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: 80 Genus: 57 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -4/9 -2/5 -3/8 -1/3 -2/7 -1/4 -3/13 -4/19 -1/7 -2/17 0/1 1/9 2/13 1/5 1/4 8/27 7/23 1/3 4/11 3/7 1/2 7/13 11/19 2/3 5/7 4/5 7/8 1/1 8/7 5/4 14/11 17/13 7/5 3/2 11/7 46/29 5/3 19/11 16/9 9/5 2/1 31/14 7/3 17/7 5/2 28/11 151/59 18/7 13/5 76/29 8/3 11/4 20/7 3/1 16/5 23/7 10/3 31/9 7/2 47/13 11/3 4/1 22/5 9/2 41/9 14/3 24/5 5/1 21/4 16/3 38/7 11/2 6/1 13/2 20/3 7/1 8/1 9/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 0/1 -1/2 0/1 1/1 -7/15 1/2 -6/13 1/1 1/0 -5/11 1/1 -9/20 0/1 1/0 -4/9 1/1 -15/34 3/2 2/1 -11/25 1/0 -7/16 0/1 -3/7 1/0 -8/19 1/1 2/1 -13/31 2/1 -18/43 1/1 3/1 -23/55 1/0 -5/12 0/1 1/0 -12/29 0/1 1/0 -7/17 1/1 -16/39 1/1 1/0 -9/22 0/1 1/1 -2/5 0/1 1/1 1/0 -11/28 0/1 1/1 -9/23 1/0 -7/18 2/1 1/0 -12/31 -1/1 1/0 -17/44 0/1 -5/13 1/0 -8/21 1/1 3/2 -11/29 2/1 -14/37 3/1 1/0 -3/8 1/0 -13/35 1/0 -10/27 0/1 1/2 -7/19 1/1 -4/11 3/1 1/0 -13/36 -6/1 1/0 -9/25 1/0 -5/14 0/1 -11/31 1/1 -6/17 1/1 2/1 -1/3 1/0 -6/19 -3/1 1/0 -5/16 -2/1 1/0 -9/29 -1/1 -4/13 -1/1 0/1 1/0 -3/10 -2/1 1/0 -8/27 -1/1 1/0 -5/17 -1/1 -2/7 -1/1 1/1 -7/25 -1/1 -5/18 -2/1 -1/1 -8/29 -1/1 -1/2 0/1 -11/40 -1/1 0/1 -14/51 -1/1 1/0 -3/11 -1/2 -13/48 -1/2 -10/37 -1/2 -1/3 0/1 -7/26 -1/4 0/1 -4/15 0/1 1/1 -5/19 1/0 -1/4 0/1 -5/21 1/0 -4/17 -1/1 -1/2 -3/13 0/1 -8/35 0/1 1/3 1/2 -5/22 0/1 1/3 -7/31 1/1 -2/9 1/1 1/0 -5/23 -1/1 -3/14 -1/2 0/1 -4/19 0/1 -5/24 0/1 1/2 -1/5 1/0 -4/21 -1/4 0/1 -3/16 0/1 1/3 -5/27 1/2 -2/11 0/1 1/1 1/0 -1/6 0/1 -3/19 1/0 -2/13 0/1 1/1 -1/7 0/1 -1/8 0/1 1/0 -2/17 0/1 -1/9 1/0 0/1 0/1 1/0 1/9 0/1 1/8 0/1 1/7 1/0 2/13 0/1 1/6 0/1 1/0 3/17 0/1 2/11 1/1 1/0 1/5 0/1 3/14 1/1 2/1 8/37 1/0 5/23 1/0 2/9 -1/1 0/1 1/4 0/1 5/19 1/1 9/34 2/1 3/1 4/15 1/1 1/0 3/11 1/0 5/18 -2/1 1/0 2/7 -1/1 0/1 1/0 5/17 -1/2 13/44 0/1 21/71 -1/2 8/27 -1/1 -1/3 11/37 0/1 3/10 -1/3 0/1 7/23 0/1 11/36 0/1 1/11 4/13 0/1 1/4 9/29 1/2 5/16 0/1 1/3 1/0 4/11 0/1 7/19 1/4 10/27 1/3 1/2 13/35 0/1 3/8 0/1 1/2 2/5 -1/1 1/0 5/12 -1/3 0/1 18/43 -1/2 0/1 13/31 -1/2 21/50 -1/4 0/1 8/19 -1/2 -1/3 0/1 3/7 0/1 10/23 0/1 1/4 1/3 7/16 0/1 1/2 11/25 0/1 4/9 1/2 1/1 5/11 1/0 1/2 0/1 8/15 1/2 1/1 7/13 1/1 6/11 0/1 1/0 5/9 1/0 19/34 -4/1 1/0 14/25 -2/1 -1/1 1/0 9/16 0/1 4/7 -1/1 0/1 11/19 0/1 18/31 0/1 1/9 7/12 0/1 1/4 10/17 0/1 1/3 1/2 3/5 1/2 14/23 1/1 1/0 11/18 0/1 1/1 19/31 0/1 27/44 0/1 1/2 8/13 0/1 1/2 1/1 21/34 2/3 34/55 2/3 1/1 13/21 3/4 5/8 1/1 2/1 2/3 -1/1 1/1 7/10 1/1 2/1 12/17 0/1 1/1 17/24 0/1 1/0 5/7 1/1 18/25 2/1 1/0 13/18 1/1 2/1 34/47 1/1 3/2 2/1 21/29 2/1 29/40 2/1 8/11 1/1 1/0 11/15 3/2 25/34 1/1 2/1 14/19 1/1 3/2 2/1 17/23 2/1 3/4 2/1 1/0 13/17 1/0 10/13 -3/1 1/0 17/22 -2/1 7/9 1/0 25/32 0/1 18/23 -1/1 1/0 11/14 0/1 4/5 0/1 1/1 1/0 17/21 1/2 13/16 0/1 1/1 9/11 1/1 5/6 2/1 1/0 11/13 2/1 6/7 3/1 1/0 13/15 1/0 7/8 1/0 1/1 1/0 8/7 1/0 15/13 1/0 7/6 -4/1 -3/1 20/17 -3/1 1/0 13/11 -2/1 6/5 -2/1 -1/1 11/9 -1/1 5/4 0/1 19/15 1/2 33/26 0/1 1/1 14/11 1/1 37/29 2/1 23/18 2/1 1/0 9/7 1/0 31/24 2/1 22/17 3/1 4/1 1/0 13/10 6/1 1/0 17/13 1/0 21/16 -12/1 1/0 4/3 -3/1 1/0 11/8 -2/1 -3/2 29/21 -1/1 18/13 -2/1 -1/1 43/31 -3/2 25/18 -4/3 -1/1 7/5 -1/1 24/17 -1/1 -1/2 41/29 0/1 17/12 -1/1 0/1 44/31 -1/1 27/19 -1/2 10/7 -1/2 0/1 33/23 1/2 23/16 0/1 59/41 0/1 36/25 0/1 1/0 13/9 1/0 16/11 0/1 1/1 1/0 3/2 1/0 20/13 -2/1 -1/1 1/0 37/24 -2/1 -1/1 17/11 1/0 31/20 -2/1 14/9 -3/1 1/0 53/34 -2/1 39/25 -5/2 25/16 -2/1 1/0 61/39 -2/1 36/23 -2/1 1/0 47/30 -3/1 -2/1 11/7 -2/1 30/19 -2/1 -1/1 49/31 -1/1 19/12 -2/1 -1/1 46/29 -1/1 27/17 1/0 8/5 -3/2 -1/1 29/18 -1/1 -6/7 21/13 -1/2 13/8 0/1 31/19 -1/1 49/30 -1/2 0/1 18/11 -1/1 0/1 23/14 -1/2 0/1 28/17 0/1 5/3 1/0 22/13 -1/1 1/1 17/10 0/1 29/17 1/0 12/7 1/1 1/0 19/11 1/0 26/15 -5/1 1/0 7/4 -2/1 1/0 30/17 -3/1 1/0 23/13 -2/1 62/35 -3/2 -1/1 39/22 -2/1 -1/1 16/9 -1/1 57/32 -1/1 0/1 41/23 -1/2 25/14 0/1 9/5 1/0 2/1 -1/1 0/1 1/0 11/5 1/0 42/19 -2/1 1/0 31/14 -2/1 51/23 -3/2 20/9 -2/1 -1/1 9/4 -1/1 0/1 25/11 -2/1 66/29 -1/1 41/18 -2/1 -1/1 16/7 -1/1 1/0 7/3 -1/1 26/11 -1/1 -1/2 45/19 1/0 64/27 -1/1 0/1 83/35 -1/2 19/8 0/1 31/13 1/0 74/31 -1/1 43/18 -1/1 0/1 12/5 0/1 1/0 41/17 1/0 29/12 -2/1 1/0 17/7 -1/1 39/16 0/1 22/9 -1/1 0/1 5/2 0/1 1/0 28/11 -3/1 -2/1 1/0 51/20 -2/1 1/0 23/9 1/0 87/34 -4/1 -3/1 151/59 -3/1 64/25 -3/1 -2/1 41/16 -2/1 18/7 -3/1 -1/1 49/19 1/0 31/12 -2/1 -1/1 44/17 -2/1 1/0 57/22 -2/1 1/0 13/5 -2/1 34/13 -1/1 1/0 55/21 -3/2 76/29 -1/1 21/8 -2/1 -1/1 29/11 -1/1 8/3 -2/1 -1/1 19/7 -3/2 11/4 -1/1 25/9 -3/4 14/5 -1/1 -1/2 17/6 -1/2 0/1 20/7 -1/1 0/1 1/0 23/8 -1/1 0/1 3/1 1/0 25/8 -2/1 22/7 -2/1 -1/1 19/6 -2/1 16/5 -3/2 -4/3 -1/1 13/4 -6/5 -1/1 23/7 -1/1 33/10 -1/1 -12/13 10/3 -1/1 -3/4 17/5 -1/2 58/17 0/1 41/12 0/1 1/0 24/7 -1/1 0/1 31/9 -1/1 7/2 0/1 39/11 0/1 32/9 1/1 1/0 57/16 2/1 3/1 25/7 1/0 118/33 -2/1 -1/1 211/59 -1/1 93/26 -1/1 0/1 68/19 -1/1 0/1 1/0 43/12 1/0 18/5 1/1 1/0 47/13 1/0 29/8 -4/1 1/0 11/3 1/0 4/1 -1/1 13/3 -1/2 61/14 0/1 48/11 -1/2 0/1 35/8 -1/1 0/1 22/5 -1/1 -1/2 0/1 9/2 0/1 1/0 50/11 0/1 1/0 41/9 0/1 32/7 0/1 1/1 1/0 55/12 -2/1 1/0 23/5 1/0 37/8 1/0 51/11 1/0 14/3 -2/1 1/0 19/4 -2/1 1/0 24/5 -2/1 -1/1 5/1 -1/1 26/5 -1/1 -2/3 21/4 -2/3 16/3 -1/1 -1/2 43/8 -2/3 27/5 -1/2 38/7 -1/2 11/2 -1/3 0/1 6/1 -1/1 1/0 19/3 -3/2 13/2 -1/1 33/5 -5/6 20/3 -1/1 -3/4 7/1 -1/2 8/1 -1/1 0/1 1/0 9/1 -1/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(229,108,282,133) (-1/2,-7/15) -> (17/21,13/16) Hyperbolic Matrix(337,156,54,25) (-7/15,-6/13) -> (6/1,19/3) Hyperbolic Matrix(113,52,-502,-231) (-6/13,-5/11) -> (-7/31,-2/9) Hyperbolic Matrix(659,298,272,123) (-5/11,-9/20) -> (29/12,17/7) Hyperbolic Matrix(215,96,-486,-217) (-9/20,-4/9) -> (-4/9,-15/34) Parabolic Matrix(967,426,2304,1015) (-15/34,-11/25) -> (13/31,21/50) Hyperbolic Matrix(537,236,694,305) (-11/25,-7/16) -> (17/22,7/9) Hyperbolic Matrix(427,186,264,115) (-7/16,-3/7) -> (21/13,13/8) Hyperbolic Matrix(417,176,154,65) (-3/7,-8/19) -> (8/3,19/7) Hyperbolic Matrix(1139,478,722,303) (-8/19,-13/31) -> (11/7,30/19) Hyperbolic Matrix(721,302,2428,1017) (-13/31,-18/43) -> (8/27,11/37) Hyperbolic Matrix(1343,562,4538,1899) (-18/43,-23/55) -> (21/71,8/27) Hyperbolic Matrix(3301,1380,720,301) (-23/55,-5/12) -> (55/12,23/5) Hyperbolic Matrix(719,298,152,63) (-5/12,-12/29) -> (14/3,19/4) Hyperbolic Matrix(305,126,564,233) (-12/29,-7/17) -> (7/13,6/11) Hyperbolic Matrix(409,168,762,313) (-7/17,-16/39) -> (8/15,7/13) Hyperbolic Matrix(713,292,608,249) (-16/39,-9/22) -> (7/6,20/17) Hyperbolic Matrix(99,40,-250,-101) (-9/22,-2/5) -> (-2/5,-11/28) Parabolic Matrix(1779,698,1282,503) (-11/28,-9/23) -> (43/31,25/18) Hyperbolic Matrix(691,270,540,211) (-9/23,-7/18) -> (23/18,9/7) Hyperbolic Matrix(685,266,394,153) (-7/18,-12/31) -> (26/15,7/4) Hyperbolic Matrix(1567,606,2004,775) (-12/31,-17/44) -> (25/32,18/23) Hyperbolic Matrix(389,150,1320,509) (-17/44,-5/13) -> (5/17,13/44) Hyperbolic Matrix(487,186,144,55) (-5/13,-8/21) -> (10/3,17/5) Hyperbolic Matrix(1259,478,482,183) (-8/21,-11/29) -> (13/5,34/13) Hyperbolic Matrix(771,292,2078,787) (-11/29,-14/37) -> (10/27,13/35) Hyperbolic Matrix(1735,656,484,183) (-14/37,-3/8) -> (43/12,18/5) Hyperbolic Matrix(479,178,-1768,-657) (-3/8,-13/35) -> (-3/11,-13/48) Hyperbolic Matrix(383,142,1238,459) (-13/35,-10/27) -> (4/13,9/29) Hyperbolic Matrix(477,176,664,245) (-10/27,-7/19) -> (5/7,18/25) Hyperbolic Matrix(93,34,-424,-155) (-7/19,-4/11) -> (-2/9,-5/23) Hyperbolic Matrix(375,136,284,103) (-4/11,-13/36) -> (21/16,4/3) Hyperbolic Matrix(655,236,1174,423) (-13/36,-9/25) -> (5/9,19/34) Hyperbolic Matrix(751,270,420,151) (-9/25,-5/14) -> (25/14,9/5) Hyperbolic Matrix(651,232,188,67) (-5/14,-11/31) -> (31/9,7/2) Hyperbolic Matrix(1763,624,1116,395) (-11/31,-6/17) -> (30/19,49/31) Hyperbolic Matrix(91,32,418,147) (-6/17,-1/3) -> (5/23,2/9) Hyperbolic Matrix(265,84,306,97) (-1/3,-6/19) -> (6/7,13/15) Hyperbolic Matrix(613,192,348,109) (-6/19,-5/16) -> (7/4,30/17) Hyperbolic Matrix(1917,596,1174,365) (-5/16,-9/29) -> (31/19,49/30) Hyperbolic Matrix(349,108,42,13) (-9/29,-4/13) -> (8/1,9/1) Hyperbolic Matrix(85,26,304,93) (-4/13,-3/10) -> (5/18,2/7) Hyperbolic Matrix(599,178,212,63) (-3/10,-8/27) -> (14/5,17/6) Hyperbolic Matrix(597,176,424,125) (-8/27,-5/17) -> (7/5,24/17) Hyperbolic Matrix(83,24,-294,-85) (-5/17,-2/7) -> (-2/7,-7/25) Parabolic Matrix(751,210,540,151) (-7/25,-5/18) -> (25/18,7/5) Hyperbolic Matrix(665,184,206,57) (-5/18,-8/29) -> (16/5,13/4) Hyperbolic Matrix(1737,478,2402,661) (-8/29,-11/40) -> (13/18,34/47) Hyperbolic Matrix(4469,1228,2522,693) (-11/40,-14/51) -> (62/35,39/22) Hyperbolic Matrix(1903,522,288,79) (-14/51,-3/11) -> (33/5,20/3) Hyperbolic Matrix(4855,1314,1356,367) (-13/48,-10/37) -> (68/19,43/12) Hyperbolic Matrix(985,266,2344,633) (-10/37,-7/26) -> (21/50,8/19) Hyperbolic Matrix(573,154,986,265) (-7/26,-4/15) -> (18/31,7/12) Hyperbolic Matrix(83,22,-532,-141) (-4/15,-5/19) -> (-3/19,-2/13) Hyperbolic Matrix(485,126,204,53) (-5/19,-1/4) -> (19/8,31/13) Hyperbolic Matrix(553,132,708,169) (-1/4,-5/21) -> (7/9,25/32) Hyperbolic Matrix(1649,390,630,149) (-5/21,-4/17) -> (34/13,55/21) Hyperbolic Matrix(77,18,432,101) (-4/17,-3/13) -> (3/17,2/11) Hyperbolic Matrix(777,178,1052,241) (-3/13,-8/35) -> (14/19,17/23) Hyperbolic Matrix(1709,390,390,89) (-8/35,-5/22) -> (35/8,22/5) Hyperbolic Matrix(389,88,1472,333) (-5/22,-7/31) -> (5/19,9/34) Hyperbolic Matrix(461,100,650,141) (-5/23,-3/14) -> (17/24,5/7) Hyperbolic Matrix(151,32,-722,-153) (-3/14,-4/19) -> (-4/19,-5/24) Parabolic Matrix(1061,220,680,141) (-5/24,-1/5) -> (39/25,25/16) Hyperbolic Matrix(743,142,518,99) (-1/5,-4/21) -> (10/7,33/23) Hyperbolic Matrix(295,56,964,183) (-4/21,-3/16) -> (11/36,4/13) Hyperbolic Matrix(1621,302,628,117) (-3/16,-5/27) -> (49/19,31/12) Hyperbolic Matrix(295,54,366,67) (-5/27,-2/11) -> (4/5,17/21) Hyperbolic Matrix(145,26,184,33) (-2/11,-1/6) -> (11/14,4/5) Hyperbolic Matrix(643,102,498,79) (-1/6,-3/19) -> (9/7,31/24) Hyperbolic Matrix(211,32,178,27) (-2/13,-1/7) -> (13/11,6/5) Hyperbolic Matrix(137,18,312,41) (-1/7,-1/8) -> (7/16,11/25) Hyperbolic Matrix(1161,140,340,41) (-1/8,-2/17) -> (58/17,41/12) Hyperbolic Matrix(811,92,238,27) (-2/17,-1/9) -> (17/5,58/17) Hyperbolic Matrix(337,36,234,25) (-1/9,0/1) -> (36/25,13/9) Hyperbolic Matrix(385,-36,246,-23) (0/1,1/9) -> (61/39,36/23) Hyperbolic Matrix(375,-46,106,-13) (1/9,1/8) -> (7/2,39/11) Hyperbolic Matrix(107,-14,344,-45) (1/8,1/7) -> (9/29,5/16) Hyperbolic Matrix(261,-38,158,-23) (1/7,2/13) -> (28/17,5/3) Hyperbolic Matrix(467,-74,284,-45) (2/13,1/6) -> (23/14,28/17) Hyperbolic Matrix(153,-26,206,-35) (1/6,3/17) -> (17/23,3/4) Hyperbolic Matrix(151,-28,178,-33) (2/11,1/5) -> (11/13,6/7) Hyperbolic Matrix(395,-84,174,-37) (1/5,3/14) -> (9/4,25/11) Hyperbolic Matrix(939,-202,172,-37) (3/14,8/37) -> (38/7,11/2) Hyperbolic Matrix(1873,-406,346,-75) (8/37,5/23) -> (27/5,38/7) Hyperbolic Matrix(97,-22,172,-39) (2/9,1/4) -> (9/16,4/7) Hyperbolic Matrix(809,-212,332,-87) (1/4,5/19) -> (17/7,39/16) Hyperbolic Matrix(1943,-516,546,-145) (9/34,4/15) -> (32/9,57/16) Hyperbolic Matrix(567,-152,332,-89) (4/15,3/11) -> (29/17,12/7) Hyperbolic Matrix(517,-142,142,-39) (3/11,5/18) -> (29/8,11/3) Hyperbolic Matrix(185,-54,24,-7) (2/7,5/17) -> (7/1,8/1) Hyperbolic Matrix(5001,-1478,2108,-623) (13/44,21/71) -> (83/35,19/8) Hyperbolic Matrix(1849,-550,1180,-351) (11/37,3/10) -> (47/30,11/7) Hyperbolic Matrix(323,-98,1058,-321) (3/10,7/23) -> (7/23,11/36) Parabolic Matrix(731,-230,410,-129) (5/16,1/3) -> (41/23,25/14) Hyperbolic Matrix(89,-32,242,-87) (1/3,4/11) -> (4/11,7/19) Parabolic Matrix(1709,-632,722,-267) (7/19,10/27) -> (26/11,45/19) Hyperbolic Matrix(2099,-780,810,-301) (13/35,3/8) -> (57/22,13/5) Hyperbolic Matrix(87,-34,64,-25) (3/8,2/5) -> (4/3,11/8) Hyperbolic Matrix(127,-52,22,-9) (2/5,5/12) -> (11/2,6/1) Hyperbolic Matrix(2453,-1026,1566,-655) (5/12,18/43) -> (36/23,47/30) Hyperbolic Matrix(1775,-744,804,-337) (18/43,13/31) -> (11/5,42/19) Hyperbolic Matrix(127,-54,294,-125) (8/19,3/7) -> (3/7,10/23) Parabolic Matrix(711,-310,250,-109) (10/23,7/16) -> (17/6,20/7) Hyperbolic Matrix(957,-422,542,-239) (11/25,4/9) -> (30/17,23/13) Hyperbolic Matrix(331,-148,208,-93) (4/9,5/11) -> (27/17,8/5) Hyperbolic Matrix(245,-114,144,-67) (5/11,1/2) -> (17/10,29/17) Hyperbolic Matrix(823,-438,528,-281) (1/2,8/15) -> (14/9,53/34) Hyperbolic Matrix(387,-212,272,-149) (6/11,5/9) -> (27/19,10/7) Hyperbolic Matrix(2463,-1378,538,-301) (19/34,14/25) -> (32/7,55/12) Hyperbolic Matrix(731,-410,230,-129) (14/25,9/16) -> (19/6,16/5) Hyperbolic Matrix(419,-242,722,-417) (4/7,11/19) -> (11/19,18/31) Parabolic Matrix(417,-244,94,-55) (7/12,10/17) -> (22/5,9/2) Hyperbolic Matrix(301,-178,208,-123) (10/17,3/5) -> (13/9,16/11) Hyperbolic Matrix(261,-158,38,-23) (3/5,14/23) -> (20/3,7/1) Hyperbolic Matrix(1231,-750,540,-329) (14/23,11/18) -> (41/18,16/7) Hyperbolic Matrix(1265,-774,894,-547) (11/18,19/31) -> (41/29,17/12) Hyperbolic Matrix(3459,-2122,2212,-1357) (19/31,27/44) -> (25/16,61/39) Hyperbolic Matrix(1895,-1164,744,-457) (27/44,8/13) -> (28/11,51/20) Hyperbolic Matrix(1151,-710,890,-549) (8/13,21/34) -> (31/24,22/17) Hyperbolic Matrix(2039,-1260,390,-241) (21/34,34/55) -> (26/5,21/4) Hyperbolic Matrix(3819,-2362,1612,-997) (34/55,13/21) -> (45/19,64/27) Hyperbolic Matrix(777,-482,482,-299) (13/21,5/8) -> (29/18,21/13) Hyperbolic Matrix(37,-24,54,-35) (5/8,2/3) -> (2/3,7/10) Parabolic Matrix(353,-248,158,-111) (7/10,12/17) -> (20/9,9/4) Hyperbolic Matrix(1265,-894,774,-547) (12/17,17/24) -> (49/30,18/11) Hyperbolic Matrix(1291,-930,540,-389) (18/25,13/18) -> (43/18,12/5) Hyperbolic Matrix(2855,-2066,626,-453) (34/47,21/29) -> (41/9,32/7) Hyperbolic Matrix(3027,-2194,2104,-1525) (21/29,29/40) -> (23/16,59/41) Hyperbolic Matrix(1113,-808,208,-151) (29/40,8/11) -> (16/3,43/8) Hyperbolic Matrix(485,-354,174,-127) (8/11,11/15) -> (25/9,14/5) Hyperbolic Matrix(2249,-1652,1262,-927) (11/15,25/34) -> (57/32,41/23) Hyperbolic Matrix(1383,-1018,898,-661) (25/34,14/19) -> (20/13,37/24) Hyperbolic Matrix(681,-518,188,-143) (3/4,13/17) -> (47/13,29/8) Hyperbolic Matrix(917,-704,254,-195) (13/17,10/13) -> (18/5,47/13) Hyperbolic Matrix(711,-548,458,-353) (10/13,17/22) -> (31/20,14/9) Hyperbolic Matrix(707,-554,134,-105) (18/23,11/14) -> (21/4,16/3) Hyperbolic Matrix(993,-808,628,-511) (13/16,9/11) -> (49/31,19/12) Hyperbolic Matrix(295,-244,214,-177) (9/11,5/6) -> (11/8,29/21) Hyperbolic Matrix(521,-438,408,-343) (5/6,11/13) -> (37/29,23/18) Hyperbolic Matrix(963,-838,208,-181) (13/15,7/8) -> (37/8,51/11) Hyperbolic Matrix(221,-198,48,-43) (7/8,1/1) -> (23/5,37/8) Hyperbolic Matrix(113,-128,98,-111) (1/1,8/7) -> (8/7,15/13) Parabolic Matrix(891,-1030,250,-289) (15/13,7/6) -> (57/16,25/7) Hyperbolic Matrix(1073,-1266,606,-715) (20/17,13/11) -> (23/13,62/35) Hyperbolic Matrix(217,-262,82,-99) (6/5,11/9) -> (29/11,8/3) Hyperbolic Matrix(241,-298,148,-183) (11/9,5/4) -> (13/8,31/19) Hyperbolic Matrix(477,-602,332,-419) (5/4,19/15) -> (33/23,23/16) Hyperbolic Matrix(423,-536,146,-185) (19/15,33/26) -> (23/8,3/1) Hyperbolic Matrix(2167,-2752,952,-1209) (33/26,14/11) -> (66/29,41/18) Hyperbolic Matrix(2189,-2792,962,-1227) (14/11,37/29) -> (25/11,66/29) Hyperbolic Matrix(365,-474,144,-187) (22/17,13/10) -> (5/2,28/11) Hyperbolic Matrix(443,-578,338,-441) (13/10,17/13) -> (17/13,21/16) Parabolic Matrix(907,-1254,264,-365) (29/21,18/13) -> (24/7,31/9) Hyperbolic Matrix(1283,-1778,578,-801) (18/13,43/31) -> (51/23,20/9) Hyperbolic Matrix(1591,-2248,448,-633) (24/17,41/29) -> (39/11,32/9) Hyperbolic Matrix(1563,-2216,596,-845) (17/12,44/31) -> (76/29,21/8) Hyperbolic Matrix(3149,-4472,1202,-1707) (44/31,27/19) -> (55/21,76/29) Hyperbolic Matrix(3075,-4426,676,-973) (59/41,36/25) -> (50/11,41/9) Hyperbolic Matrix(73,-108,48,-71) (16/11,3/2) -> (3/2,20/13) Parabolic Matrix(1509,-2330,590,-911) (37/24,17/11) -> (23/9,87/34) Hyperbolic Matrix(1013,-1568,188,-291) (17/11,31/20) -> (43/8,27/5) Hyperbolic Matrix(727,-1134,234,-365) (53/34,39/25) -> (3/1,25/8) Hyperbolic Matrix(2135,-3384,894,-1417) (19/12,46/29) -> (74/31,43/18) Hyperbolic Matrix(2157,-3424,904,-1435) (46/29,27/17) -> (31/13,74/31) Hyperbolic Matrix(345,-554,104,-167) (8/5,29/18) -> (33/10,10/3) Hyperbolic Matrix(545,-894,114,-187) (18/11,23/14) -> (19/4,24/5) Hyperbolic Matrix(691,-1168,268,-453) (5/3,22/13) -> (18/7,49/19) Hyperbolic Matrix(713,-1208,278,-471) (22/13,17/10) -> (41/16,18/7) Hyperbolic Matrix(419,-722,242,-417) (12/7,19/11) -> (19/11,26/15) Parabolic Matrix(865,-1536,486,-863) (39/22,16/9) -> (16/9,57/32) Parabolic Matrix(21,-40,10,-19) (9/5,2/1) -> (2/1,11/5) Parabolic Matrix(1831,-4050,420,-929) (42/19,31/14) -> (61/14,48/11) Hyperbolic Matrix(1585,-3514,364,-807) (31/14,51/23) -> (13/3,61/14) Hyperbolic Matrix(127,-294,54,-125) (16/7,7/3) -> (7/3,26/11) Parabolic Matrix(4805,-11394,1344,-3187) (64/27,83/35) -> (25/7,118/33) Hyperbolic Matrix(493,-1186,106,-255) (12/5,41/17) -> (51/11,14/3) Hyperbolic Matrix(1143,-2758,448,-1081) (41/17,29/12) -> (51/20,23/9) Hyperbolic Matrix(523,-1276,166,-405) (39/16,22/9) -> (22/7,19/6) Hyperbolic Matrix(417,-1022,122,-299) (22/9,5/2) -> (41/12,24/7) Hyperbolic Matrix(12661,-32400,3540,-9059) (87/34,151/59) -> (211/59,93/26) Hyperbolic Matrix(12237,-31322,3422,-8759) (151/59,64/25) -> (118/33,211/59) Hyperbolic Matrix(977,-2502,312,-799) (64/25,41/16) -> (25/8,22/7) Hyperbolic Matrix(1171,-3028,268,-693) (31/12,44/17) -> (48/11,35/8) Hyperbolic Matrix(1253,-3246,276,-715) (44/17,57/22) -> (9/2,50/11) Hyperbolic Matrix(83,-218,8,-21) (21/8,29/11) -> (9/1,1/0) Hyperbolic Matrix(177,-484,64,-175) (19/7,11/4) -> (11/4,25/9) Parabolic Matrix(1195,-3424,334,-957) (20/7,23/8) -> (93/26,68/19) Hyperbolic Matrix(323,-1058,98,-321) (13/4,23/7) -> (23/7,33/10) Parabolic Matrix(25,-96,6,-23) (11/3,4/1) -> (4/1,13/3) Parabolic Matrix(51,-250,10,-49) (24/5,5/1) -> (5/1,26/5) Parabolic Matrix(105,-676,16,-103) (19/3,13/2) -> (13/2,33/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,2,1) Matrix(229,108,282,133) -> Matrix(1,0,0,1) Matrix(337,156,54,25) -> Matrix(1,-2,0,1) Matrix(113,52,-502,-231) -> Matrix(1,0,0,1) Matrix(659,298,272,123) -> Matrix(1,-2,0,1) Matrix(215,96,-486,-217) -> Matrix(3,-2,2,-1) Matrix(967,426,2304,1015) -> Matrix(1,-2,-2,5) Matrix(537,236,694,305) -> Matrix(1,-2,0,1) Matrix(427,186,264,115) -> Matrix(1,0,-2,1) Matrix(417,176,154,65) -> Matrix(3,-4,-2,3) Matrix(1139,478,722,303) -> Matrix(3,-4,-2,3) Matrix(721,302,2428,1017) -> Matrix(1,-2,-2,5) Matrix(1343,562,4538,1899) -> Matrix(1,-2,-2,5) Matrix(3301,1380,720,301) -> Matrix(1,-2,0,1) Matrix(719,298,152,63) -> Matrix(1,-2,0,1) Matrix(305,126,564,233) -> Matrix(1,0,0,1) Matrix(409,168,762,313) -> Matrix(1,-2,2,-3) Matrix(713,292,608,249) -> Matrix(1,-4,0,1) Matrix(99,40,-250,-101) -> Matrix(1,0,0,1) Matrix(1779,698,1282,503) -> Matrix(3,-4,-2,3) Matrix(691,270,540,211) -> Matrix(1,0,0,1) Matrix(685,266,394,153) -> Matrix(1,-4,0,1) Matrix(1567,606,2004,775) -> Matrix(1,0,0,1) Matrix(389,150,1320,509) -> Matrix(1,0,-2,1) Matrix(487,186,144,55) -> Matrix(1,0,-2,1) Matrix(1259,478,482,183) -> Matrix(3,-4,-2,3) Matrix(771,292,2078,787) -> Matrix(1,-2,2,-3) Matrix(1735,656,484,183) -> Matrix(1,-2,0,1) Matrix(479,178,-1768,-657) -> Matrix(1,0,-2,1) Matrix(383,142,1238,459) -> Matrix(1,0,2,1) Matrix(477,176,664,245) -> Matrix(3,-2,2,-1) Matrix(93,34,-424,-155) -> Matrix(1,-2,0,1) Matrix(375,136,284,103) -> Matrix(1,-6,0,1) Matrix(655,236,1174,423) -> Matrix(1,2,0,1) Matrix(751,270,420,151) -> Matrix(1,0,0,1) Matrix(651,232,188,67) -> Matrix(1,0,-2,1) Matrix(1763,624,1116,395) -> Matrix(3,-4,-2,3) Matrix(91,32,418,147) -> Matrix(1,-2,0,1) Matrix(265,84,306,97) -> Matrix(1,6,0,1) Matrix(613,192,348,109) -> Matrix(1,0,0,1) Matrix(1917,596,1174,365) -> Matrix(1,2,-2,-3) Matrix(349,108,42,13) -> Matrix(1,0,0,1) Matrix(85,26,304,93) -> Matrix(1,0,0,1) Matrix(599,178,212,63) -> Matrix(1,2,-2,-3) Matrix(597,176,424,125) -> Matrix(1,2,-2,-3) Matrix(83,24,-294,-85) -> Matrix(1,0,0,1) Matrix(751,210,540,151) -> Matrix(3,2,-2,-1) Matrix(665,184,206,57) -> Matrix(5,4,-4,-3) Matrix(1737,478,2402,661) -> Matrix(1,2,0,1) Matrix(4469,1228,2522,693) -> Matrix(3,2,-2,-1) Matrix(1903,522,288,79) -> Matrix(3,4,-4,-5) Matrix(4855,1314,1356,367) -> Matrix(1,0,2,1) Matrix(985,266,2344,633) -> Matrix(1,0,0,1) Matrix(573,154,986,265) -> Matrix(1,0,8,1) Matrix(83,22,-532,-141) -> Matrix(1,0,0,1) Matrix(485,126,204,53) -> Matrix(1,0,0,1) Matrix(553,132,708,169) -> Matrix(1,0,0,1) Matrix(1649,390,630,149) -> Matrix(3,2,-2,-1) Matrix(77,18,432,101) -> Matrix(1,0,2,1) Matrix(777,178,1052,241) -> Matrix(7,-2,4,-1) Matrix(1709,390,390,89) -> Matrix(1,0,-4,1) Matrix(389,88,1472,333) -> Matrix(3,-2,2,-1) Matrix(461,100,650,141) -> Matrix(1,0,2,1) Matrix(151,32,-722,-153) -> Matrix(1,0,4,1) Matrix(1061,220,680,141) -> Matrix(5,-2,-2,1) Matrix(743,142,518,99) -> Matrix(1,0,2,1) Matrix(295,56,964,183) -> Matrix(1,0,8,1) Matrix(1621,302,628,117) -> Matrix(5,-2,-2,1) Matrix(295,54,366,67) -> Matrix(1,0,0,1) Matrix(145,26,184,33) -> Matrix(1,0,0,1) Matrix(643,102,498,79) -> Matrix(1,2,0,1) Matrix(211,32,178,27) -> Matrix(1,-2,0,1) Matrix(137,18,312,41) -> Matrix(1,0,2,1) Matrix(1161,140,340,41) -> Matrix(1,0,0,1) Matrix(811,92,238,27) -> Matrix(1,0,-2,1) Matrix(337,36,234,25) -> Matrix(1,0,0,1) Matrix(385,-36,246,-23) -> Matrix(1,-2,0,1) Matrix(375,-46,106,-13) -> Matrix(1,0,0,1) Matrix(107,-14,344,-45) -> Matrix(1,0,2,1) Matrix(261,-38,158,-23) -> Matrix(1,0,0,1) Matrix(467,-74,284,-45) -> Matrix(1,0,-2,1) Matrix(153,-26,206,-35) -> Matrix(1,2,0,1) Matrix(151,-28,178,-33) -> Matrix(1,2,0,1) Matrix(395,-84,174,-37) -> Matrix(1,-2,0,1) Matrix(939,-202,172,-37) -> Matrix(1,-2,-2,5) Matrix(1873,-406,346,-75) -> Matrix(1,4,-2,-7) Matrix(97,-22,172,-39) -> Matrix(1,0,0,1) Matrix(809,-212,332,-87) -> Matrix(1,0,-2,1) Matrix(1943,-516,546,-145) -> Matrix(1,0,0,1) Matrix(567,-152,332,-89) -> Matrix(1,0,0,1) Matrix(517,-142,142,-39) -> Matrix(1,-2,0,1) Matrix(185,-54,24,-7) -> Matrix(1,0,0,1) Matrix(5001,-1478,2108,-623) -> Matrix(1,0,0,1) Matrix(1849,-550,1180,-351) -> Matrix(3,2,-2,-1) Matrix(323,-98,1058,-321) -> Matrix(1,0,14,1) Matrix(731,-230,410,-129) -> Matrix(1,0,-2,1) Matrix(89,-32,242,-87) -> Matrix(1,0,4,1) Matrix(1709,-632,722,-267) -> Matrix(1,0,-4,1) Matrix(2099,-780,810,-301) -> Matrix(5,-2,-2,1) Matrix(87,-34,64,-25) -> Matrix(1,-2,0,1) Matrix(127,-52,22,-9) -> Matrix(1,0,0,1) Matrix(2453,-1026,1566,-655) -> Matrix(3,2,-2,-1) Matrix(1775,-744,804,-337) -> Matrix(3,2,-2,-1) Matrix(127,-54,294,-125) -> Matrix(1,0,6,1) Matrix(711,-310,250,-109) -> Matrix(1,0,-4,1) Matrix(957,-422,542,-239) -> Matrix(5,-2,-2,1) Matrix(331,-148,208,-93) -> Matrix(1,-2,0,1) Matrix(245,-114,144,-67) -> Matrix(1,0,0,1) Matrix(823,-438,528,-281) -> Matrix(5,-2,-2,1) Matrix(387,-212,272,-149) -> Matrix(1,0,-2,1) Matrix(2463,-1378,538,-301) -> Matrix(1,2,0,1) Matrix(731,-410,230,-129) -> Matrix(3,2,-2,-1) Matrix(419,-242,722,-417) -> Matrix(1,0,10,1) Matrix(417,-244,94,-55) -> Matrix(1,0,-4,1) Matrix(301,-178,208,-123) -> Matrix(1,0,-2,1) Matrix(261,-158,38,-23) -> Matrix(3,-2,-4,3) Matrix(1231,-750,540,-329) -> Matrix(1,-2,0,1) Matrix(1265,-774,894,-547) -> Matrix(1,0,-2,1) Matrix(3459,-2122,2212,-1357) -> Matrix(5,-2,-2,1) Matrix(1895,-1164,744,-457) -> Matrix(5,-2,-2,1) Matrix(1151,-710,890,-549) -> Matrix(7,-4,2,-1) Matrix(2039,-1260,390,-241) -> Matrix(5,-4,-6,5) Matrix(3819,-2362,1612,-997) -> Matrix(3,-2,-4,3) Matrix(777,-482,482,-299) -> Matrix(5,-4,-6,5) Matrix(37,-24,54,-35) -> Matrix(1,0,0,1) Matrix(353,-248,158,-111) -> Matrix(1,-2,0,1) Matrix(1265,-894,774,-547) -> Matrix(1,0,-2,1) Matrix(1291,-930,540,-389) -> Matrix(1,-2,0,1) Matrix(2855,-2066,626,-453) -> Matrix(1,-2,2,-3) Matrix(3027,-2194,2104,-1525) -> Matrix(1,-2,0,1) Matrix(1113,-808,208,-151) -> Matrix(1,0,-2,1) Matrix(485,-354,174,-127) -> Matrix(1,0,-2,1) Matrix(2249,-1652,1262,-927) -> Matrix(1,-2,0,1) Matrix(1383,-1018,898,-661) -> Matrix(3,-4,-2,3) Matrix(681,-518,188,-143) -> Matrix(1,-6,0,1) Matrix(917,-704,254,-195) -> Matrix(1,4,0,1) Matrix(711,-548,458,-353) -> Matrix(1,0,0,1) Matrix(707,-554,134,-105) -> Matrix(1,2,-2,-3) Matrix(993,-808,628,-511) -> Matrix(1,-2,0,1) Matrix(295,-244,214,-177) -> Matrix(3,-4,-2,3) Matrix(521,-438,408,-343) -> Matrix(1,0,0,1) Matrix(963,-838,208,-181) -> Matrix(1,-10,0,1) Matrix(221,-198,48,-43) -> Matrix(1,0,0,1) Matrix(113,-128,98,-111) -> Matrix(1,-6,0,1) Matrix(891,-1030,250,-289) -> Matrix(1,6,0,1) Matrix(1073,-1266,606,-715) -> Matrix(3,8,-2,-5) Matrix(217,-262,82,-99) -> Matrix(1,0,0,1) Matrix(241,-298,148,-183) -> Matrix(1,0,0,1) Matrix(477,-602,332,-419) -> Matrix(1,0,0,1) Matrix(423,-536,146,-185) -> Matrix(1,0,-2,1) Matrix(2167,-2752,952,-1209) -> Matrix(1,-2,0,1) Matrix(2189,-2792,962,-1227) -> Matrix(3,-4,-2,3) Matrix(365,-474,144,-187) -> Matrix(1,-6,0,1) Matrix(443,-578,338,-441) -> Matrix(1,-18,0,1) Matrix(907,-1254,264,-365) -> Matrix(1,2,-2,-3) Matrix(1283,-1778,578,-801) -> Matrix(1,0,0,1) Matrix(1591,-2248,448,-633) -> Matrix(1,0,2,1) Matrix(1563,-2216,596,-845) -> Matrix(3,2,-2,-1) Matrix(3149,-4472,1202,-1707) -> Matrix(5,4,-4,-3) Matrix(3075,-4426,676,-973) -> Matrix(1,0,0,1) Matrix(73,-108,48,-71) -> Matrix(1,-2,0,1) Matrix(1509,-2330,590,-911) -> Matrix(1,-2,0,1) Matrix(1013,-1568,188,-291) -> Matrix(1,4,-2,-7) Matrix(727,-1134,234,-365) -> Matrix(3,8,-2,-5) Matrix(2135,-3384,894,-1417) -> Matrix(1,2,-2,-3) Matrix(2157,-3424,904,-1435) -> Matrix(1,0,0,1) Matrix(345,-554,104,-167) -> Matrix(5,6,-6,-7) Matrix(545,-894,114,-187) -> Matrix(3,2,-2,-1) Matrix(691,-1168,268,-453) -> Matrix(1,-2,0,1) Matrix(713,-1208,278,-471) -> Matrix(1,-2,0,1) Matrix(419,-722,242,-417) -> Matrix(1,-6,0,1) Matrix(865,-1536,486,-863) -> Matrix(1,2,-2,-3) Matrix(21,-40,10,-19) -> Matrix(1,0,0,1) Matrix(1831,-4050,420,-929) -> Matrix(1,2,-2,-3) Matrix(1585,-3514,364,-807) -> Matrix(1,2,-4,-7) Matrix(127,-294,54,-125) -> Matrix(1,2,-2,-3) Matrix(4805,-11394,1344,-3187) -> Matrix(3,2,-2,-1) Matrix(493,-1186,106,-255) -> Matrix(1,-2,0,1) Matrix(1143,-2758,448,-1081) -> Matrix(1,0,0,1) Matrix(523,-1276,166,-405) -> Matrix(3,2,-2,-1) Matrix(417,-1022,122,-299) -> Matrix(1,0,0,1) Matrix(12661,-32400,3540,-9059) -> Matrix(1,4,-2,-7) Matrix(12237,-31322,3422,-8759) -> Matrix(3,8,-2,-5) Matrix(977,-2502,312,-799) -> Matrix(3,8,-2,-5) Matrix(1171,-3028,268,-693) -> Matrix(1,2,-2,-3) Matrix(1253,-3246,276,-715) -> Matrix(1,2,0,1) Matrix(83,-218,8,-21) -> Matrix(1,2,-2,-3) Matrix(177,-484,64,-175) -> Matrix(5,6,-6,-7) Matrix(1195,-3424,334,-957) -> Matrix(1,0,0,1) Matrix(323,-1058,98,-321) -> Matrix(17,18,-18,-19) Matrix(25,-96,6,-23) -> Matrix(1,2,-2,-3) Matrix(51,-250,10,-49) -> Matrix(3,4,-4,-5) Matrix(105,-676,16,-103) -> Matrix(7,8,-8,-9) 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): 38 Degree of the the map X: 38 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. Imminent integer overflow caused the modular group computation to abort.