24,-46/17) -> (10/9,9/8) 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(755,1988,308,811) (-29/11,-50/19) -> (22/9,27/11) Hyperbolic Matrix(309,812,-266,-699) (-50/19,-21/8) -> (-7/6,-22/19) Hyperbolic Matrix(139,364,-118,-309) (-21/8,-13/5) -> (-13/11,-7/6) Hyperbolic Matrix(141,364,98,253) (-13/5,-18/7) -> (10/7,13/9) Hyperbolic Matrix(251,644,76,195) (-18/7,-23/9) -> (23/7,10/3) 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(113,280,-90,-223) (-5/2,-27/11) -> (-29/23,-5/4) Hyperbolic Matrix(811,1988,308,755) (-27/11,-22/9) -> (50/19,29/11) Hyperbolic Matrix(195,476,34,83) (-22/9,-17/7) -> (17/3,6/1) Hyperbolic Matrix(393,952,116,281) (-17/7,-29/12) -> (27/8,17/5) Hyperbolic Matrix(1345,3248,928,2241) (-29/12,-70/29) -> (42/29,29/20) Hyperbolic Matrix(2379,5740,986,2379) (-70/29,-41/17) -> (41/17,70/29) Hyperbolic Matrix(477,1148,268,645) (-41/17,-12/5) -> (16/9,41/23) Hyperbolic Matrix(83,196,-36,-85) (-12/5,-7/3) -> (-7/3,-16/7) Parabolic Matrix(701,1596,-430,-979) (-16/7,-25/11) -> (-31/19,-44/27) Hyperbolic Matrix(1765,4004,-1024,-2323) (-25/11,-34/15) -> (-50/29,-81/47) Hyperbolic Matrix(139,308,88,195) (-9/4,-11/5) -> (11/7,19/12) Hyperbolic Matrix(197,420,-144,-307) (-13/6,-2/1) -> (-26/19,-41/30) Hyperbolic Matrix(253,476,194,365) (-2/1,-15/8) -> (13/10,30/23) Hyperbolic Matrix(449,840,240,449) (-15/8,-28/15) -> (28/15,15/8) Hyperbolic Matrix(391,728,210,391) (-28/15,-13/7) -> (13/7,28/15) Hyperbolic Matrix(197,364,46,85) (-13/7,-11/6) -> (17/4,13/3) Hyperbolic Matrix(953,1736,-768,-1399) (-31/17,-51/28) -> (-5/4,-31/25) Hyperbolic Matrix(2045,3724,1246,2269) (-51/28,-20/11) -> (64/39,23/14) Hyperbolic Matrix(897,1624,248,449) (-29/16,-9/5) -> (47/13,29/8) Hyperbolic Matrix(281,504,-218,-391) (-9/5,-25/14) -> (-31/24,-9/7) Hyperbolic Matrix(1931,3444,-1178,-2101) (-25/14,-41/23) -> (-41/25,-59/36) Hyperbolic Matrix(645,1148,268,477) (-41/23,-16/9) -> (12/5,41/17) Hyperbolic Matrix(867,1540,362,643) (-16/9,-55/31) -> (55/23,12/5) Hyperbolic Matrix(363,644,-332,-589) (-55/31,-39/22) -> (-11/10,-1/1) Hyperbolic Matrix(727,1288,600,1063) (-39/22,-23/13) -> (23/19,17/14) Hyperbolic Matrix(223,392,-128,-225) (-23/13,-7/4) -> (-7/4,-33/19) Parabolic Matrix(1903,3304,580,1007) (-33/19,-59/34) -> (59/18,23/7) Hyperbolic Matrix(2211,3836,532,923) (-59/34,-85/49) -> (29/7,25/6) Hyperbolic Matrix(25311,43904,7102,12319) (-85/49,-196/113) -> (196/55,139/39) Hyperbolic Matrix(18985,32928,5328,9241) (-196/113,-111/64) -> (57/16,196/55) Hyperbolic Matrix(615,1064,226,391) (-26/15,-19/11) -> (19/7,30/11) Hyperbolic Matrix(617,1064,98,169) (-19/11,-50/29) -> (6/1,19/3) Hyperbolic Matrix(5963,10276,1348,2323) (-81/47,-112/65) -> (84/19,31/7) Hyperbolic Matrix(4957,8540,1122,1933) (-112/65,-31/18) -> (53/12,84/19) Hyperbolic Matrix(309,532,212,365) (-31/18,-12/7) -> (16/11,3/2) Hyperbolic Matrix(2213,3780,-1360,-2323) (-41/24,-70/41) -> (-70/43,-13/8) 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(83,140,16,27) (-17/10,-5/3) -> (5/1,11/2) 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(785,1288,-682,-1119) (-23/14,-41/25) -> (-15/13,-23/20) Hyperbolic Matrix(617,1008,172,281) (-18/11,-31/19) -> (25/7,18/5) Hyperbolic Matrix(2045,3332,1152,1877) (-44/27,-57/35) -> (55/31,16/9) Hyperbolic Matrix(3835,6244,1186,1931) (-57/35,-70/43) -> (42/13,55/17) Hyperbolic Matrix(449,728,346,561) (-13/8,-34/21) -> (22/17,13/10) Hyperbolic Matrix(1091,1764,-676,-1093) (-34/21,-21/13) -> (-21/13,-50/31) Parabolic Matrix(1007,1624,-834,-1345) (-50/31,-29/18) -> (-29/24,-6/5) 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(1147,1820,-830,-1317) (-27/17,-19/12) -> (-47/34,-29/21) Hyperbolic Matrix(195,308,88,139) (-19/12,-11/7) -> (11/5,9/4) Hyperbolic Matrix(197,308,126,197) (-11/7,-14/9) -> (14/9,11/7) Hyperbolic Matrix(307,476,198,307) (-14/9,-17/11) -> (17/11,14/9) Hyperbolic Matrix(309,476,-272,-419) (-17/11,-20/13) -> (-8/7,-17/15) Hyperbolic Matrix(841,1288,476,729) (-23/15,-3/2) -> (53/30,23/13) Hyperbolic Matrix(365,532,212,309) (-3/2,-16/11) -> (12/7,31/18) Hyperbolic Matrix(1119,1624,308,447) (-16/11,-29/20) -> (29/8,40/11) Hyperbolic Matrix(2241,3248,928,1345) (-29/20,-42/29) -> (70/29,29/12) Hyperbolic Matrix(755,1092,522,755) (-42/29,-13/9) -> (13/9,42/29) Hyperbolic Matrix(253,364,98,141) (-13/9,-10/7) -> (18/7,13/5) Hyperbolic Matrix(139,196,-100,-141) (-10/7,-7/5) -> (-7/5,-18/13) Parabolic 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(589,812,346,477) (-29/21,-11/8) -> (17/10,29/17) Hyperbolic Matrix(449,616,164,225) (-11/8,-26/19) -> (30/11,11/4) 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(617,840,-534,-727) (-15/11,-34/25) -> (-22/19,-15/13) Hyperbolic Matrix(2801,3808,1566,2129) (-34/25,-53/39) -> (59/33,34/19) Hyperbolic Matrix(2715,3668,1678,2267) (-23/17,-27/20) -> (55/34,89/55) Hyperbolic Matrix(811,1092,228,307) (-27/20,-4/3) -> (32/9,57/16) Hyperbolic Matrix(363,476,106,139) (-4/3,-17/13) -> (17/5,24/7) Hyperbolic Matrix(1093,1428,708,925) (-17/13,-47/36) -> (37/24,17/11) Hyperbolic Matrix(2939,3836,-2382,-3109) (-47/36,-30/23) -> (-58/47,-37/30) Hyperbolic Matrix(365,476,194,253) (-30/23,-13/10) -> (15/8,2/1) Hyperbolic Matrix(561,728,346,449) (-13/10,-22/17) -> (34/21,13/8) Hyperbolic Matrix(953,1232,304,393) (-22/17,-53/41) -> (3/1,22/7) Hyperbolic Matrix(7279,9408,4072,5263) (-53/41,-84/65) -> (84/47,59/33) Hyperbolic Matrix(3641,4704,2038,2633) (-84/65,-31/24) -> (25/14,84/47) Hyperbolic Matrix(197,252,154,197) (-9/7,-14/11) -> (14/11,9/7) Hyperbolic Matrix(419,532,330,419) (-14/11,-19/15) -> (19/15,14/11) Hyperbolic Matrix(4705,5936,2664,3361) (-53/42,-29/23) -> (83/47,53/30) Hyperbolic Matrix(2575,3192,722,895) (-31/25,-26/21) -> (82/23,25/7) Hyperbolic Matrix(1427,1764,-1156,-1429) (-26/21,-21/17) -> (-21/17,-58/47) Parabolic Matrix(729,896,502,617) (-16/13,-27/22) -> (29/20,16/11) 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(1063,1288,600,727) (-17/14,-23/19) -> (23/13,39/22) Hyperbolic Matrix(1597,1932,348,421) (-23/19,-29/24) -> (55/12,23/5) Hyperbolic Matrix(307,364,70,83) (-6/5,-13/11) -> (13/3,22/5) Hyperbolic Matrix(1147,1316,414,475) (-23/20,-8/7) -> (36/13,61/22) Hyperbolic Matrix(841,952,644,729) (-17/15,-9/8) -> (47/36,17/13) Hyperbolic Matrix(503,560,150,167) (-9/8,-10/9) -> (10/3,47/14) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(533,-588,126,-139) (1/1,10/9) -> (38/9,55/13) Hyperbolic Matrix(419,-476,272,-309) (9/8,8/7) -> (20/13,37/24) Hyperbolic Matrix(1119,-1288,682,-785) (8/7,15/13) -> (41/25,64/39) Hyperbolic Matrix(699,-812,266,-309) (15/13,7/6) -> (21/8,71/27) Hyperbolic Matrix(309,-364,118,-139) (7/6,6/5) -> (34/13,21/8) Hyperbolic Matrix(1091,-1316,674,-813) (6/5,23/19) -> (89/55,34/21) Hyperbolic Matrix(503,-616,138,-169) (11/9,16/13) -> (40/11,11/3) Hyperbolic Matrix(727,-896,228,-281) (16/13,21/17) -> (35/11,16/5) Hyperbolic Matrix(1653,-2044,520,-643) (21/17,26/21) -> (54/17,35/11) Hyperbolic Matrix(1625,-2016,586,-727) (26/21,5/4) -> (61/22,86/31) Hyperbolic Matrix(421,-532,110,-139) (5/4,19/15) -> (19/5,23/6) Hyperbolic Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(2381,-3108,750,-979) (30/23,47/36) -> (19/6,54/17) Hyperbolic Matrix(475,-644,104,-141) (4/3,19/14) -> (9/2,32/7) Hyperbolic Matrix(783,-1064,248,-337) (19/14,34/25) -> (22/7,19/6) Hyperbolic Matrix(2325,-3164,884,-1203) (34/25,15/11) -> (71/27,50/19) Hyperbolic Matrix(1065,-1456,286,-391) (15/11,26/19) -> (26/7,41/11) Hyperbolic Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(1063,-1512,670,-953) (27/19,10/7) -> (46/29,27/17) Hyperbolic Matrix(839,-1288,256,-393) (3/2,20/13) -> (36/11,59/18) Hyperbolic Matrix(2101,-3332,582,-923) (19/12,46/29) -> (18/5,65/18) Hyperbolic Matrix(1093,-1764,676,-1091) (29/18,21/13) -> (21/13,55/34) Parabolic Matrix(1065,-1736,446,-727) (13/8,31/19) -> (31/13,43/18) Hyperbolic Matrix(2101,-3444,1178,-1931) (18/11,41/25) -> (41/23,66/37) Hyperbolic Matrix(475,-812,148,-253) (29/17,12/7) -> (16/5,29/9) Hyperbolic Matrix(1933,-3332,438,-755) (31/18,50/29) -> (22/5,53/12) Hyperbolic Matrix(225,-392,128,-223) (26/15,7/4) -> (7/4,30/17) Parabolic Matrix(6217,-10976,1744,-3079) (30/17,83/47) -> (139/39,82/23) Hyperbolic Matrix(1737,-3080,410,-727) (39/22,55/31) -> (55/13,17/4) Hyperbolic Matrix(2715,-4844,644,-1149) (66/37,25/14) -> (59/14,38/9) Hyperbolic Matrix(139,-252,16,-29) (9/5,20/11) -> (8/1,9/1) Hyperbolic Matrix(337,-616,122,-223) (20/11,11/6) -> (11/4,36/13) Hyperbolic Matrix(141,-308,38,-83) (2/1,11/5) -> (11/3,26/7) Hyperbolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(365,-868,82,-195) (19/8,31/13) -> (31/7,9/2) Hyperbolic Matrix(1289,-3080,398,-951) (43/18,55/23) -> (55/17,13/4) Hyperbolic Matrix(307,-756,80,-197) (27/11,5/2) -> (23/6,27/7) Hyperbolic Matrix(559,-1512,166,-449) (27/10,19/7) -> (37/11,27/8) Hyperbolic Matrix(113,-392,32,-111) (24/7,7/2) -> (7/2,32/9) Parabolic Matrix(141,-532,22,-83) (15/4,19/5) -> (19/3,13/2) Hyperbolic Matrix(57,-224,14,-55) (27/7,4/1) -> (4/1,29/7) Parabolic Matrix(421,-1764,100,-419) (25/6,21/5) -> (21/5,59/14) Parabolic Matrix(29,-196,4,-27) (13/2,7/1) -> (7/1,15/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(29,252,-16,-139) -> Matrix(7,-4,2,-1) Matrix(27,196,-4,-29) -> Matrix(3,-2,2,-1) Matrix(111,728,34,223) -> Matrix(1,0,2,1) Matrix(83,532,-22,-141) -> Matrix(1,-2,2,-3) Matrix(83,476,34,195) -> Matrix(1,0,2,1) Matrix(169,952,30,169) -> Matrix(5,-2,8,-3) Matrix(111,616,20,111) -> Matrix(7,-4,16,-9) Matrix(27,140,16,83) -> Matrix(3,-2,8,-5) Matrix(29,140,6,29) -> Matrix(3,-2,8,-5) Matrix(139,644,30,139) -> Matrix(7,-8,22,-25) Matrix(141,644,-104,-475) -> Matrix(1,-2,0,1) Matrix(113,504,-50,-223) -> Matrix(1,0,2,1) Matrix(167,728,64,279) -> Matrix(3,-2,8,-5) Matrix(85,364,46,197) -> Matrix(3,-4,10,-13) Matrix(139,588,-126,-533) -> Matrix(1,-2,0,1) Matrix(783,3304,-478,-2017) -> Matrix(5,-14,4,-11) Matrix(757,3164,-462,-1931) -> Matrix(5,-4,4,-3) Matrix(197,812,-156,-643) -> Matrix(1,0,0,1) Matrix(139,532,-110,-421) -> Matrix(1,0,-2,1) Matrix(421,1596,244,925) -> Matrix(3,-2,8,-5) Matrix(83,308,-38,-141) -> Matrix(1,-2,2,-3) Matrix(169,616,-138,-503) -> Matrix(1,0,-4,1) Matrix(85,308,8,29) -> Matrix(1,0,0,1) Matrix(559,2016,-404,-1457) -> Matrix(3,-2,2,-1) Matrix(281,1008,172,617) -> Matrix(1,-2,4,-7) Matrix(111,392,-32,-113) -> Matrix(3,-2,2,-1) Matrix(1399,4816,504,1735) -> Matrix(1,-2,2,-3) Matrix(3191,10976,-1840,-6329) -> Matrix(1,-8,2,-15) Matrix(897,3080,196,673) -> Matrix(3,2,10,7) Matrix(139,476,106,363) -> Matrix(1,0,2,1) Matrix(281,952,116,393) -> Matrix(1,0,4,1) Matrix(449,1512,-166,-559) -> Matrix(1,0,2,1) Matrix(195,644,76,251) -> Matrix(3,-2,8,-5) Matrix(393,1288,-256,-839) -> Matrix(1,0,0,1) Matrix(197,644,26,85) -> Matrix(3,-2,8,-5) Matrix(253,812,-148,-475) -> Matrix(1,0,2,1) Matrix(281,896,-228,-727) -> Matrix(1,0,-2,1) Matrix(337,1064,-248,-783) -> Matrix(1,0,-2,1) Matrix(29,84,10,29) -> Matrix(1,0,2,1) Matrix(251,700,90,251) -> Matrix(1,0,0,1) Matrix(223,616,-122,-337) -> Matrix(3,-2,2,-1) Matrix(225,616,164,449) -> Matrix(3,-2,14,-9) Matrix(391,1064,226,615) -> Matrix(1,0,2,1) Matrix(1735,4704,516,1399) -> Matrix(1,0,6,1) Matrix(3473,9408,1034,2801) -> Matrix(1,0,-6,1) Matrix(393,1064,352,953) -> Matrix(1,0,0,1) Matrix(167,448,104,279) -> Matrix(1,-2,4,-7) Matrix(169,448,106,281) -> Matrix(5,-2,18,-7) Matrix(755,1988,308,811) -> Matrix(3,-2,14,-9) Matrix(309,812,-266,-699) -> Matrix(1,0,-2,1) Matrix(139,364,-118,-309) -> Matrix(3,-2,2,-1) Matrix(141,364,98,253) -> Matrix(1,0,2,1) Matrix(251,644,76,195) -> Matrix(3,-2,8,-5) Matrix(505,1288,198,505) -> Matrix(9,-8,26,-23) Matrix(111,280,44,111) -> Matrix(1,-2,4,-7) Matrix(113,280,-90,-223) -> Matrix(1,-2,0,1) Matrix(811,1988,308,755) -> Matrix(1,2,2,5) Matrix(195,476,34,83) -> Matrix(1,0,2,1) Matrix(393,952,116,281) -> Matrix(1,0,4,1) Matrix(1345,3248,928,2241) -> Matrix(1,2,2,5) Matrix(2379,5740,986,2379) -> Matrix(1,0,6,1) Matrix(477,1148,268,645) -> Matrix(1,0,6,1) Matrix(83,196,-36,-85) -> Matrix(1,0,2,1) Matrix(701,1596,-430,-979) -> Matrix(7,-2,4,-1) Matrix(1765,4004,-1024,-2323) -> Matrix(1,0,-2,1) Matrix(139,308,88,195) -> Matrix(1,0,2,1) Matrix(197,420,-144,-307) -> Matrix(3,-4,-2,3) Matrix(253,476,194,365) -> Matrix(5,-4,14,-11) Matrix(449,840,240,449) -> Matrix(15,-14,44,-41) Matrix(391,728,210,391) -> Matrix(11,-12,34,-37) Matrix(197,364,46,85) -> Matrix(3,-4,10,-13) Matrix(953,1736,-768,-1399) -> Matrix(1,0,-2,1) Matrix(2045,3724,1246,2269) -> Matrix(7,-8,22,-25) Matrix(897,1624,248,449) -> Matrix(1,-4,2,-7) Matrix(281,504,-218,-391) -> Matrix(1,2,0,1) Matrix(1931,3444,-1178,-2101) -> Matrix(5,6,4,5) Matrix(645,1148,268,477) -> Matrix(1,0,6,1) Matrix(867,1540,362,643) -> Matrix(1,0,2,1) Matrix(363,644,-332,-589) -> Matrix(1,0,0,1) Matrix(727,1288,600,1063) -> Matrix(1,0,0,1) Matrix(223,392,-128,-225) -> Matrix(1,0,2,1) Matrix(1903,3304,580,1007) -> Matrix(5,-2,18,-7) Matrix(2211,3836,532,923) -> Matrix(9,-4,34,-15) Matrix(25311,43904,7102,12319) -> Matrix(49,-24,96,-47) Matrix(18985,32928,5328,9241) -> Matrix(43,-22,88,-45) Matrix(615,1064,226,391) -> Matrix(1,0,2,1) Matrix(617,1064,98,169) -> Matrix(1,0,2,1) Matrix(5963,10276,1348,2323) -> Matrix(1,0,4,1) Matrix(4957,8540,1122,1933) -> Matrix(1,0,0,1) Matrix(309,532,212,365) -> Matrix(1,0,2,1) Matrix(2213,3780,-1360,-2323) -> Matrix(1,0,-2,1) Matrix(1903,3248,590,1007) -> Matrix(5,-2,18,-7) Matrix(559,952,394,671) -> Matrix(1,0,2,1) Matrix(83,140,16,27) -> Matrix(3,-2,8,-5) Matrix(169,280,102,169) -> Matrix(3,-2,8,-5) Matrix(783,1288,476,783) -> Matrix(17,-18,52,-55) Matrix(785,1288,-682,-1119) -> Matrix(5,-6,-4,5) Matrix(617,1008,172,281) -> Matrix(1,-2,4,-7) Matrix(2045,3332,1152,1877) -> Matrix(1,-2,4,-7) Matrix(3835,6244,1186,1931) -> Matrix(1,-4,4,-15) Matrix(449,728,346,561) -> Matrix(3,-4,10,-13) Matrix(1091,1764,-676,-1093) -> Matrix(3,-2,2,-1) Matrix(1007,1624,-834,-1345) -> Matrix(3,-4,4,-5) Matrix(279,448,104,167) -> Matrix(1,-2,4,-7) Matrix(281,448,106,169) -> Matrix(1,-2,2,-3) Matrix(1147,1820,-830,-1317) -> Matrix(1,-4,0,1) Matrix(195,308,88,139) -> Matrix(1,0,2,1) Matrix(197,308,126,197) -> Matrix(1,-4,4,-15) Matrix(307,476,198,307) -> Matrix(1,2,4,9) Matrix(309,476,-272,-419) -> Matrix(1,0,0,1) Matrix(841,1288,476,729) -> Matrix(1,-2,4,-7) Matrix(365,532,212,309) -> Matrix(1,0,2,1) Matrix(1119,1624,308,447) -> Matrix(1,0,0,1) Matrix(2241,3248,928,1345) -> Matrix(3,-2,14,-9) Matrix(755,1092,522,755) -> Matrix(1,0,2,1) Matrix(253,364,98,141) -> Matrix(1,0,2,1) Matrix(139,196,-100,-141) -> Matrix(1,-2,0,1) Matrix(9071,12544,2510,3471) -> Matrix(1,-12,2,-23) Matrix(9073,12544,2512,3473) -> Matrix(1,14,2,29) Matrix(589,812,346,477) -> Matrix(1,2,2,5) Matrix(449,616,164,225) -> Matrix(1,2,2,5) Matrix(2295,3136,614,839) -> Matrix(11,12,32,35) Matrix(2297,3136,616,841) -> Matrix(11,10,34,31) Matrix(617,840,-534,-727) -> Matrix(3,2,-2,-1) Matrix(2801,3808,1566,2129) -> Matrix(1,0,6,1) Matrix(2715,3668,1678,2267) -> Matrix(7,4,26,15) Matrix(811,1092,228,307) -> Matrix(5,2,12,5) Matrix(363,476,106,139) -> Matrix(1,0,2,1) Matrix(1093,1428,708,925) -> Matrix(3,-2,14,-9) Matrix(2939,3836,-2382,-3109) -> Matrix(3,-2,-4,3) Matrix(365,476,194,253) -> Matrix(5,-4,14,-11) Matrix(561,728,346,449) -> Matrix(3,-4,10,-13) Matrix(953,1232,304,393) -> Matrix(1,-2,4,-7) Matrix(7279,9408,4072,5263) -> Matrix(1,-2,6,-11) Matrix(3641,4704,2038,2633) -> Matrix(1,-2,4,-7) Matrix(197,252,154,197) -> Matrix(1,-2,4,-7) Matrix(419,532,330,419) -> Matrix(1,4,4,17) Matrix(4705,5936,2664,3361) -> Matrix(1,-4,4,-15) Matrix(2575,3192,722,895) -> Matrix(3,2,4,3) Matrix(1427,1764,-1156,-1429) -> Matrix(1,0,2,1) Matrix(729,896,502,617) -> Matrix(1,0,4,1) Matrix(505,616,414,505) -> Matrix(1,0,12,1) Matrix(783,952,644,783) -> Matrix(1,0,-8,1) Matrix(1063,1288,600,727) -> Matrix(1,0,0,1) Matrix(1597,1932,348,421) -> Matrix(11,-4,36,-13) Matrix(307,364,70,83) -> Matrix(1,0,2,1) Matrix(1147,1316,414,475) -> Matrix(1,0,4,1) Matrix(841,952,644,729) -> Matrix(1,2,2,5) Matrix(503,560,150,167) -> Matrix(1,0,2,1) Matrix(1,0,2,1) -> Matrix(1,0,4,1) Matrix(533,-588,126,-139) -> Matrix(9,-2,32,-7) Matrix(419,-476,272,-309) -> Matrix(1,0,0,1) Matrix(1119,-1288,682,-785) -> Matrix(29,-6,92,-19) Matrix(699,-812,266,-309) -> Matrix(1,0,-2,1) Matrix(309,-364,118,-139) -> Matrix(7,-2,18,-5) Matrix(1091,-1316,674,-813) -> Matrix(5,-2,18,-7) Matrix(503,-616,138,-169) -> Matrix(1,0,-4,1) Matrix(727,-896,228,-281) -> Matrix(1,0,-2,1) Matrix(1653,-2044,520,-643) -> Matrix(1,0,-4,1) Matrix(1625,-2016,586,-727) -> Matrix(11,-2,28,-5) Matrix(421,-532,110,-139) -> Matrix(1,0,-2,1) Matrix(391,-504,218,-281) -> Matrix(7,-2,32,-9) Matrix(2381,-3108,750,-979) -> Matrix(5,-2,18,-7) Matrix(475,-644,104,-141) -> Matrix(9,-2,32,-7) Matrix(783,-1064,248,-337) -> Matrix(1,0,-2,1) Matrix(2325,-3164,884,-1203) -> Matrix(11,-2,28,-5) Matrix(1065,-1456,286,-391) -> Matrix(29,-6,92,-19) Matrix(141,-196,100,-139) -> Matrix(9,-2,32,-7) Matrix(1063,-1512,670,-953) -> Matrix(9,-2,32,-7) Matrix(839,-1288,256,-393) -> Matrix(1,0,0,1) Matrix(2101,-3332,582,-923) -> Matrix(23,-6,50,-13) Matrix(1093,-1764,676,-1091) -> Matrix(7,-2,18,-5) Matrix(1065,-1736,446,-727) -> Matrix(7,-2,18,-5) Matrix(2101,-3444,1178,-1931) -> Matrix(19,-6,92,-29) Matrix(475,-812,148,-253) -> Matrix(1,0,2,1) Matrix(1933,-3332,438,-755) -> Matrix(1,0,0,1) Matrix(225,-392,128,-223) -> Matrix(1,0,2,1) Matrix(6217,-10976,1744,-3079) -> Matrix(25,-6,46,-11) Matrix(1737,-3080,410,-727) -> Matrix(9,-2,32,-7) Matrix(2715,-4844,644,-1149) -> Matrix(17,-4,64,-15) Matrix(139,-252,16,-29) -> Matrix(15,-4,34,-9) Matrix(337,-616,122,-223) -> Matrix(7,-2,18,-5) Matrix(141,-308,38,-83) -> Matrix(5,-2,18,-7) Matrix(85,-196,36,-83) -> Matrix(1,0,2,1) Matrix(365,-868,82,-195) -> Matrix(1,0,0,1) Matrix(1289,-3080,398,-951) -> Matrix(5,-2,18,-7) Matrix(307,-756,80,-197) -> Matrix(7,-2,18,-5) Matrix(559,-1512,166,-449) -> Matrix(1,0,2,1) Matrix(113,-392,32,-111) -> Matrix(7,-2,18,-5) Matrix(141,-532,22,-83) -> Matrix(5,-2,18,-7) Matrix(57,-224,14,-55) -> Matrix(1,0,2,1) Matrix(421,-1764,100,-419) -> Matrix(9,-2,32,-7) Matrix(29,-196,4,-27) -> Matrix(7,-2,18,-5) 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): 52 Degree of the the map X: 52 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 2 1 1/1 (0/1,1/4) 0 28 10/9 0/1 1 14 9/8 (0/1,1/6) 0 28 8/7 0/1 2 7 15/13 (0/1,1/5) 0 28 7/6 1/4 1 4 6/5 0/1 1 14 23/19 (0/1,1/1) 0 28 17/14 (-1/2,0/1) 0 28 28/23 0/1 10 1 11/9 (0/1,1/8) 0 28 16/13 0/1 1 7 21/17 0/1 2 4 26/21 2/13 1 14 5/4 (1/5,1/4) 0 28 19/15 (2/9,1/4) 0 28 14/11 1/4 3 2 9/7 (1/4,1/3) 0 28 22/17 2/7 1 14 13/10 (3/10,1/3) 0 28 30/23 4/11 1 14 47/36 (3/8,2/5) 0 28 17/13 (1/3,1/2) 0 28 4/3 0/1 2 7 19/14 (0/1,1/4) 0 28 34/25 0/1 1 14 15/11 (2/11,1/5) 0 28 26/19 4/19 1 14 11/8 (2/9,1/4) 0 28 7/5 1/4 2 4 17/12 (0/1,1/4) 0 28 27/19 (1/5,1/4) 0 28 10/7 2/7 1 14 13/9 (0/1,1/3) 0 28 42/29 1/3 2 2 29/20 (0/1,1/2) 0 28 16/11 0/1 1 7 3/2 (0/1,1/4) 0 28 20/13 0/1 2 7 37/24 (0/1,1/6) 0 28 17/11 (1/5,1/4) 0 28 14/9 1/4 3 2 11/7 (1/4,2/7) 0 28 19/12 (2/9,1/4) 0 28 46/29 4/15 1 14 27/17 (1/4,1/3) 0 28 8/5 2/7 1 7 29/18 (8/27,3/10) 0 28 21/13 1/3 2 4 55/34 (2/9,1/4) 0 28 89/55 (3/11,2/7) 0 28 34/21 2/7 1 14 13/8 (1/4,1/3) 0 28 31/19 (2/7,3/10) 0 28 18/11 4/13 1 14 41/25 (6/19,1/3) 0 28 64/39 6/19 2 7 23/14 (9/28,1/3) 0 28 28/17 1/3 10 1 5/3 (1/3,1/2) 0 28 17/10 (0/1,1/2) 0 28 29/17 (1/2,1/1) 0 28 12/7 0/1 1 7 31/18 (0/1,1/2) 0 28 50/29 0/1 1 14 19/11 (0/1,1/2) 0 28 26/15 2/5 1 14 7/4 0/1 1 4 30/17 2/9 1 14 83/47 (1/4,9/35) 0 28 53/30 (1/4,2/7) 0 28 23/13 (0/1,1/3) 0 28 39/22 (0/1,1/6) 0 28 55/31 (0/1,1/4) 0 28 16/9 0/1 2 7 41/23 (0/1,1/5) 0 28 66/37 2/9 1 14 25/14 (0/1,1/4) 0 28 84/47 0/1 1 1 59/33 (0/1,1/5) 0 28 34/19 0/1 1 14 9/5 (1/5,1/4) 0 28 20/11 2/7 2 7 11/6 (1/4,2/7) 0 28 13/7 (6/19,1/3) 0 28 28/15 1/3 13 1 15/8 (1/3,7/20) 0 28 2/1 0/1 1 14 11/5 (2/5,1/2) 0 28 9/4 (1/2,2/3) 0 28 7/3 0/1 2 4 19/8 (1/4,2/7) 0 28 31/13 (0/1,1/4) 0 28 43/18 (1/3,1/2) 0 28 55/23 (0/1,1/2) 0 28 12/5 0/1 2 7 41/17 (0/1,1/5) 0 28 70/29 1/5 2 2 29/12 (2/9,1/4) 0 28 17/7 (1/5,1/4) 0 28 22/9 0/1 1 14 27/11 (3/13,1/4) 0 28 5/2 (1/4,1/3) 0 28 28/11 1/3 5 1 23/9 (1/3,4/11) 0 28 18/7 2/5 1 14 13/5 (0/1,1/3) 0 28 34/13 2/5 1 14 21/8 1/2 1 4 71/27 (0/1,1/3) 0 28 50/19 2/5 1 14 29/11 (1/2,1/1) 0 28 8/3 0/1 1 7 27/10 (1/2,2/3) 0 28 19/7 (0/1,1/4) 0 28 30/11 2/7 1 14 11/4 (0/1,1/2) 0 28 36/13 0/1 2 7 61/22 (1/3,3/8) 0 28 86/31 4/9 1 14 25/9 (0/1,1/2) 0 28 14/5 0/1 1 2 3/1 (0/1,1/3) 0 28 22/7 0/1 1 14 19/6 (0/1,1/2) 0 28 54/17 2/5 1 14 35/11 0/1 2 4 16/5 0/1 1 7 29/9 (1/4,1/3) 0 28 42/13 1/4 1 2 55/17 (1/4,2/7) 0 28 13/4 (1/4,1/3) 0 28 36/11 0/1 2 7 59/18 (0/1,1/4) 0 28 23/7 (2/7,1/3) 0 28 10/3 0/1 1 14 47/14 (0/1,1/0) 0 28 84/25 0/1 6 1 37/11 (0/1,1/6) 0 28 27/8 (1/4,2/7) 0 28 17/5 (1/4,1/3) 0 28 24/7 0/1 2 7 7/2 1/3 1 4 32/9 2/5 2 7 57/16 (8/17,1/2) 0 28 196/55 1/2 23 1 139/39 (1/2,15/29) 0 28 82/23 4/7 1 14 25/7 (0/1,1/2) 0 28 18/5 2/5 1 14 65/18 (8/17,1/2) 0 28 112/31 1/2 13 1 47/13 (1/2,5/9) 0 28 29/8 (0/1,1/2) 0 28 40/11 0/1 1 7 11/3 (0/1,1/4) 0 28 26/7 2/7 1 14 41/11 (8/25,1/3) 0 28 56/15 1/3 11 1 15/4 (1/3,3/8) 0 28 19/5 (2/5,1/2) 0 28 23/6 (1/3,1/2) 0 28 27/7 (5/11,1/2) 0 28 4/1 0/1 1 7 29/7 (5/21,1/4) 0 28 25/6 (1/4,2/7) 0 28 21/5 1/4 2 4 59/14 (1/4,4/15) 0 28 38/9 2/7 1 14 55/13 (1/4,2/7) 0 28 17/4 (2/7,3/10) 0 28 13/3 (1/3,2/5) 0 28 22/5 0/1 1 14 53/12 (0/1,1/2) 0 28 84/19 0/1 2 1 31/7 (0/1,1/4) 0 28 9/2 (1/4,2/7) 0 28 32/7 2/7 2 7 55/12 (3/10,16/53) 0 28 23/5 (4/13,1/3) 0 28 14/3 1/3 5 2 5/1 (1/3,1/2) 0 28 11/2 (2/5,1/2) 0 28 28/5 1/2 3 1 17/3 (1/2,1/1) 0 28 6/1 0/1 1 14 19/3 (0/1,1/4) 0 28 13/2 (1/3,1/2) 0 28 7/1 1/3 2 4 15/2 (1/3,3/8) 0 28 8/1 2/5 2 7 9/1 (5/11,1/2) 0 28 1/0 (0/1,1/2) 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(533,-588,126,-139) (1/1,10/9) -> (38/9,55/13) Hyperbolic Matrix(503,-560,150,-167) (10/9,9/8) -> (10/3,47/14) Glide Reflection Matrix(419,-476,272,-309) (9/8,8/7) -> (20/13,37/24) Hyperbolic Matrix(1119,-1288,682,-785) (8/7,15/13) -> (41/25,64/39) Hyperbolic Matrix(699,-812,266,-309) (15/13,7/6) -> (21/8,71/27) Hyperbolic Matrix(309,-364,118,-139) (7/6,6/5) -> (34/13,21/8) Hyperbolic Matrix(1091,-1316,674,-813) (6/5,23/19) -> (89/55,34/21) Hyperbolic Matrix(1063,-1288,600,-727) (23/19,17/14) -> (23/13,39/22) 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(503,-616,138,-169) (11/9,16/13) -> (40/11,11/3) Hyperbolic Matrix(727,-896,228,-281) (16/13,21/17) -> (35/11,16/5) Hyperbolic Matrix(1653,-2044,520,-643) (21/17,26/21) -> (54/17,35/11) Hyperbolic Matrix(1625,-2016,586,-727) (26/21,5/4) -> (61/22,86/31) Hyperbolic Matrix(421,-532,110,-139) (5/4,19/15) -> (19/5,23/6) Hyperbolic Matrix(419,-532,330,-419) (19/15,14/11) -> (19/15,14/11) Reflection Matrix(197,-252,154,-197) (14/11,9/7) -> (14/11,9/7) Reflection Matrix(391,-504,218,-281) (9/7,22/17) -> (34/19,9/5) Hyperbolic Matrix(561,-728,346,-449) (22/17,13/10) -> (34/21,13/8) Glide Reflection Matrix(365,-476,194,-253) (13/10,30/23) -> (15/8,2/1) Glide Reflection Matrix(2381,-3108,750,-979) (30/23,47/36) -> (19/6,54/17) Hyperbolic Matrix(1093,-1428,708,-925) (47/36,17/13) -> (37/24,17/11) Glide Reflection Matrix(363,-476,106,-139) (17/13,4/3) -> (17/5,24/7) Glide Reflection Matrix(475,-644,104,-141) (4/3,19/14) -> (9/2,32/7) Hyperbolic Matrix(783,-1064,248,-337) (19/14,34/25) -> (22/7,19/6) Hyperbolic Matrix(2325,-3164,884,-1203) (34/25,15/11) -> (71/27,50/19) Hyperbolic Matrix(1065,-1456,286,-391) (15/11,26/19) -> (26/7,41/11) Hyperbolic Matrix(449,-616,164,-225) (26/19,11/8) -> (30/11,11/4) Glide Reflection Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic 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(253,-364,98,-141) (10/7,13/9) -> (18/7,13/5) Glide Reflection Matrix(755,-1092,522,-755) (13/9,42/29) -> (13/9,42/29) Reflection Matrix(2241,-3248,928,-1345) (42/29,29/20) -> (70/29,29/12) Glide Reflection Matrix(1119,-1624,308,-447) (29/20,16/11) -> (29/8,40/11) Glide Reflection Matrix(365,-532,212,-309) (16/11,3/2) -> (12/7,31/18) Glide Reflection Matrix(839,-1288,256,-393) (3/2,20/13) -> (36/11,59/18) Hyperbolic Matrix(307,-476,198,-307) (17/11,14/9) -> (17/11,14/9) Reflection Matrix(197,-308,126,-197) (14/9,11/7) -> (14/9,11/7) Reflection Matrix(195,-308,88,-139) (11/7,19/12) -> (11/5,9/4) Glide Reflection Matrix(2101,-3332,582,-923) (19/12,46/29) -> (18/5,65/18) Hyperbolic 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(1093,-1764,676,-1091) (29/18,21/13) -> (21/13,55/34) Parabolic Matrix(3807,-6160,830,-1343) (55/34,89/55) -> (55/12,23/5) Glide Reflection Matrix(1065,-1736,446,-727) (13/8,31/19) -> (31/13,43/18) Hyperbolic Matrix(617,-1008,172,-281) (31/19,18/11) -> (25/7,18/5) Glide Reflection Matrix(2101,-3444,1178,-1931) (18/11,41/25) -> (41/23,66/37) Hyperbolic Matrix(2883,-4732,1040,-1707) (64/39,23/14) -> (36/13,61/22) 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(83,-140,16,-27) (5/3,17/10) -> (5/1,11/2) Glide Reflection Matrix(475,-812,148,-253) (29/17,12/7) -> (16/5,29/9) Hyperbolic Matrix(1933,-3332,438,-755) (31/18,50/29) -> (22/5,53/12) Hyperbolic Matrix(617,-1064,98,-169) (50/29,19/11) -> (6/1,19/3) Glide Reflection Matrix(615,-1064,226,-391) (19/11,26/15) -> (19/7,30/11) Glide Reflection Matrix(225,-392,128,-223) (26/15,7/4) -> (7/4,30/17) Parabolic Matrix(6217,-10976,1744,-3079) (30/17,83/47) -> (139/39,82/23) Hyperbolic Matrix(2045,-3612,492,-869) (83/47,53/30) -> (29/7,25/6) Glide Reflection Matrix(1457,-2576,444,-785) (53/30,23/13) -> (59/18,23/7) Glide Reflection Matrix(1737,-3080,410,-727) (39/22,55/31) -> (55/13,17/4) Hyperbolic Matrix(867,-1540,362,-643) (55/31,16/9) -> (55/23,12/5) Glide Reflection Matrix(645,-1148,268,-477) (16/9,41/23) -> (12/5,41/17) Glide Reflection Matrix(2715,-4844,644,-1149) (66/37,25/14) -> (59/14,38/9) Hyperbolic Matrix(2351,-4200,1316,-2351) (25/14,84/47) -> (25/14,84/47) Reflection Matrix(5545,-9912,3102,-5545) (84/47,59/33) -> (84/47,59/33) Reflection Matrix(783,-1400,250,-447) (59/33,34/19) -> (3/1,22/7) Glide Reflection Matrix(139,-252,16,-29) (9/5,20/11) -> (8/1,9/1) Hyperbolic Matrix(337,-616,122,-223) (20/11,11/6) -> (11/4,36/13) Hyperbolic Matrix(197,-364,46,-85) (11/6,13/7) -> (17/4,13/3) Glide Reflection Matrix(391,-728,210,-391) (13/7,28/15) -> (13/7,28/15) Reflection Matrix(449,-840,240,-449) (28/15,15/8) -> (28/15,15/8) Reflection Matrix(141,-308,38,-83) (2/1,11/5) -> (11/3,26/7) Hyperbolic Matrix(85,-196,36,-83) (9/4,7/3) -> (7/3,19/8) Parabolic Matrix(365,-868,82,-195) (19/8,31/13) -> (31/7,9/2) Hyperbolic Matrix(1289,-3080,398,-951) (43/18,55/23) -> (55/17,13/4) Hyperbolic Matrix(2379,-5740,986,-2379) (41/17,70/29) -> (41/17,70/29) Reflection Matrix(393,-952,116,-281) (29/12,17/7) -> (27/8,17/5) Glide Reflection Matrix(195,-476,34,-83) (17/7,22/9) -> (17/3,6/1) Glide Reflection Matrix(811,-1988,308,-755) (22/9,27/11) -> (50/19,29/11) Glide Reflection Matrix(307,-756,80,-197) (27/11,5/2) -> (23/6,27/7) Hyperbolic 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(251,-644,76,-195) (23/9,18/7) -> (23/7,10/3) Glide Reflection Matrix(279,-728,64,-167) (13/5,34/13) -> (13/3,22/5) Glide Reflection Matrix(559,-1512,166,-449) (27/10,19/7) -> (37/11,27/8) Hyperbolic Matrix(1513,-4200,424,-1177) (86/31,25/9) -> (82/23,25/7) Glide Reflection Matrix(251,-700,90,-251) (25/9,14/5) -> (25/9,14/5) Reflection Matrix(29,-84,10,-29) (14/5,3/1) -> (14/5,3/1) Reflection Matrix(755,-2436,234,-755) (29/9,42/13) -> (29/9,42/13) Reflection Matrix(1429,-4620,442,-1429) (42/13,55/17) -> (42/13,55/17) Reflection Matrix(197,-644,26,-85) (13/4,36/11) -> (15/2,8/1) Glide Reflection Matrix(2351,-7896,700,-2351) (47/14,84/25) -> (47/14,84/25) Reflection Matrix(1849,-6216,550,-1849) (84/25,37/11) -> (84/25,37/11) Reflection Matrix(113,-392,32,-111) (24/7,7/2) -> (7/2,32/9) Parabolic Matrix(1007,-3584,220,-783) (32/9,57/16) -> (32/7,55/12) Glide Reflection Matrix(6271,-22344,1760,-6271) (57/16,196/55) -> (57/16,196/55) Reflection Matrix(15289,-54488,4290,-15289) (196/55,139/39) -> (196/55,139/39) Reflection 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(85,-308,8,-29) (47/13,29/8) -> (9/1,1/0) Glide 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(141,-532,22,-83) (15/4,19/5) -> (19/3,13/2) Hyperbolic Matrix(57,-224,14,-55) (27/7,4/1) -> (4/1,29/7) Parabolic Matrix(421,-1764,100,-419) (25/6,21/5) -> (21/5,59/14) Parabolic 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(139,-644,30,-139) (23/5,14/3) -> (23/5,14/3) Reflection Matrix(29,-140,6,-29) (14/3,5/1) -> (14/3,5/1) Reflection 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 Matrix(29,-196,4,-27) (13/2,7/1) -> (7/1,15/2) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,4,-1) (0/1,1/0) -> (0/1,1/2) Matrix(1,0,2,-1) -> Matrix(1,0,8,-1) (0/1,1/1) -> (0/1,1/4) Matrix(533,-588,126,-139) -> Matrix(9,-2,32,-7) 1/4 Matrix(503,-560,150,-167) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(419,-476,272,-309) -> Matrix(1,0,0,1) Matrix(1119,-1288,682,-785) -> Matrix(29,-6,92,-19) Matrix(699,-812,266,-309) -> Matrix(1,0,-2,1) 0/1 Matrix(309,-364,118,-139) -> Matrix(7,-2,18,-5) 1/3 Matrix(1091,-1316,674,-813) -> Matrix(5,-2,18,-7) 1/3 Matrix(1063,-1288,600,-727) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(783,-952,644,-783) -> Matrix(-1,0,4,1) (17/14,28/23) -> (-1/2,0/1) Matrix(505,-616,414,-505) -> Matrix(1,0,16,-1) (28/23,11/9) -> (0/1,1/8) Matrix(503,-616,138,-169) -> Matrix(1,0,-4,1) 0/1 Matrix(727,-896,228,-281) -> Matrix(1,0,-2,1) 0/1 Matrix(1653,-2044,520,-643) -> Matrix(1,0,-4,1) 0/1 Matrix(1625,-2016,586,-727) -> Matrix(11,-2,28,-5) Matrix(421,-532,110,-139) -> Matrix(1,0,-2,1) 0/1 Matrix(419,-532,330,-419) -> Matrix(17,-4,72,-17) (19/15,14/11) -> (2/9,1/4) Matrix(197,-252,154,-197) -> Matrix(7,-2,24,-7) (14/11,9/7) -> (1/4,1/3) Matrix(391,-504,218,-281) -> Matrix(7,-2,32,-9) 1/4 Matrix(561,-728,346,-449) -> Matrix(13,-4,42,-13) *** -> (2/7,1/3) Matrix(365,-476,194,-253) -> Matrix(11,-4,30,-11) *** -> (1/3,2/5) Matrix(2381,-3108,750,-979) -> Matrix(5,-2,18,-7) 1/3 Matrix(1093,-1428,708,-925) -> Matrix(5,-2,22,-9) Matrix(363,-476,106,-139) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(475,-644,104,-141) -> Matrix(9,-2,32,-7) 1/4 Matrix(783,-1064,248,-337) -> Matrix(1,0,-2,1) 0/1 Matrix(2325,-3164,884,-1203) -> Matrix(11,-2,28,-5) Matrix(1065,-1456,286,-391) -> Matrix(29,-6,92,-19) Matrix(449,-616,164,-225) -> Matrix(9,-2,22,-5) Matrix(141,-196,100,-139) -> Matrix(9,-2,32,-7) 1/4 Matrix(671,-952,394,-559) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(1063,-1512,670,-953) -> Matrix(9,-2,32,-7) 1/4 Matrix(253,-364,98,-141) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(755,-1092,522,-755) -> Matrix(1,0,6,-1) (13/9,42/29) -> (0/1,1/3) Matrix(2241,-3248,928,-1345) -> Matrix(5,-2,22,-9) Matrix(1119,-1624,308,-447) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(365,-532,212,-309) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(839,-1288,256,-393) -> Matrix(1,0,0,1) Matrix(307,-476,198,-307) -> Matrix(9,-2,40,-9) (17/11,14/9) -> (1/5,1/4) Matrix(197,-308,126,-197) -> Matrix(15,-4,56,-15) (14/9,11/7) -> (1/4,2/7) Matrix(195,-308,88,-139) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(2101,-3332,582,-923) -> Matrix(23,-6,50,-13) Matrix(281,-448,106,-169) -> Matrix(7,-2,10,-3) Matrix(279,-448,104,-167) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(1093,-1764,676,-1091) -> Matrix(7,-2,18,-5) 1/3 Matrix(3807,-6160,830,-1343) -> Matrix(37,-10,122,-33) Matrix(1065,-1736,446,-727) -> Matrix(7,-2,18,-5) 1/3 Matrix(617,-1008,172,-281) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(2101,-3444,1178,-1931) -> Matrix(19,-6,92,-29) Matrix(2883,-4732,1040,-1707) -> Matrix(19,-6,60,-19) *** -> (3/10,1/3) Matrix(783,-1288,476,-783) -> Matrix(55,-18,168,-55) (23/14,28/17) -> (9/28,1/3) Matrix(169,-280,102,-169) -> Matrix(5,-2,12,-5) (28/17,5/3) -> (1/3,1/2) Matrix(83,-140,16,-27) -> Matrix(5,-2,12,-5) *** -> (1/3,1/2) Matrix(475,-812,148,-253) -> Matrix(1,0,2,1) 0/1 Matrix(1933,-3332,438,-755) -> Matrix(1,0,0,1) Matrix(617,-1064,98,-169) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(615,-1064,226,-391) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(225,-392,128,-223) -> Matrix(1,0,2,1) 0/1 Matrix(6217,-10976,1744,-3079) -> Matrix(25,-6,46,-11) Matrix(2045,-3612,492,-869) -> Matrix(15,-4,56,-15) *** -> (1/4,2/7) Matrix(1457,-2576,444,-785) -> Matrix(7,-2,24,-7) *** -> (1/4,1/3) Matrix(1737,-3080,410,-727) -> Matrix(9,-2,32,-7) 1/4 Matrix(867,-1540,362,-643) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(645,-1148,268,-477) -> Matrix(1,0,10,-1) *** -> (0/1,1/5) Matrix(2715,-4844,644,-1149) -> Matrix(17,-4,64,-15) 1/4 Matrix(2351,-4200,1316,-2351) -> Matrix(1,0,8,-1) (25/14,84/47) -> (0/1,1/4) Matrix(5545,-9912,3102,-5545) -> Matrix(1,0,10,-1) (84/47,59/33) -> (0/1,1/5) Matrix(783,-1400,250,-447) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(139,-252,16,-29) -> Matrix(15,-4,34,-9) Matrix(337,-616,122,-223) -> Matrix(7,-2,18,-5) 1/3 Matrix(197,-364,46,-85) -> Matrix(13,-4,42,-13) *** -> (2/7,1/3) Matrix(391,-728,210,-391) -> Matrix(37,-12,114,-37) (13/7,28/15) -> (6/19,1/3) Matrix(449,-840,240,-449) -> Matrix(41,-14,120,-41) (28/15,15/8) -> (1/3,7/20) Matrix(141,-308,38,-83) -> Matrix(5,-2,18,-7) 1/3 Matrix(85,-196,36,-83) -> Matrix(1,0,2,1) 0/1 Matrix(365,-868,82,-195) -> Matrix(1,0,0,1) Matrix(1289,-3080,398,-951) -> Matrix(5,-2,18,-7) 1/3 Matrix(2379,-5740,986,-2379) -> Matrix(1,0,10,-1) (41/17,70/29) -> (0/1,1/5) Matrix(393,-952,116,-281) -> Matrix(1,0,8,-1) *** -> (0/1,1/4) Matrix(195,-476,34,-83) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(811,-1988,308,-755) -> Matrix(9,-2,22,-5) Matrix(307,-756,80,-197) -> Matrix(7,-2,18,-5) 1/3 Matrix(111,-280,44,-111) -> Matrix(7,-2,24,-7) (5/2,28/11) -> (1/4,1/3) Matrix(505,-1288,198,-505) -> Matrix(23,-8,66,-23) (28/11,23/9) -> (1/3,4/11) Matrix(251,-644,76,-195) -> Matrix(5,-2,12,-5) *** -> (1/3,1/2) Matrix(279,-728,64,-167) -> Matrix(5,-2,12,-5) *** -> (1/3,1/2) Matrix(559,-1512,166,-449) -> Matrix(1,0,2,1) 0/1 Matrix(1513,-4200,424,-1177) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(251,-700,90,-251) -> Matrix(1,0,4,-1) (25/9,14/5) -> (0/1,1/2) Matrix(29,-84,10,-29) -> Matrix(1,0,6,-1) (14/5,3/1) -> (0/1,1/3) Matrix(755,-2436,234,-755) -> Matrix(7,-2,24,-7) (29/9,42/13) -> (1/4,1/3) Matrix(1429,-4620,442,-1429) -> Matrix(15,-4,56,-15) (42/13,55/17) -> (1/4,2/7) Matrix(197,-644,26,-85) -> Matrix(5,-2,12,-5) *** -> (1/3,1/2) Matrix(2351,-7896,700,-2351) -> Matrix(1,0,0,-1) (47/14,84/25) -> (0/1,1/0) Matrix(1849,-6216,550,-1849) -> Matrix(1,0,12,-1) (84/25,37/11) -> (0/1,1/6) Matrix(113,-392,32,-111) -> Matrix(7,-2,18,-5) 1/3 Matrix(1007,-3584,220,-783) -> Matrix(19,-8,64,-27) Matrix(6271,-22344,1760,-6271) -> Matrix(33,-16,68,-33) (57/16,196/55) -> (8/17,1/2) Matrix(15289,-54488,4290,-15289) -> Matrix(59,-30,116,-59) (196/55,139/39) -> (1/2,15/29) Matrix(4031,-14560,1116,-4031) -> Matrix(33,-16,68,-33) (65/18,112/31) -> (8/17,1/2) Matrix(2913,-10528,806,-2913) -> Matrix(19,-10,36,-19) (112/31,47/13) -> (1/2,5/9) Matrix(85,-308,8,-29) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(1231,-4592,330,-1231) -> Matrix(49,-16,150,-49) (41/11,56/15) -> (8/25,1/3) Matrix(449,-1680,120,-449) -> Matrix(17,-6,48,-17) (56/15,15/4) -> (1/3,3/8) Matrix(141,-532,22,-83) -> Matrix(5,-2,18,-7) 1/3 Matrix(57,-224,14,-55) -> Matrix(1,0,2,1) 0/1 Matrix(421,-1764,100,-419) -> Matrix(9,-2,32,-7) 1/4 Matrix(2015,-8904,456,-2015) -> Matrix(1,0,4,-1) (53/12,84/19) -> (0/1,1/2) Matrix(1177,-5208,266,-1177) -> Matrix(1,0,8,-1) (84/19,31/7) -> (0/1,1/4) Matrix(139,-644,30,-139) -> Matrix(25,-8,78,-25) (23/5,14/3) -> (4/13,1/3) Matrix(29,-140,6,-29) -> Matrix(5,-2,12,-5) (14/3,5/1) -> (1/3,1/2) Matrix(111,-616,20,-111) -> Matrix(9,-4,20,-9) (11/2,28/5) -> (2/5,1/2) Matrix(169,-952,30,-169) -> Matrix(3,-2,4,-3) (28/5,17/3) -> (1/2,1/1) Matrix(29,-196,4,-27) -> Matrix(7,-2,18,-5) 1/3 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.