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): 1008 Minimal number of generators: 169 Number of equivalence classes of cusps: 60 Genus: 55 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -10/23 -8/21 -1/3 -4/17 0/1 2/11 5/21 3/10 1/3 7/19 4/9 1/2 14/25 5/8 11/15 6/7 1/1 8/7 7/6 15/11 7/5 3/2 8/5 5/3 25/14 17/9 2/1 11/5 9/4 7/3 64/27 55/23 5/2 28/11 8/3 19/7 77/27 3/1 10/3 7/2 18/5 11/3 4/1 21/5 22/5 9/2 32/7 14/3 43/9 5/1 26/5 16/3 11/2 17/3 6/1 7/1 23/3 8/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 1/1 -6/13 0/1 1/1 -5/11 1/1 -14/31 2/1 1/0 -9/20 3/1 -13/29 3/1 -17/38 9/1 -4/9 -1/1 1/0 -7/16 -1/1 -10/23 0/1 -13/30 1/1 -3/7 1/1 -11/26 3/1 -8/19 -2/1 1/0 -5/12 -1/1 -17/41 -1/1 -12/29 -1/2 0/1 -19/46 -1/1 -26/63 -2/3 -1/2 -33/80 -5/9 -7/17 -1/3 -2/5 0/1 1/1 -13/33 1/1 -11/28 1/1 -9/23 1/1 -16/41 1/1 1/0 -7/18 1/1 -19/49 -1/1 -12/31 -1/1 1/0 -17/44 -1/1 -22/57 -1/2 0/1 -5/13 -1/1 -8/21 0/1 -11/29 1/5 -3/8 1/3 -10/27 1/2 2/3 -7/19 1/1 -18/49 2/3 3/4 -11/30 1/1 -4/11 1/1 2/1 -5/14 -1/1 -6/17 0/1 1/0 -1/3 1/1 -6/19 1/0 -5/16 -1/1 -14/45 0/1 1/2 -9/29 1/1 -4/13 1/1 1/0 -11/36 -1/1 -7/23 -1/1 -3/10 1/1 -8/27 1/1 3/2 -5/17 1/1 -12/41 3/2 2/1 -7/24 1/1 -2/7 1/1 1/0 -3/11 -1/1 -10/37 -1/1 1/0 -7/26 -1/1 -4/15 -2/1 1/0 -9/34 -1/1 -14/53 -1/1 -5/19 -1/1 -6/23 -1/2 0/1 -7/27 -1/3 -1/4 1/1 -4/17 1/0 -7/30 -3/1 -3/13 -1/1 -11/48 -1/1 -8/35 -1/1 1/0 -13/57 -1/1 -5/22 -3/1 -2/9 -1/1 0/1 -7/32 -1/1 -12/55 -3/5 -1/2 -17/78 -3/7 -5/23 -1/3 -3/14 -1/3 -4/19 0/1 1/4 -5/24 1/1 -1/5 1/1 -2/11 -1/1 1/0 -7/39 -1/1 -12/67 -2/1 -1/1 -5/28 -1/1 -3/17 -1/1 -4/23 -1/1 -1/2 -1/6 -1/1 -4/25 0/1 1/4 -7/44 1/1 -3/19 1/1 -5/32 1/1 -2/13 0/1 1/0 -3/20 -1/1 -4/27 -1/2 0/1 -5/34 1/5 -1/7 1/1 -2/15 1/0 -1/8 -1/1 -1/9 -1/1 -2/19 -1/2 0/1 -1/10 1/1 0/1 0/1 1/0 1/9 1/1 1/8 -1/1 1/7 1/1 1/6 1/1 2/11 1/0 3/16 -1/1 4/21 -1/1 1/0 1/5 -1/1 2/9 0/1 1/0 3/13 -1/1 4/17 -1/4 0/1 5/21 0/1 6/25 0/1 1/6 1/4 1/1 3/11 1/1 8/29 3/2 2/1 5/18 1/1 2/7 1/1 1/0 5/17 3/1 3/10 1/0 4/13 -2/1 1/0 5/16 1/1 11/35 -1/1 6/19 -1/1 1/0 1/3 -1/1 5/14 -1/1 9/25 -1/1 4/11 -1/4 0/1 7/19 0/1 10/27 0/1 1/10 3/8 1/3 8/21 0/1 1/2 13/34 1/1 5/13 1/3 2/5 0/1 1/1 3/7 1/1 4/9 1/0 5/11 -3/1 16/35 -2/1 1/0 11/24 -1/1 6/13 -1/1 1/0 7/15 -1/1 1/2 -1/1 5/9 1/1 14/25 1/1 23/41 1/1 9/16 1/1 4/7 2/1 1/0 3/5 1/1 17/28 1/1 14/23 2/1 5/2 39/64 3/1 25/41 3/1 11/18 3/1 41/67 3/1 30/49 3/1 1/0 19/31 3/1 27/44 3/1 8/13 4/1 1/0 5/8 1/0 12/19 -6/1 1/0 19/30 -5/1 26/41 -9/2 -4/1 7/11 -3/1 2/3 -1/1 1/0 5/7 -1/1 13/18 -1/1 34/47 -2/1 -3/2 21/29 -1/1 29/40 -1/1 8/11 -3/2 -1/1 11/15 -1/1 14/19 -1/1 -3/4 3/4 -1/1 13/17 -1/1 23/30 -1/1 33/43 -1/3 10/13 -1/2 0/1 7/9 1/1 18/23 0/1 1/2 11/14 1/1 4/5 -1/1 1/0 13/16 -1/1 9/11 -1/1 14/17 -1/2 0/1 19/23 1/1 5/6 1/1 6/7 1/0 7/8 -1/1 8/9 -2/1 1/0 1/1 -1/1 9/8 -1/1 17/15 -1/1 25/22 -3/5 8/7 -1/2 0/1 7/6 0/1 20/17 0/1 1/2 13/11 1/1 6/5 0/1 1/0 11/9 -1/1 5/4 1/1 14/11 -1/1 1/0 9/7 -1/1 4/3 -2/1 -1/1 15/11 -1/1 26/19 -1/1 -12/13 11/8 -1/1 18/13 -3/4 -2/3 7/5 -1/1 17/12 -5/7 10/7 -2/3 -1/2 23/16 -1/2 13/9 -1/1 16/11 -1/1 -1/2 3/2 -1/3 8/5 0/1 13/8 1/3 44/27 1/3 1/2 75/46 1/3 31/19 1/3 80/49 1/3 1/2 129/79 1/2 49/30 1/1 18/11 0/1 1/2 41/25 1/3 23/14 1/1 5/3 1/1 17/10 1/1 46/27 0/1 1/0 29/17 1/1 12/7 1/1 1/0 7/4 -1/1 16/9 -1/1 1/0 41/23 -1/1 25/14 1/0 34/19 -2/1 1/0 77/43 -3/1 43/24 -3/1 9/5 -1/1 20/11 -1/2 0/1 51/28 -1/1 31/17 -1/1 11/6 -1/1 35/19 -1/1 24/13 0/1 1/0 13/7 -1/1 15/8 -1/1 17/9 -1/1 19/10 -1/1 2/1 -1/1 0/1 11/5 -1/5 9/4 0/1 25/11 1/9 16/7 0/1 1/6 39/17 1/5 23/10 1/5 7/3 1/3 26/11 1/2 2/3 45/19 1/1 64/27 1/1 19/8 1/1 31/13 1/1 43/18 -1/1 55/23 0/1 67/28 1/5 12/5 0/1 1/2 17/7 1/1 39/16 1/1 22/9 1/2 2/3 5/2 1/1 28/11 1/0 23/9 1/1 41/16 -1/1 18/7 1/1 1/0 31/12 3/1 13/5 1/1 8/3 2/1 1/0 19/7 1/0 30/11 -8/1 1/0 11/4 -3/1 14/5 -1/1 1/0 45/16 -1/1 31/11 1/1 17/6 -1/1 37/13 -1/1 57/20 1/1 77/27 1/0 20/7 -1/1 1/0 3/1 -1/1 10/3 0/1 17/5 1/1 58/17 0/1 1/2 41/12 1/1 24/7 0/1 1/2 31/9 1/1 7/2 1/1 25/7 -1/1 18/5 0/1 1/2 29/8 1/3 69/19 1/3 40/11 0/1 1/2 51/14 1/2 11/3 1/1 4/1 1/1 1/0 21/5 1/0 38/9 -19/1 1/0 17/4 -9/1 47/11 -7/1 30/7 -6/1 1/0 13/3 -3/1 22/5 -3/1 1/0 9/2 -3/1 32/7 1/0 23/5 -3/1 14/3 -2/1 1/0 19/4 -7/3 43/9 -2/1 67/14 -21/11 24/5 -2/1 -7/4 5/1 -1/1 26/5 -2/1 -3/2 21/4 -1/1 16/3 -3/2 -1/1 11/2 -1/1 28/5 -1/1 -3/4 17/3 -1/1 6/1 -1/1 0/1 7/1 1/1 15/2 3/1 23/3 1/0 31/4 -9/1 8/1 -3/1 1/0 1/0 -1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(95,44,-434,-201) (-1/2,-6/13) -> (-2/9,-7/32) Hyperbolic Matrix(287,132,50,23) (-6/13,-5/11) -> (17/3,6/1) Hyperbolic Matrix(283,128,-1090,-493) (-5/11,-14/31) -> (-6/23,-7/27) Hyperbolic Matrix(377,170,428,193) (-14/31,-9/20) -> (7/8,8/9) Hyperbolic Matrix(379,170,-1652,-741) (-9/20,-13/29) -> (-3/13,-11/48) Hyperbolic Matrix(1223,548,-2966,-1329) (-13/29,-17/38) -> (-33/80,-7/17) Hyperbolic Matrix(1597,714,378,169) (-17/38,-4/9) -> (38/9,17/4) Hyperbolic Matrix(95,42,-328,-145) (-4/9,-7/16) -> (-7/24,-2/7) Hyperbolic Matrix(459,200,-1058,-461) (-7/16,-10/23) -> (-10/23,-13/30) Parabolic Matrix(1007,436,552,239) (-13/30,-3/7) -> (31/17,11/6) Hyperbolic Matrix(543,230,-1400,-593) (-3/7,-11/26) -> (-7/18,-19/49) Hyperbolic Matrix(989,418,362,153) (-11/26,-8/19) -> (30/11,11/4) Hyperbolic Matrix(181,76,-674,-283) (-8/19,-5/12) -> (-7/26,-4/15) Hyperbolic Matrix(1335,554,2176,903) (-5/12,-17/41) -> (19/31,27/44) Hyperbolic Matrix(357,148,398,165) (-17/41,-12/29) -> (8/9,1/1) Hyperbolic Matrix(1505,622,-3898,-1611) (-12/29,-19/46) -> (-17/44,-22/57) Hyperbolic Matrix(3101,1280,5090,2101) (-19/46,-26/63) -> (14/23,39/64) Hyperbolic Matrix(2215,914,1946,803) (-26/63,-33/80) -> (25/22,8/7) Hyperbolic Matrix(89,36,42,17) (-7/17,-2/5) -> (2/1,11/5) Hyperbolic Matrix(431,170,-2406,-949) (-2/5,-13/33) -> (-7/39,-12/67) Hyperbolic Matrix(773,304,684,269) (-13/33,-11/28) -> (9/8,17/15) Hyperbolic Matrix(1029,404,298,117) (-11/28,-9/23) -> (31/9,7/2) Hyperbolic Matrix(2049,800,1150,449) (-9/23,-16/41) -> (16/9,41/23) Hyperbolic Matrix(595,232,-2598,-1013) (-16/41,-7/18) -> (-11/48,-8/35) Hyperbolic Matrix(511,198,1102,427) (-19/49,-12/31) -> (6/13,7/15) Hyperbolic Matrix(1355,524,256,99) (-12/31,-17/44) -> (21/4,16/3) Hyperbolic Matrix(83,32,-760,-293) (-22/57,-5/13) -> (-1/9,-2/19) Hyperbolic Matrix(335,128,-882,-337) (-5/13,-8/21) -> (-8/21,-11/29) Parabolic Matrix(417,158,1090,413) (-11/29,-3/8) -> (13/34,5/13) Hyperbolic Matrix(167,62,536,199) (-3/8,-10/27) -> (4/13,5/16) Hyperbolic Matrix(249,92,-950,-351) (-10/27,-7/19) -> (-5/19,-6/23) Hyperbolic Matrix(1975,726,574,211) (-7/19,-18/49) -> (24/7,31/9) Hyperbolic Matrix(1563,574,2546,935) (-18/49,-11/30) -> (27/44,8/13) Hyperbolic Matrix(901,330,658,241) (-11/30,-4/11) -> (26/19,11/8) Hyperbolic Matrix(83,30,-368,-133) (-4/11,-5/14) -> (-5/22,-2/9) Hyperbolic Matrix(79,28,-522,-185) (-5/14,-6/17) -> (-2/13,-3/20) Hyperbolic Matrix(239,84,202,71) (-6/17,-1/3) -> (13/11,6/5) Hyperbolic Matrix(533,170,116,37) (-1/3,-6/19) -> (32/7,23/5) Hyperbolic Matrix(683,214,150,47) (-6/19,-5/16) -> (9/2,32/7) Hyperbolic Matrix(379,118,-2380,-741) (-5/16,-14/45) -> (-4/25,-7/44) Hyperbolic Matrix(979,304,190,59) (-14/45,-9/29) -> (5/1,26/5) Hyperbolic Matrix(149,46,-826,-255) (-9/29,-4/13) -> (-2/11,-7/39) Hyperbolic Matrix(523,160,-2396,-733) (-4/13,-11/36) -> (-7/32,-12/55) Hyperbolic Matrix(223,68,-1420,-433) (-11/36,-7/23) -> (-3/19,-5/32) Hyperbolic Matrix(599,182,260,79) (-7/23,-3/10) -> (23/10,7/3) Hyperbolic Matrix(221,66,298,89) (-3/10,-8/27) -> (14/19,3/4) Hyperbolic Matrix(149,44,-850,-251) (-8/27,-5/17) -> (-3/17,-4/23) Hyperbolic Matrix(1987,582,1212,355) (-5/17,-12/41) -> (18/11,41/25) Hyperbolic Matrix(219,64,-1468,-429) (-12/41,-7/24) -> (-3/20,-4/27) Hyperbolic Matrix(71,20,110,31) (-2/7,-3/11) -> (7/11,2/3) Hyperbolic Matrix(569,154,-2494,-675) (-3/11,-10/37) -> (-8/35,-13/57) Hyperbolic Matrix(215,58,1138,307) (-10/37,-7/26) -> (3/16,4/21) Hyperbolic Matrix(143,38,-922,-245) (-4/15,-9/34) -> (-5/32,-2/13) Hyperbolic Matrix(3183,842,1342,355) (-9/34,-14/53) -> (64/27,19/8) Hyperbolic Matrix(3601,950,1520,401) (-14/53,-5/19) -> (45/19,64/27) Hyperbolic Matrix(139,36,-946,-245) (-7/27,-1/4) -> (-5/34,-1/7) Hyperbolic Matrix(135,32,-578,-137) (-1/4,-4/17) -> (-4/17,-7/30) Parabolic Matrix(1151,268,408,95) (-7/30,-3/13) -> (31/11,17/6) Hyperbolic Matrix(1079,246,-4952,-1129) (-13/57,-5/22) -> (-17/78,-5/23) Hyperbolic Matrix(2329,508,298,65) (-12/55,-17/78) -> (31/4,8/1) Hyperbolic Matrix(599,130,364,79) (-5/23,-3/14) -> (23/14,5/3) Hyperbolic Matrix(197,42,530,113) (-3/14,-4/19) -> (10/27,3/8) Hyperbolic Matrix(659,138,1084,227) (-4/19,-5/24) -> (17/28,14/23) Hyperbolic Matrix(1051,218,458,95) (-5/24,-1/5) -> (39/17,23/10) Hyperbolic Matrix(65,12,222,41) (-1/5,-2/11) -> (2/7,5/17) Hyperbolic Matrix(1329,238,698,125) (-12/67,-5/28) -> (19/10,2/1) Hyperbolic Matrix(887,158,1454,259) (-5/28,-3/17) -> (25/41,11/18) Hyperbolic Matrix(563,96,346,59) (-4/23,-1/6) -> (13/8,44/27) Hyperbolic Matrix(61,10,250,41) (-1/6,-4/25) -> (6/25,1/4) Hyperbolic Matrix(4205,668,2348,373) (-7/44,-3/19) -> (77/43,43/24) Hyperbolic Matrix(2625,388,548,81) (-4/27,-5/34) -> (67/14,24/5) Hyperbolic Matrix(541,74,212,29) (-1/7,-2/15) -> (28/11,23/9) Hyperbolic Matrix(299,38,118,15) (-2/15,-1/8) -> (5/2,28/11) Hyperbolic Matrix(177,20,292,33) (-1/8,-1/9) -> (3/5,17/28) Hyperbolic Matrix(1393,146,582,61) (-2/19,-1/10) -> (67/28,12/5) Hyperbolic Matrix(171,16,374,35) (-1/10,0/1) -> (16/35,11/24) Hyperbolic Matrix(429,-40,118,-11) (0/1,1/9) -> (69/19,40/11) Hyperbolic Matrix(653,-76,232,-27) (1/9,1/8) -> (45/16,31/11) Hyperbolic Matrix(549,-74,230,-31) (1/8,1/7) -> (31/13,43/18) Hyperbolic Matrix(89,-14,248,-39) (1/7,1/6) -> (5/14,9/25) Hyperbolic Matrix(45,-8,242,-43) (1/6,2/11) -> (2/11,3/16) Parabolic Matrix(261,-50,830,-159) (4/21,1/5) -> (11/35,6/19) Hyperbolic Matrix(129,-28,106,-23) (1/5,2/9) -> (6/5,11/9) Hyperbolic Matrix(297,-68,380,-87) (2/9,3/13) -> (7/9,18/23) Hyperbolic Matrix(505,-118,612,-143) (3/13,4/17) -> (14/17,19/23) Hyperbolic Matrix(211,-50,882,-209) (4/17,5/21) -> (5/21,6/25) Parabolic Matrix(163,-44,226,-61) (1/4,3/11) -> (5/7,13/18) Hyperbolic Matrix(1591,-438,672,-185) (3/11,8/29) -> (26/11,45/19) Hyperbolic Matrix(1019,-282,1608,-445) (8/29,5/18) -> (19/30,26/41) Hyperbolic Matrix(163,-46,202,-57) (5/18,2/7) -> (4/5,13/16) Hyperbolic Matrix(521,-154,362,-107) (5/17,3/10) -> (23/16,13/9) Hyperbolic Matrix(399,-122,278,-85) (3/10,4/13) -> (10/7,23/16) Hyperbolic Matrix(1147,-360,1010,-317) (5/16,11/35) -> (17/15,25/22) Hyperbolic Matrix(869,-276,1420,-451) (6/19,1/3) -> (41/67,30/49) Hyperbolic Matrix(191,-68,250,-89) (1/3,5/14) -> (3/4,13/17) Hyperbolic Matrix(727,-262,1146,-413) (9/25,4/11) -> (26/41,7/11) Hyperbolic Matrix(267,-98,722,-265) (4/11,7/19) -> (7/19,10/27) Parabolic Matrix(753,-286,208,-79) (3/8,8/21) -> (18/5,29/8) Hyperbolic Matrix(1429,-546,1976,-755) (8/21,13/34) -> (13/18,34/47) Hyperbolic Matrix(113,-44,18,-7) (5/13,2/5) -> (6/1,7/1) Hyperbolic Matrix(73,-30,56,-23) (2/5,3/7) -> (9/7,4/3) Hyperbolic Matrix(73,-32,162,-71) (3/7,4/9) -> (4/9,5/11) Parabolic Matrix(3069,-1402,1714,-783) (5/11,16/35) -> (34/19,77/43) Hyperbolic Matrix(2031,-934,1246,-573) (11/24,6/13) -> (44/27,75/46) Hyperbolic Matrix(247,-118,404,-193) (7/15,1/2) -> (11/18,41/67) Hyperbolic Matrix(167,-92,118,-65) (1/2,5/9) -> (7/5,17/12) Hyperbolic Matrix(701,-392,1250,-699) (5/9,14/25) -> (14/25,23/41) Parabolic Matrix(1999,-1122,3280,-1841) (23/41,9/16) -> (39/64,25/41) Hyperbolic Matrix(365,-206,466,-263) (9/16,4/7) -> (18/23,11/14) Hyperbolic Matrix(131,-76,50,-29) (4/7,3/5) -> (13/5,8/3) Hyperbolic Matrix(3999,-2450,2450,-1501) (30/49,19/31) -> (31/19,80/49) Hyperbolic Matrix(161,-100,256,-159) (8/13,5/8) -> (5/8,12/19) Parabolic Matrix(1401,-886,574,-363) (12/19,19/30) -> (39/16,22/9) Hyperbolic Matrix(61,-42,16,-11) (2/3,5/7) -> (11/3,4/1) Hyperbolic Matrix(1841,-1332,2398,-1735) (34/47,21/29) -> (33/43,10/13) Hyperbolic Matrix(1719,-1246,934,-677) (21/29,29/40) -> (11/6,35/19) Hyperbolic Matrix(1055,-766,376,-273) (29/40,8/11) -> (14/5,45/16) Hyperbolic Matrix(331,-242,450,-329) (8/11,11/15) -> (11/15,14/19) Parabolic Matrix(1797,-1376,986,-755) (13/17,23/30) -> (51/28,31/17) Hyperbolic Matrix(3561,-2732,1250,-959) (23/30,33/43) -> (37/13,57/20) Hyperbolic Matrix(469,-362,206,-159) (10/13,7/9) -> (25/11,16/7) Hyperbolic Matrix(117,-92,14,-11) (11/14,4/5) -> (8/1,1/0) Hyperbolic Matrix(373,-304,200,-163) (13/16,9/11) -> (13/7,15/8) Hyperbolic Matrix(999,-820,586,-481) (9/11,14/17) -> (46/27,29/17) Hyperbolic Matrix(1081,-896,298,-247) (19/23,5/6) -> (29/8,69/19) Hyperbolic Matrix(85,-72,98,-83) (5/6,6/7) -> (6/7,7/8) Parabolic Matrix(323,-354,198,-217) (1/1,9/8) -> (75/46,31/19) Hyperbolic Matrix(169,-196,144,-167) (8/7,7/6) -> (7/6,20/17) Parabolic Matrix(859,-1012,466,-549) (20/17,13/11) -> (35/19,24/13) Hyperbolic Matrix(163,-202,46,-57) (11/9,5/4) -> (7/2,25/7) Hyperbolic Matrix(413,-524,160,-203) (5/4,14/11) -> (18/7,31/12) Hyperbolic Matrix(297,-380,68,-87) (14/11,9/7) -> (13/3,22/5) Hyperbolic Matrix(331,-450,242,-329) (4/3,15/11) -> (15/11,26/19) Parabolic Matrix(241,-332,98,-135) (11/8,18/13) -> (22/9,5/2) Hyperbolic Matrix(217,-302,120,-167) (18/13,7/5) -> (9/5,20/11) Hyperbolic Matrix(301,-428,64,-91) (17/12,10/7) -> (14/3,19/4) Hyperbolic Matrix(213,-308,74,-107) (13/9,16/11) -> (20/7,3/1) Hyperbolic Matrix(487,-710,190,-277) (16/11,3/2) -> (41/16,18/7) Hyperbolic Matrix(81,-128,50,-79) (3/2,8/5) -> (8/5,13/8) Parabolic Matrix(5353,-8740,1876,-3063) (80/49,129/79) -> (77/27,20/7) Hyperbolic Matrix(6813,-11126,2390,-3903) (129/79,49/30) -> (57/20,77/27) Hyperbolic Matrix(2191,-3580,642,-1049) (49/30,18/11) -> (58/17,41/12) Hyperbolic Matrix(1201,-1970,670,-1099) (41/25,23/14) -> (43/24,9/5) Hyperbolic Matrix(367,-622,154,-261) (5/3,17/10) -> (19/8,31/13) Hyperbolic Matrix(1577,-2686,866,-1475) (17/10,46/27) -> (20/11,51/28) Hyperbolic Matrix(595,-1016,106,-181) (29/17,12/7) -> (28/5,17/3) Hyperbolic Matrix(133,-230,48,-83) (12/7,7/4) -> (11/4,14/5) Hyperbolic Matrix(169,-298,38,-67) (7/4,16/9) -> (22/5,9/2) Hyperbolic Matrix(1327,-2366,364,-649) (41/23,25/14) -> (51/14,11/3) Hyperbolic Matrix(1529,-2734,420,-751) (25/14,34/19) -> (40/11,51/14) Hyperbolic Matrix(821,-1518,192,-355) (24/13,13/7) -> (47/11,30/7) Hyperbolic Matrix(307,-578,162,-305) (15/8,17/9) -> (17/9,19/10) Parabolic Matrix(145,-324,64,-143) (11/5,9/4) -> (9/4,25/11) Parabolic Matrix(1105,-2534,324,-743) (16/7,39/17) -> (17/5,58/17) Hyperbolic Matrix(233,-548,54,-127) (7/3,26/11) -> (30/7,13/3) Hyperbolic Matrix(2531,-6050,1058,-2529) (43/18,55/23) -> (55/23,67/28) Parabolic Matrix(213,-514,46,-111) (12/5,17/7) -> (23/5,14/3) Hyperbolic Matrix(711,-1732,250,-609) (17/7,39/16) -> (17/6,37/13) Hyperbolic Matrix(905,-2318,212,-543) (23/9,41/16) -> (17/4,47/11) Hyperbolic Matrix(159,-412,22,-57) (31/12,13/5) -> (7/1,15/2) Hyperbolic Matrix(267,-722,98,-265) (8/3,19/7) -> (19/7,30/11) Parabolic Matrix(61,-200,18,-59) (3/1,10/3) -> (10/3,17/5) Parabolic Matrix(459,-1570,88,-301) (41/12,24/7) -> (26/5,21/4) Hyperbolic Matrix(193,-690,40,-143) (25/7,18/5) -> (24/5,5/1) Hyperbolic Matrix(211,-882,50,-209) (4/1,21/5) -> (21/5,38/9) Parabolic Matrix(775,-3698,162,-773) (19/4,43/9) -> (43/9,67/14) Parabolic Matrix(89,-484,16,-87) (16/3,11/2) -> (11/2,28/5) Parabolic Matrix(139,-1058,18,-137) (15/2,23/3) -> (23/3,31/4) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(95,44,-434,-201) -> Matrix(1,0,-2,1) Matrix(287,132,50,23) -> Matrix(1,0,-2,1) Matrix(283,128,-1090,-493) -> Matrix(1,-2,-2,5) Matrix(377,170,428,193) -> Matrix(1,-4,0,1) Matrix(379,170,-1652,-741) -> Matrix(1,-4,0,1) Matrix(1223,548,-2966,-1329) -> Matrix(1,-4,-2,9) Matrix(1597,714,378,169) -> Matrix(1,-18,0,1) Matrix(95,42,-328,-145) -> Matrix(1,2,0,1) Matrix(459,200,-1058,-461) -> Matrix(1,0,2,1) Matrix(1007,436,552,239) -> Matrix(1,0,-2,1) Matrix(543,230,-1400,-593) -> Matrix(1,-2,0,1) Matrix(989,418,362,153) -> Matrix(1,-6,0,1) Matrix(181,76,-674,-283) -> Matrix(1,0,0,1) Matrix(1335,554,2176,903) -> Matrix(5,2,2,1) Matrix(357,148,398,165) -> Matrix(3,2,-2,-1) Matrix(1505,622,-3898,-1611) -> Matrix(1,0,0,1) Matrix(3101,1280,5090,2101) -> Matrix(11,8,4,3) Matrix(2215,914,1946,803) -> Matrix(3,2,-8,-5) Matrix(89,36,42,17) -> Matrix(1,0,-2,1) Matrix(431,170,-2406,-949) -> Matrix(1,-2,0,1) Matrix(773,304,684,269) -> Matrix(1,0,-2,1) Matrix(1029,404,298,117) -> Matrix(1,0,0,1) Matrix(2049,800,1150,449) -> Matrix(1,-2,0,1) Matrix(595,232,-2598,-1013) -> Matrix(1,-2,0,1) Matrix(511,198,1102,427) -> Matrix(1,0,0,1) Matrix(1355,524,256,99) -> Matrix(3,2,-2,-1) Matrix(83,32,-760,-293) -> Matrix(1,0,0,1) Matrix(335,128,-882,-337) -> Matrix(1,0,6,1) Matrix(417,158,1090,413) -> Matrix(1,0,-2,1) Matrix(167,62,536,199) -> Matrix(1,0,-2,1) Matrix(249,92,-950,-351) -> Matrix(3,-2,-4,3) Matrix(1975,726,574,211) -> Matrix(3,-2,2,-1) Matrix(1563,574,2546,935) -> Matrix(13,-10,4,-3) Matrix(901,330,658,241) -> Matrix(11,-10,-12,11) Matrix(83,30,-368,-133) -> Matrix(1,-2,0,1) Matrix(79,28,-522,-185) -> Matrix(1,0,0,1) Matrix(239,84,202,71) -> Matrix(1,0,0,1) Matrix(533,170,116,37) -> Matrix(1,-4,0,1) Matrix(683,214,150,47) -> Matrix(1,-2,0,1) Matrix(379,118,-2380,-741) -> Matrix(1,0,2,1) Matrix(979,304,190,59) -> Matrix(1,-2,0,1) Matrix(149,46,-826,-255) -> Matrix(1,-2,0,1) Matrix(523,160,-2396,-733) -> Matrix(1,2,-2,-3) Matrix(223,68,-1420,-433) -> Matrix(1,0,2,1) Matrix(599,182,260,79) -> Matrix(1,0,4,1) Matrix(221,66,298,89) -> Matrix(1,0,-2,1) Matrix(149,44,-850,-251) -> Matrix(1,-2,0,1) Matrix(1987,582,1212,355) -> Matrix(1,-2,4,-7) Matrix(219,64,-1468,-429) -> Matrix(1,-2,0,1) Matrix(71,20,110,31) -> Matrix(1,-2,0,1) Matrix(569,154,-2494,-675) -> Matrix(1,0,0,1) Matrix(215,58,1138,307) -> Matrix(1,0,0,1) Matrix(143,38,-922,-245) -> Matrix(1,2,0,1) Matrix(3183,842,1342,355) -> Matrix(3,4,2,3) Matrix(3601,950,1520,401) -> Matrix(5,4,6,5) Matrix(139,36,-946,-245) -> Matrix(1,0,4,1) Matrix(135,32,-578,-137) -> Matrix(1,-4,0,1) Matrix(1151,268,408,95) -> Matrix(1,2,0,1) Matrix(1079,246,-4952,-1129) -> Matrix(1,0,-2,1) Matrix(2329,508,298,65) -> Matrix(11,6,-2,-1) Matrix(599,130,364,79) -> Matrix(1,0,4,1) Matrix(197,42,530,113) -> Matrix(1,0,6,1) Matrix(659,138,1084,227) -> Matrix(3,-2,2,-1) Matrix(1051,218,458,95) -> Matrix(1,0,4,1) Matrix(65,12,222,41) -> Matrix(1,2,0,1) Matrix(1329,238,698,125) -> Matrix(1,2,-2,-3) Matrix(887,158,1454,259) -> Matrix(1,4,0,1) Matrix(563,96,346,59) -> Matrix(1,0,4,1) Matrix(61,10,250,41) -> Matrix(1,0,2,1) Matrix(4205,668,2348,373) -> Matrix(5,-2,-2,1) Matrix(2625,388,548,81) -> Matrix(11,2,-6,-1) Matrix(541,74,212,29) -> Matrix(1,0,0,1) Matrix(299,38,118,15) -> Matrix(1,2,0,1) Matrix(177,20,292,33) -> Matrix(1,2,0,1) Matrix(1393,146,582,61) -> Matrix(1,0,4,1) Matrix(171,16,374,35) -> Matrix(1,-2,0,1) Matrix(429,-40,118,-11) -> Matrix(1,0,2,1) Matrix(653,-76,232,-27) -> Matrix(1,0,0,1) Matrix(549,-74,230,-31) -> Matrix(1,0,0,1) Matrix(89,-14,248,-39) -> Matrix(1,0,-2,1) Matrix(45,-8,242,-43) -> Matrix(1,-2,0,1) Matrix(261,-50,830,-159) -> Matrix(1,0,0,1) Matrix(129,-28,106,-23) -> Matrix(1,0,0,1) Matrix(297,-68,380,-87) -> Matrix(1,0,2,1) Matrix(505,-118,612,-143) -> Matrix(1,0,2,1) Matrix(211,-50,882,-209) -> Matrix(1,0,10,1) Matrix(163,-44,226,-61) -> Matrix(1,-2,0,1) Matrix(1591,-438,672,-185) -> Matrix(3,-4,4,-5) Matrix(1019,-282,1608,-445) -> Matrix(1,-6,0,1) Matrix(163,-46,202,-57) -> Matrix(1,-2,0,1) Matrix(521,-154,362,-107) -> Matrix(1,-2,-2,5) Matrix(399,-122,278,-85) -> Matrix(1,4,-2,-7) Matrix(1147,-360,1010,-317) -> Matrix(1,2,-2,-3) Matrix(869,-276,1420,-451) -> Matrix(1,4,0,1) Matrix(191,-68,250,-89) -> Matrix(1,0,0,1) Matrix(727,-262,1146,-413) -> Matrix(7,4,-2,-1) Matrix(267,-98,722,-265) -> Matrix(1,0,14,1) Matrix(753,-286,208,-79) -> Matrix(1,0,0,1) Matrix(1429,-546,1976,-755) -> Matrix(1,-2,0,1) Matrix(113,-44,18,-7) -> Matrix(1,0,-2,1) Matrix(73,-30,56,-23) -> Matrix(1,-2,0,1) Matrix(73,-32,162,-71) -> Matrix(1,-4,0,1) Matrix(3069,-1402,1714,-783) -> Matrix(1,0,0,1) Matrix(2031,-934,1246,-573) -> Matrix(1,2,2,5) Matrix(247,-118,404,-193) -> Matrix(1,4,0,1) Matrix(167,-92,118,-65) -> Matrix(3,-2,-4,3) Matrix(701,-392,1250,-699) -> Matrix(9,-8,8,-7) Matrix(1999,-1122,3280,-1841) -> Matrix(17,-20,6,-7) Matrix(365,-206,466,-263) -> Matrix(1,-2,2,-3) Matrix(131,-76,50,-29) -> Matrix(1,0,0,1) Matrix(3999,-2450,2450,-1501) -> Matrix(1,-2,2,-3) Matrix(161,-100,256,-159) -> Matrix(1,-10,0,1) Matrix(1401,-886,574,-363) -> Matrix(1,4,2,9) Matrix(61,-42,16,-11) -> Matrix(1,2,0,1) Matrix(1841,-1332,2398,-1735) -> Matrix(1,2,-4,-7) Matrix(1719,-1246,934,-677) -> Matrix(1,2,-2,-3) Matrix(1055,-766,376,-273) -> Matrix(1,2,-2,-3) Matrix(331,-242,450,-329) -> Matrix(5,6,-6,-7) Matrix(1797,-1376,986,-755) -> Matrix(1,0,0,1) Matrix(3561,-2732,1250,-959) -> Matrix(1,0,2,1) Matrix(469,-362,206,-159) -> Matrix(1,0,8,1) Matrix(117,-92,14,-11) -> Matrix(1,-2,0,1) Matrix(373,-304,200,-163) -> Matrix(1,0,0,1) Matrix(999,-820,586,-481) -> Matrix(1,0,2,1) Matrix(1081,-896,298,-247) -> Matrix(1,0,2,1) Matrix(85,-72,98,-83) -> Matrix(1,-2,0,1) Matrix(323,-354,198,-217) -> Matrix(1,0,4,1) Matrix(169,-196,144,-167) -> Matrix(1,0,4,1) Matrix(859,-1012,466,-549) -> Matrix(1,0,-2,1) Matrix(163,-202,46,-57) -> Matrix(1,0,0,1) Matrix(413,-524,160,-203) -> Matrix(1,2,0,1) Matrix(297,-380,68,-87) -> Matrix(1,-2,0,1) Matrix(331,-450,242,-329) -> Matrix(13,14,-14,-15) Matrix(241,-332,98,-135) -> Matrix(5,4,6,5) Matrix(217,-302,120,-167) -> Matrix(3,2,-2,-1) Matrix(301,-428,64,-91) -> Matrix(7,4,-2,-1) Matrix(213,-308,74,-107) -> Matrix(3,2,-2,-1) Matrix(487,-710,190,-277) -> Matrix(1,0,2,1) Matrix(81,-128,50,-79) -> Matrix(1,0,6,1) Matrix(5353,-8740,1876,-3063) -> Matrix(5,-2,-2,1) Matrix(6813,-11126,2390,-3903) -> Matrix(3,-2,2,-1) Matrix(2191,-3580,642,-1049) -> Matrix(1,0,0,1) Matrix(1201,-1970,670,-1099) -> Matrix(5,-2,-2,1) Matrix(367,-622,154,-261) -> Matrix(1,0,0,1) Matrix(1577,-2686,866,-1475) -> Matrix(1,0,-2,1) Matrix(595,-1016,106,-181) -> Matrix(3,-2,-4,3) Matrix(133,-230,48,-83) -> Matrix(1,-2,0,1) Matrix(169,-298,38,-67) -> Matrix(1,-2,0,1) Matrix(1327,-2366,364,-649) -> Matrix(1,0,2,1) Matrix(1529,-2734,420,-751) -> Matrix(1,2,2,5) Matrix(821,-1518,192,-355) -> Matrix(1,-6,0,1) Matrix(307,-578,162,-305) -> Matrix(1,2,-2,-3) Matrix(145,-324,64,-143) -> Matrix(1,0,14,1) Matrix(1105,-2534,324,-743) -> Matrix(1,0,-4,1) Matrix(233,-548,54,-127) -> Matrix(9,-4,-2,1) Matrix(2531,-6050,1058,-2529) -> Matrix(1,0,6,1) Matrix(213,-514,46,-111) -> Matrix(5,-2,-2,1) Matrix(711,-1732,250,-609) -> Matrix(1,0,-2,1) Matrix(905,-2318,212,-543) -> Matrix(1,-8,0,1) Matrix(159,-412,22,-57) -> Matrix(1,0,0,1) Matrix(267,-722,98,-265) -> Matrix(1,-10,0,1) Matrix(61,-200,18,-59) -> Matrix(1,0,2,1) Matrix(459,-1570,88,-301) -> Matrix(1,-2,0,1) Matrix(193,-690,40,-143) -> Matrix(3,2,-2,-1) Matrix(211,-882,50,-209) -> Matrix(1,-20,0,1) Matrix(775,-3698,162,-773) -> Matrix(27,56,-14,-29) Matrix(89,-484,16,-87) -> Matrix(5,6,-6,-7) Matrix(139,-1058,18,-137) -> Matrix(1,-12,0,1) 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): 40 Degree of the the map X: 40 Degree of the the map Y: 168 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 0/1 1 1 0/1 (0/1,1/0) 0 26 1/9 1/1 1 13 1/8 -1/1 1 26 1/7 1/1 1 13 1/6 1/1 1 26 2/11 1/0 2 2 3/16 -1/1 1 26 1/5 -1/1 1 13 2/9 (0/1,1/0) 0 26 3/13 -1/1 1 13 4/17 (-1/4,0/1) 0 26 5/21 0/1 5 1 1/4 1/1 1 26 3/11 1/1 1 13 8/29 (3/2,2/1) 0 26 5/18 1/1 1 26 2/7 (1/1,1/0) 0 26 3/10 1/0 3 2 4/13 (-2/1,1/0) 0 26 1/3 -1/1 1 13 5/14 -1/1 1 26 9/25 -1/1 1 13 4/11 (-1/4,0/1) 0 26 7/19 0/1 7 1 3/8 1/3 1 26 8/21 (0/1,1/2) 0 26 5/13 1/3 1 13 2/5 (0/1,1/1) 0 26 3/7 1/1 1 13 4/9 1/0 4 2 5/11 -3/1 1 13 11/24 -1/1 1 26 6/13 (-1/1,1/0) 0 26 1/2 -1/1 1 26 5/9 1/1 1 13 14/25 1/1 8 2 23/41 1/1 1 13 9/16 1/1 1 26 4/7 (2/1,1/0) 0 26 3/5 1/1 1 13 14/23 (2/1,5/2) 0 26 11/18 3/1 1 26 30/49 (3/1,1/0) 0 26 19/31 3/1 1 13 8/13 (4/1,1/0) 0 26 5/8 1/0 5 2 2/3 (-1/1,1/0) 0 26 5/7 -1/1 1 13 13/18 -1/1 1 26 21/29 -1/1 1 13 29/40 -1/1 1 26 8/11 (-3/2,-1/1) 0 26 11/15 -1/1 3 1 3/4 -1/1 1 26 13/17 -1/1 1 13 23/30 -1/1 1 26 10/13 (-1/2,0/1) 0 26 7/9 1/1 1 13 18/23 (0/1,1/2) 0 26 11/14 1/1 1 26 4/5 (-1/1,1/0) 0 26 13/16 -1/1 1 26 9/11 -1/1 1 13 14/17 (-1/2,0/1) 0 26 19/23 1/1 1 13 5/6 1/1 1 26 6/7 1/0 2 2 7/8 -1/1 1 26 1/1 -1/1 1 13 9/8 -1/1 1 26 8/7 (-1/2,0/1) 0 26 7/6 0/1 2 2 6/5 (0/1,1/0) 0 26 11/9 -1/1 1 13 5/4 1/1 1 26 14/11 (-1/1,1/0) 0 26 9/7 -1/1 1 13 4/3 (-2/1,-1/1) 0 26 15/11 -1/1 7 1 11/8 -1/1 1 26 18/13 (-3/4,-2/3) 0 26 7/5 -1/1 1 13 17/12 -5/7 1 26 10/7 (-2/3,-1/2) 0 26 13/9 -1/1 1 13 16/11 (-1/1,-1/2) 0 26 3/2 -1/3 1 26 8/5 0/1 6 2 13/8 1/3 1 26 31/19 1/3 1 13 80/49 (1/3,1/2) 0 26 129/79 1/2 2 1 49/30 1/1 1 26 18/11 (0/1,1/2) 0 26 5/3 1/1 1 13 17/10 1/1 1 26 46/27 (0/1,1/0) 0 26 29/17 1/1 1 13 12/7 (1/1,1/0) 0 26 7/4 -1/1 1 26 16/9 (-1/1,1/0) 0 26 25/14 1/0 1 2 34/19 (-2/1,1/0) 0 26 9/5 -1/1 1 13 20/11 (-1/2,0/1) 0 26 11/6 -1/1 1 26 24/13 (0/1,1/0) 0 26 13/7 -1/1 1 13 15/8 -1/1 1 26 17/9 -1/1 1 1 2/1 (-1/1,0/1) 0 26 9/4 0/1 7 2 16/7 (0/1,1/6) 0 26 7/3 1/3 1 13 26/11 (1/2,2/3) 0 26 45/19 1/1 1 13 19/8 1/1 1 26 31/13 1/1 1 13 43/18 -1/1 1 26 55/23 0/1 3 1 12/5 (0/1,1/2) 0 26 17/7 1/1 1 13 22/9 (1/2,2/3) 0 26 5/2 1/1 1 26 23/9 1/1 1 13 41/16 -1/1 1 26 18/7 (1/1,1/0) 0 26 31/12 3/1 1 26 13/5 1/1 1 13 8/3 (2/1,1/0) 0 26 19/7 1/0 5 1 11/4 -3/1 1 26 14/5 (-1/1,1/0) 0 26 17/6 -1/1 1 26 20/7 (-1/1,1/0) 0 26 3/1 -1/1 1 13 10/3 0/1 2 2 17/5 1/1 1 13 41/12 1/1 1 26 24/7 (0/1,1/2) 0 26 7/2 1/1 1 26 25/7 -1/1 1 13 18/5 (0/1,1/2) 0 26 29/8 1/3 1 26 69/19 1/3 1 13 40/11 (0/1,1/2) 0 26 11/3 1/1 1 13 4/1 (1/1,1/0) 0 26 21/5 1/0 10 1 17/4 -9/1 1 26 47/11 -7/1 1 13 30/7 (-6/1,1/0) 0 26 13/3 -3/1 1 13 22/5 (-3/1,1/0) 0 26 9/2 -3/1 1 26 23/5 -3/1 1 13 14/3 (-2/1,1/0) 0 26 19/4 -7/3 1 26 43/9 -2/1 7 1 24/5 (-2/1,-7/4) 0 26 5/1 -1/1 1 13 16/3 (-3/2,-1/1) 0 26 11/2 -1/1 3 2 6/1 (-1/1,0/1) 0 26 7/1 1/1 1 13 15/2 3/1 1 26 23/3 1/0 6 1 8/1 (-3/1,1/0) 0 26 1/0 -1/1 1 26 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(-1,0,2,1) (-1/1,0/1) -> (-1/1,0/1) Reflection Matrix(429,-40,118,-11) (0/1,1/9) -> (69/19,40/11) Hyperbolic Matrix(139,-16,304,-35) (1/9,1/8) -> (5/11,11/24) Glide Reflection Matrix(549,-74,230,-31) (1/8,1/7) -> (31/13,43/18) Hyperbolic Matrix(89,-14,248,-39) (1/7,1/6) -> (5/14,9/25) Hyperbolic Matrix(45,-8,242,-43) (1/6,2/11) -> (2/11,3/16) Parabolic Matrix(393,-74,154,-29) (3/16,1/5) -> (5/2,23/9) Glide Reflection Matrix(129,-28,106,-23) (1/5,2/9) -> (6/5,11/9) Hyperbolic Matrix(297,-68,380,-87) (2/9,3/13) -> (7/9,18/23) Hyperbolic Matrix(505,-118,612,-143) (3/13,4/17) -> (14/17,19/23) Hyperbolic Matrix(169,-40,714,-169) (4/17,5/21) -> (4/17,5/21) Reflection Matrix(41,-10,168,-41) (5/21,1/4) -> (5/21,1/4) Reflection Matrix(163,-44,226,-61) (1/4,3/11) -> (5/7,13/18) Hyperbolic Matrix(1591,-438,672,-185) (3/11,8/29) -> (26/11,45/19) Hyperbolic Matrix(571,-158,936,-259) (8/29,5/18) -> (14/23,11/18) Glide Reflection Matrix(163,-46,202,-57) (5/18,2/7) -> (4/5,13/16) Hyperbolic Matrix(41,-12,140,-41) (2/7,3/10) -> (2/7,3/10) Reflection Matrix(79,-24,260,-79) (3/10,4/13) -> (3/10,4/13) Reflection Matrix(199,-62,138,-43) (4/13,1/3) -> (10/7,13/9) Glide Reflection Matrix(191,-68,250,-89) (1/3,5/14) -> (3/4,13/17) Hyperbolic Matrix(383,-138,630,-227) (9/25,4/11) -> (3/5,14/23) Glide Reflection Matrix(153,-56,418,-153) (4/11,7/19) -> (4/11,7/19) Reflection Matrix(113,-42,304,-113) (7/19,3/8) -> (7/19,3/8) Reflection Matrix(753,-286,208,-79) (3/8,8/21) -> (18/5,29/8) Hyperbolic Matrix(339,-130,206,-79) (8/21,5/13) -> (18/11,5/3) Glide Reflection Matrix(113,-44,18,-7) (5/13,2/5) -> (6/1,7/1) Hyperbolic Matrix(73,-30,56,-23) (2/5,3/7) -> (9/7,4/3) Hyperbolic Matrix(73,-32,162,-71) (3/7,4/9) -> (4/9,5/11) Parabolic Matrix(569,-262,784,-361) (11/24,6/13) -> (29/40,8/11) Glide Reflection Matrix(249,-116,88,-41) (6/13,1/2) -> (14/5,17/6) Glide Reflection Matrix(167,-92,118,-65) (1/2,5/9) -> (7/5,17/12) Hyperbolic Matrix(701,-392,1250,-699) (5/9,14/25) -> (14/25,23/41) Parabolic Matrix(1499,-842,632,-355) (23/41,9/16) -> (45/19,19/8) Glide Reflection Matrix(365,-206,466,-263) (9/16,4/7) -> (18/23,11/14) Hyperbolic Matrix(131,-76,50,-29) (4/7,3/5) -> (13/5,8/3) Hyperbolic Matrix(1193,-730,420,-257) (11/18,30/49) -> (17/6,20/7) Glide Reflection Matrix(3999,-2450,2450,-1501) (30/49,19/31) -> (31/19,80/49) Hyperbolic Matrix(903,-554,370,-227) (19/31,8/13) -> (17/7,22/9) Glide Reflection Matrix(129,-80,208,-129) (8/13,5/8) -> (8/13,5/8) Reflection Matrix(31,-20,48,-31) (5/8,2/3) -> (5/8,2/3) Reflection Matrix(61,-42,16,-11) (2/3,5/7) -> (11/3,4/1) Hyperbolic Matrix(935,-676,574,-415) (13/18,21/29) -> (13/8,31/19) Glide Reflection Matrix(301,-218,272,-197) (21/29,29/40) -> (1/1,9/8) Glide Reflection Matrix(241,-176,330,-241) (8/11,11/15) -> (8/11,11/15) Reflection Matrix(89,-66,120,-89) (11/15,3/4) -> (11/15,3/4) Reflection Matrix(1207,-924,354,-271) (13/17,23/30) -> (17/5,41/12) Glide Reflection Matrix(1177,-904,720,-553) (23/30,10/13) -> (49/30,18/11) Glide Reflection Matrix(235,-182,102,-79) (10/13,7/9) -> (16/7,7/3) Glide Reflection Matrix(117,-92,14,-11) (11/14,4/5) -> (8/1,1/0) Hyperbolic Matrix(373,-304,200,-163) (13/16,9/11) -> (13/7,15/8) Hyperbolic Matrix(999,-820,586,-481) (9/11,14/17) -> (46/27,29/17) Hyperbolic Matrix(1081,-896,298,-247) (19/23,5/6) -> (29/8,69/19) Hyperbolic Matrix(85,-72,98,-83) (5/6,6/7) -> (6/7,7/8) Parabolic Matrix(193,-170,42,-37) (7/8,1/1) -> (9/2,23/5) Glide Reflection Matrix(269,-304,146,-165) (9/8,8/7) -> (11/6,24/13) Glide Reflection Matrix(97,-112,84,-97) (8/7,7/6) -> (8/7,7/6) Reflection Matrix(71,-84,60,-71) (7/6,6/5) -> (7/6,6/5) Reflection Matrix(163,-202,46,-57) (11/9,5/4) -> (7/2,25/7) Hyperbolic Matrix(413,-524,160,-203) (5/4,14/11) -> (18/7,31/12) Hyperbolic Matrix(297,-380,68,-87) (14/11,9/7) -> (13/3,22/5) Hyperbolic Matrix(89,-120,66,-89) (4/3,15/11) -> (4/3,15/11) Reflection Matrix(241,-330,176,-241) (15/11,11/8) -> (15/11,11/8) Reflection Matrix(241,-332,98,-135) (11/8,18/13) -> (22/9,5/2) Hyperbolic Matrix(217,-302,120,-167) (18/13,7/5) -> (9/5,20/11) Hyperbolic Matrix(301,-428,64,-91) (17/12,10/7) -> (14/3,19/4) Hyperbolic Matrix(213,-308,74,-107) (13/9,16/11) -> (20/7,3/1) Hyperbolic Matrix(487,-710,190,-277) (16/11,3/2) -> (41/16,18/7) Hyperbolic Matrix(81,-128,50,-79) (3/2,8/5) -> (8/5,13/8) Parabolic Matrix(12641,-20640,7742,-12641) (80/49,129/79) -> (80/49,129/79) Reflection Matrix(7741,-12642,4740,-7741) (129/79,49/30) -> (129/79,49/30) Reflection Matrix(367,-622,154,-261) (5/3,17/10) -> (19/8,31/13) Hyperbolic Matrix(1347,-2294,394,-671) (17/10,46/27) -> (41/12,24/7) Glide Reflection Matrix(307,-524,58,-99) (29/17,12/7) -> (5/1,16/3) Glide Reflection Matrix(133,-230,48,-83) (12/7,7/4) -> (11/4,14/5) Hyperbolic Matrix(169,-298,38,-67) (7/4,16/9) -> (22/5,9/2) Hyperbolic Matrix(449,-800,252,-449) (16/9,25/14) -> (16/9,25/14) Reflection Matrix(951,-1700,532,-951) (25/14,34/19) -> (25/14,34/19) Reflection Matrix(409,-734,112,-201) (34/19,9/5) -> (40/11,11/3) Glide Reflection Matrix(221,-404,64,-117) (20/11,11/6) -> (24/7,7/2) Glide Reflection Matrix(821,-1518,192,-355) (24/13,13/7) -> (47/11,30/7) Hyperbolic Matrix(271,-510,144,-271) (15/8,17/9) -> (15/8,17/9) Reflection Matrix(35,-68,18,-35) (17/9,2/1) -> (17/9,2/1) Reflection Matrix(17,-36,8,-17) (2/1,9/4) -> (2/1,9/4) Reflection Matrix(127,-288,56,-127) (9/4,16/7) -> (9/4,16/7) Reflection Matrix(233,-548,54,-127) (7/3,26/11) -> (30/7,13/3) Hyperbolic Matrix(1979,-4730,828,-1979) (43/18,55/23) -> (43/18,55/23) Reflection Matrix(551,-1320,230,-551) (55/23,12/5) -> (55/23,12/5) Reflection Matrix(213,-514,46,-111) (12/5,17/7) -> (23/5,14/3) Hyperbolic Matrix(905,-2318,212,-543) (23/9,41/16) -> (17/4,47/11) Hyperbolic Matrix(159,-412,22,-57) (31/12,13/5) -> (7/1,15/2) Hyperbolic Matrix(113,-304,42,-113) (8/3,19/7) -> (8/3,19/7) Reflection Matrix(153,-418,56,-153) (19/7,11/4) -> (19/7,11/4) Reflection Matrix(61,-200,18,-59) (3/1,10/3) -> (10/3,17/5) Parabolic Matrix(193,-690,40,-143) (25/7,18/5) -> (24/5,5/1) Hyperbolic Matrix(41,-168,10,-41) (4/1,21/5) -> (4/1,21/5) Reflection Matrix(169,-714,40,-169) (21/5,17/4) -> (21/5,17/4) Reflection Matrix(343,-1634,72,-343) (19/4,43/9) -> (19/4,43/9) Reflection Matrix(431,-2064,90,-431) (43/9,24/5) -> (43/9,24/5) Reflection Matrix(65,-352,12,-65) (16/3,11/2) -> (16/3,11/2) Reflection Matrix(23,-132,4,-23) (11/2,6/1) -> (11/2,6/1) Reflection Matrix(91,-690,12,-91) (15/2,23/3) -> (15/2,23/3) Reflection Matrix(47,-368,6,-47) (23/3,8/1) -> (23/3,8/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(-1,0,2,1) -> Matrix(1,0,0,-1) (-1/1,0/1) -> (0/1,1/0) Matrix(429,-40,118,-11) -> Matrix(1,0,2,1) 0/1 Matrix(139,-16,304,-35) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(549,-74,230,-31) -> Matrix(1,0,0,1) Matrix(89,-14,248,-39) -> Matrix(1,0,-2,1) 0/1 Matrix(45,-8,242,-43) -> Matrix(1,-2,0,1) 1/0 Matrix(393,-74,154,-29) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(129,-28,106,-23) -> Matrix(1,0,0,1) Matrix(297,-68,380,-87) -> Matrix(1,0,2,1) 0/1 Matrix(505,-118,612,-143) -> Matrix(1,0,2,1) 0/1 Matrix(169,-40,714,-169) -> Matrix(-1,0,8,1) (4/17,5/21) -> (-1/4,0/1) Matrix(41,-10,168,-41) -> Matrix(1,0,2,-1) (5/21,1/4) -> (0/1,1/1) Matrix(163,-44,226,-61) -> Matrix(1,-2,0,1) 1/0 Matrix(1591,-438,672,-185) -> Matrix(3,-4,4,-5) 1/1 Matrix(571,-158,936,-259) -> Matrix(-1,4,0,1) *** -> (2/1,1/0) Matrix(163,-46,202,-57) -> Matrix(1,-2,0,1) 1/0 Matrix(41,-12,140,-41) -> Matrix(-1,2,0,1) (2/7,3/10) -> (1/1,1/0) Matrix(79,-24,260,-79) -> Matrix(1,4,0,-1) (3/10,4/13) -> (-2/1,1/0) Matrix(199,-62,138,-43) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(191,-68,250,-89) -> Matrix(1,0,0,1) Matrix(383,-138,630,-227) -> Matrix(3,2,2,1) Matrix(153,-56,418,-153) -> Matrix(-1,0,8,1) (4/11,7/19) -> (-1/4,0/1) Matrix(113,-42,304,-113) -> Matrix(1,0,6,-1) (7/19,3/8) -> (0/1,1/3) Matrix(753,-286,208,-79) -> Matrix(1,0,0,1) Matrix(339,-130,206,-79) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(113,-44,18,-7) -> Matrix(1,0,-2,1) 0/1 Matrix(73,-30,56,-23) -> Matrix(1,-2,0,1) 1/0 Matrix(73,-32,162,-71) -> Matrix(1,-4,0,1) 1/0 Matrix(569,-262,784,-361) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(249,-116,88,-41) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(167,-92,118,-65) -> Matrix(3,-2,-4,3) Matrix(701,-392,1250,-699) -> Matrix(9,-8,8,-7) 1/1 Matrix(1499,-842,632,-355) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(365,-206,466,-263) -> Matrix(1,-2,2,-3) 1/1 Matrix(131,-76,50,-29) -> Matrix(1,0,0,1) Matrix(1193,-730,420,-257) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(3999,-2450,2450,-1501) -> Matrix(1,-2,2,-3) 1/1 Matrix(903,-554,370,-227) -> Matrix(1,-2,2,-5) Matrix(129,-80,208,-129) -> Matrix(-1,8,0,1) (8/13,5/8) -> (4/1,1/0) Matrix(31,-20,48,-31) -> Matrix(1,2,0,-1) (5/8,2/3) -> (-1/1,1/0) Matrix(61,-42,16,-11) -> Matrix(1,2,0,1) 1/0 Matrix(935,-676,574,-415) -> Matrix(1,2,4,7) Matrix(301,-218,272,-197) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(241,-176,330,-241) -> Matrix(5,6,-4,-5) (8/11,11/15) -> (-3/2,-1/1) Matrix(89,-66,120,-89) -> Matrix(-1,0,2,1) (11/15,3/4) -> (-1/1,0/1) Matrix(1207,-924,354,-271) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(1177,-904,720,-553) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(235,-182,102,-79) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(117,-92,14,-11) -> Matrix(1,-2,0,1) 1/0 Matrix(373,-304,200,-163) -> Matrix(1,0,0,1) Matrix(999,-820,586,-481) -> Matrix(1,0,2,1) 0/1 Matrix(1081,-896,298,-247) -> Matrix(1,0,2,1) 0/1 Matrix(85,-72,98,-83) -> Matrix(1,-2,0,1) 1/0 Matrix(193,-170,42,-37) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(269,-304,146,-165) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(97,-112,84,-97) -> Matrix(-1,0,4,1) (8/7,7/6) -> (-1/2,0/1) Matrix(71,-84,60,-71) -> Matrix(1,0,0,-1) (7/6,6/5) -> (0/1,1/0) Matrix(163,-202,46,-57) -> Matrix(1,0,0,1) Matrix(413,-524,160,-203) -> Matrix(1,2,0,1) 1/0 Matrix(297,-380,68,-87) -> Matrix(1,-2,0,1) 1/0 Matrix(89,-120,66,-89) -> Matrix(3,4,-2,-3) (4/3,15/11) -> (-2/1,-1/1) Matrix(241,-330,176,-241) -> Matrix(11,10,-12,-11) (15/11,11/8) -> (-1/1,-5/6) Matrix(241,-332,98,-135) -> Matrix(5,4,6,5) Matrix(217,-302,120,-167) -> Matrix(3,2,-2,-1) -1/1 Matrix(301,-428,64,-91) -> Matrix(7,4,-2,-1) Matrix(213,-308,74,-107) -> Matrix(3,2,-2,-1) -1/1 Matrix(487,-710,190,-277) -> Matrix(1,0,2,1) 0/1 Matrix(81,-128,50,-79) -> Matrix(1,0,6,1) 0/1 Matrix(12641,-20640,7742,-12641) -> Matrix(5,-2,12,-5) (80/49,129/79) -> (1/3,1/2) Matrix(7741,-12642,4740,-7741) -> Matrix(3,-2,4,-3) (129/79,49/30) -> (1/2,1/1) Matrix(367,-622,154,-261) -> Matrix(1,0,0,1) Matrix(1347,-2294,394,-671) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(307,-524,58,-99) -> Matrix(3,-2,-2,1) Matrix(133,-230,48,-83) -> Matrix(1,-2,0,1) 1/0 Matrix(169,-298,38,-67) -> Matrix(1,-2,0,1) 1/0 Matrix(449,-800,252,-449) -> Matrix(1,2,0,-1) (16/9,25/14) -> (-1/1,1/0) Matrix(951,-1700,532,-951) -> Matrix(1,4,0,-1) (25/14,34/19) -> (-2/1,1/0) Matrix(409,-734,112,-201) -> Matrix(1,2,2,3) Matrix(221,-404,64,-117) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(821,-1518,192,-355) -> Matrix(1,-6,0,1) 1/0 Matrix(271,-510,144,-271) -> Matrix(1,2,0,-1) (15/8,17/9) -> (-1/1,1/0) Matrix(35,-68,18,-35) -> Matrix(-1,0,2,1) (17/9,2/1) -> (-1/1,0/1) Matrix(17,-36,8,-17) -> Matrix(-1,0,2,1) (2/1,9/4) -> (-1/1,0/1) Matrix(127,-288,56,-127) -> Matrix(1,0,12,-1) (9/4,16/7) -> (0/1,1/6) Matrix(233,-548,54,-127) -> Matrix(9,-4,-2,1) Matrix(1979,-4730,828,-1979) -> Matrix(-1,0,2,1) (43/18,55/23) -> (-1/1,0/1) Matrix(551,-1320,230,-551) -> Matrix(1,0,4,-1) (55/23,12/5) -> (0/1,1/2) Matrix(213,-514,46,-111) -> Matrix(5,-2,-2,1) Matrix(905,-2318,212,-543) -> Matrix(1,-8,0,1) 1/0 Matrix(159,-412,22,-57) -> Matrix(1,0,0,1) Matrix(113,-304,42,-113) -> Matrix(-1,4,0,1) (8/3,19/7) -> (2/1,1/0) Matrix(153,-418,56,-153) -> Matrix(1,6,0,-1) (19/7,11/4) -> (-3/1,1/0) Matrix(61,-200,18,-59) -> Matrix(1,0,2,1) 0/1 Matrix(193,-690,40,-143) -> Matrix(3,2,-2,-1) -1/1 Matrix(41,-168,10,-41) -> Matrix(-1,2,0,1) (4/1,21/5) -> (1/1,1/0) Matrix(169,-714,40,-169) -> Matrix(1,18,0,-1) (21/5,17/4) -> (-9/1,1/0) Matrix(343,-1634,72,-343) -> Matrix(13,28,-6,-13) (19/4,43/9) -> (-7/3,-2/1) Matrix(431,-2064,90,-431) -> Matrix(15,28,-8,-15) (43/9,24/5) -> (-2/1,-7/4) Matrix(65,-352,12,-65) -> Matrix(5,6,-4,-5) (16/3,11/2) -> (-3/2,-1/1) Matrix(23,-132,4,-23) -> Matrix(-1,0,2,1) (11/2,6/1) -> (-1/1,0/1) Matrix(91,-690,12,-91) -> Matrix(-1,6,0,1) (15/2,23/3) -> (3/1,1/0) Matrix(47,-368,6,-47) -> Matrix(1,6,0,-1) (23/3,8/1) -> (-3/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.