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): 1728 Minimal number of generators: 289 Number of equivalence classes of cusps: 80 Genus: 105 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -14/17 -12/17 -35/51 -10/17 -1/2 -8/17 -103/272 -6/17 -5/16 -1/4 -4/17 -31/136 -3/14 -18/85 -4/21 -3/16 -1/6 -2/15 -1/8 -2/17 -1/10 -1/12 0/1 1/11 1/10 1/9 2/17 1/8 1/7 5/34 4/27 2/13 4/25 1/6 4/23 3/17 2/11 1/5 7/34 6/29 4/19 3/14 2/9 23/102 3/13 4/17 1/4 9/34 2/7 5/17 10/33 1/3 6/17 13/34 12/31 2/5 7/17 5/12 15/34 7/15 8/17 1/2 9/17 19/34 10/17 52/85 21/34 11/17 2/3 71/102 12/17 25/34 13/17 79/102 27/34 14/17 29/34 15/17 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/1 -9/10 1/1 -17/19 1/3 -8/9 1/2 1/1 -15/17 1/1 -7/8 1/1 -6/7 3/1 1/0 -29/34 1/0 -23/27 -7/1 -17/20 -1/1 -11/13 -1/1 -16/19 0/1 1/0 -21/25 -1/1 -5/6 1/1 -14/17 1/1 -23/28 1/1 -9/11 1/1 -4/5 2/1 1/0 -27/34 1/0 -23/29 -11/1 -19/24 -5/1 -34/43 -3/1 -2/1 -15/19 -1/1 -26/33 -1/1 1/0 -11/14 -1/1 -29/37 -3/1 -18/23 -2/1 1/0 -25/32 -1/1 -7/9 -1/1 -17/22 1/1 -44/57 -3/1 1/0 -27/35 -1/1 -10/13 -1/1 0/1 -13/17 0/1 -16/21 0/1 1/2 -35/46 1/1 -19/25 1/1 -3/4 1/1 -14/19 4/1 1/0 -25/34 1/0 -11/15 -3/1 -8/11 -1/1 1/0 -13/18 -1/1 -18/25 -1/1 -4/5 -23/32 -1/1 -5/7 -1/1 -12/17 0/1 -19/27 1/7 -26/37 0/1 1/4 -7/10 1/3 -30/43 2/3 1/1 -23/33 1/1 -39/56 1/1 -55/79 -1/1 -71/102 0/1 -16/23 0/1 1/2 -25/36 1/1 -34/49 0/1 1/2 -9/13 1/1 -11/16 1/1 -35/51 1/0 -24/35 1/1 1/0 -13/19 1/1 -2/3 0/1 1/0 -11/17 0/1 -20/31 0/1 1/10 -9/14 1/5 -34/53 2/9 1/4 -59/92 3/13 -25/39 3/11 -41/64 1/3 -16/25 2/7 1/3 -23/36 1/3 -53/83 1/1 -30/47 0/1 1/2 -7/11 1/3 -26/41 2/5 1/2 -19/30 1/3 -12/19 1/2 2/3 -5/8 1/1 -23/37 1/1 -64/103 1/2 1/1 -41/66 1/1 -18/29 1/2 2/3 -13/21 1/1 -21/34 1/1 -8/13 1/1 2/1 -11/18 1/1 -14/23 2/1 1/0 -17/28 1/1 -20/33 1/1 1/0 -23/38 1/1 -3/5 -1/1 -10/17 0/1 -17/29 1/5 -41/70 1/5 -24/41 0/1 1/4 -7/12 1/3 -25/43 1/1 -43/74 -1/1 -18/31 0/1 1/4 -11/19 1/1 -26/45 0/1 1/4 -41/71 1/3 -15/26 1/3 -4/7 1/2 1/1 -9/16 1/1 -14/25 8/9 1/1 -19/34 1/1 -5/9 1/1 -6/11 1/1 1/0 -19/35 -1/1 -13/24 -1/1 -7/13 1/1 -15/28 1/1 -23/43 1/1 -8/15 0/1 1/0 -9/17 0/1 -10/19 0/1 1/2 -1/2 1/1 -8/17 1/0 -15/32 -1/1 -7/15 1/1 -6/13 0/1 1/1 -5/11 -1/1 -4/9 1/2 1/1 -15/34 1/1 -11/25 1/1 -29/66 1/1 -18/41 4/3 3/2 -7/16 1/1 -10/23 3/2 2/1 -13/30 1/1 -29/67 1/1 -16/37 3/2 2/1 -3/7 3/1 -20/47 0/1 1/0 -17/40 1/1 -14/33 1/1 1/0 -25/59 1/1 -11/26 1/1 -8/19 0/1 1/0 -13/31 5/3 -57/136 2/1 -44/105 2/1 17/8 -31/74 7/3 -18/43 2/1 3/1 -23/55 1/1 -28/67 2/1 1/0 -5/12 3/1 -17/41 5/1 -29/70 5/1 -12/29 6/1 1/0 -7/17 1/0 -2/5 0/1 1/0 -9/23 -1/1 -16/41 -2/1 1/0 -7/18 -1/1 -33/85 -1/2 -26/67 -1/2 0/1 -19/49 -1/3 -12/31 0/1 1/0 -17/44 1/1 -5/13 -1/1 -13/34 0/1 -8/21 0/1 1/2 -11/29 1/1 -25/66 1/1 -64/169 1/1 1/0 -103/272 1/0 -39/103 -1/1 -14/37 0/1 1/0 -3/8 1/1 -19/51 1/1 -16/43 1/1 4/3 -13/35 1/1 -23/62 1/1 -33/89 1/1 -10/27 2/1 1/0 -17/46 3/1 -41/111 3/1 -24/65 2/1 1/0 -7/19 3/1 -4/11 1/1 1/0 -9/25 1/1 -23/64 1/1 -14/39 3/2 2/1 -19/53 1/1 -24/67 2/1 1/0 -5/14 3/1 -6/17 1/0 -7/20 -3/1 -1/3 -1/1 -6/19 1/2 2/3 -5/16 1/1 -4/13 1/1 2/1 -7/23 3/1 -10/33 1/1 1/0 -13/43 1/1 -16/53 2/1 1/0 -3/10 1/1 -17/57 3/1 -14/47 2/1 1/0 -11/37 3/1 -30/101 3/1 1/0 -19/64 3/1 -8/27 4/1 1/0 -5/17 1/0 -2/7 -1/1 1/0 -5/18 -1/1 -13/47 -1/1 -8/29 -1/2 0/1 -27/98 -1/1 -19/69 -1/1 -11/40 -1/1 -3/11 -1/1 -10/37 0/1 1/0 -7/26 -1/1 -4/15 -1/4 0/1 -9/34 0/1 -5/19 1/5 -6/23 0/1 1/2 -1/4 1/1 -4/17 1/0 -7/30 -3/1 -10/43 -3/1 -2/1 -3/13 -1/1 -11/48 -1/1 -8/35 -1/1 1/0 -13/57 1/1 -31/136 1/0 -18/79 -5/1 1/0 -5/22 -1/1 -12/53 -2/1 -3/2 -7/31 -1/1 -23/102 1/0 -16/71 -2/1 1/0 -25/111 -1/1 -9/40 -1/1 -20/89 -2/1 1/0 -11/49 -3/1 -2/9 -1/1 1/0 -5/23 -1/3 -8/37 -1/4 0/1 -3/14 1/1 -13/61 -5/1 -10/47 -2/1 1/0 -17/80 -1/1 -7/33 -1/1 -18/85 -1/1 -29/137 -1/1 -11/52 -1/1 -4/19 -1/2 0/1 -9/43 -1/1 -5/24 -1/3 -11/53 -1/5 -6/29 -1/6 0/1 -7/34 0/1 -1/5 1/1 -4/21 0/1 1/2 -7/37 1/1 -10/53 2/3 3/4 -3/16 1/1 -2/11 1/1 1/0 -3/17 1/0 -4/23 -2/1 1/0 -1/6 -1/1 -4/25 0/1 1/1 -3/19 -1/1 -2/13 -1/1 0/1 -5/33 -1/1 -13/86 -1/1 -8/53 -2/3 -1/2 -3/20 -1/1 -10/67 -1/2 0/1 -7/47 -1/3 -4/27 -1/4 0/1 -5/34 0/1 -1/7 1/1 -3/22 -1/1 -2/15 -1/2 0/1 -1/8 1/1 -2/17 1/0 -3/26 -1/1 -1/9 -1/1 -1/10 1/1 -1/11 -1/1 -1/12 1/1 0/1 0/1 1/0 1/11 1/1 1/10 -1/1 1/9 1/1 2/17 1/0 1/8 -1/1 1/7 -1/1 5/34 0/1 4/27 0/1 1/4 7/47 1/3 3/20 1/1 2/13 0/1 1/1 3/19 1/1 4/25 -1/1 0/1 1/6 1/1 4/23 2/1 1/0 3/17 1/0 2/11 -1/1 1/0 1/5 -1/1 7/34 0/1 6/29 0/1 1/6 5/24 1/3 9/43 1/1 4/19 0/1 1/2 7/33 1/1 10/47 2/1 1/0 3/14 -1/1 2/9 1/1 1/0 11/49 3/1 9/40 1/1 16/71 2/1 1/0 23/102 1/0 7/31 1/1 12/53 3/2 2/1 5/22 1/1 8/35 1/1 1/0 3/13 1/1 4/17 1/0 5/21 -3/1 6/25 -2/1 -1/1 1/4 -1/1 6/23 -1/2 0/1 5/19 -1/5 9/34 0/1 4/15 0/1 1/4 11/41 1/1 7/26 1/1 10/37 0/1 1/0 3/11 1/1 11/40 1/1 19/69 1/1 8/29 0/1 1/2 5/18 1/1 2/7 1/1 1/0 5/17 1/0 8/27 -4/1 1/0 11/37 -3/1 14/47 -2/1 1/0 3/10 -1/1 16/53 -2/1 1/0 13/43 -1/1 10/33 -1/1 1/0 17/56 -1/1 7/23 -3/1 4/13 -2/1 -1/1 1/3 1/1 6/17 1/0 11/31 -5/1 5/14 -3/1 4/11 -1/1 1/0 7/19 -3/1 17/46 -3/1 10/27 -2/1 1/0 23/62 -1/1 13/35 -1/1 16/43 -4/3 -1/1 3/8 -1/1 14/37 0/1 1/0 39/103 1/1 25/66 -1/1 11/29 -1/1 8/21 -1/2 0/1 13/34 0/1 5/13 1/1 17/44 -1/1 12/31 0/1 1/0 7/18 1/1 2/5 0/1 1/0 7/17 1/0 12/29 -6/1 1/0 17/41 -5/1 22/53 -4/1 -7/2 5/12 -3/1 28/67 -2/1 1/0 23/55 -1/1 18/43 -3/1 -2/1 31/74 -7/3 13/31 -5/3 8/19 0/1 1/0 3/7 -3/1 13/30 -1/1 10/23 -2/1 -3/2 7/16 -1/1 18/41 -3/2 -4/3 11/25 -1/1 15/34 -1/1 4/9 -1/1 -1/2 9/20 -1/3 14/31 0/1 1/2 5/11 1/1 6/13 -1/1 0/1 7/15 -1/1 8/17 1/0 9/19 -3/1 1/2 -1/1 9/17 0/1 8/15 0/1 1/0 23/43 -1/1 15/28 -1/1 22/41 -1/2 0/1 7/13 -1/1 13/24 1/1 19/35 1/1 6/11 -1/1 1/0 11/20 -3/1 27/49 -1/1 43/78 -3/1 16/29 -2/1 -3/2 37/67 -1/1 21/38 -1/1 5/9 -1/1 19/34 -1/1 14/25 -1/1 -8/9 9/16 -1/1 4/7 -1/1 -1/2 15/26 -1/3 26/45 -1/4 0/1 11/19 -1/1 51/88 -1/3 91/157 -1/1 40/69 -1/2 0/1 69/119 -1/2 29/50 -1/3 18/31 -1/4 0/1 7/12 -1/3 10/17 0/1 13/22 1/3 16/27 0/1 1/2 19/32 1/1 3/5 1/1 20/33 -1/1 1/0 17/28 -1/1 14/23 -2/1 1/0 11/18 -1/1 52/85 -1/1 93/152 -1/1 41/67 -1/1 30/49 -2/3 -1/2 19/31 1/1 8/13 -2/1 -1/1 21/34 -1/1 13/21 -1/1 18/29 -2/3 -1/2 41/66 -1/1 105/169 -3/5 169/272 -1/2 64/103 -1/1 -1/2 23/37 -1/1 5/8 -1/1 32/51 -1/2 27/43 -1/1 22/35 -1/1 -1/2 39/62 -1/1 56/89 -2/3 -1/2 17/27 -1/3 12/19 -2/3 -1/2 19/30 -1/3 64/101 -1/2 -1/3 45/71 -1/3 26/41 -1/2 -2/5 7/11 -1/3 37/58 -1/1 30/47 -1/2 0/1 83/130 -1/3 53/83 -1/1 23/36 -1/3 16/25 -1/3 -2/7 41/64 -1/3 66/103 -1/3 -1/4 25/39 -3/11 34/53 -1/4 -2/9 9/14 -1/5 20/31 -1/10 0/1 11/17 0/1 2/3 0/1 1/0 19/28 -1/1 17/25 -1/1 15/22 -1/1 13/19 -1/1 11/16 -1/1 20/29 0/1 1/0 9/13 -1/1 25/36 -1/1 16/23 -1/2 0/1 71/102 0/1 55/79 1/1 94/135 0/1 1/0 39/56 -1/1 62/89 0/1 1/0 23/33 -1/1 30/43 -1/1 -2/3 7/10 -1/3 12/17 0/1 17/24 1/5 22/31 0/1 1/4 49/69 1/3 27/38 1/3 5/7 1/1 28/39 1/2 2/3 23/32 1/1 18/25 4/5 1/1 13/18 1/1 60/83 5/4 4/3 47/65 1/1 34/47 3/2 2/1 21/29 1/1 8/11 1/1 1/0 11/15 3/1 25/34 1/0 14/19 -4/1 1/0 3/4 -1/1 19/25 -1/1 35/46 -1/1 16/21 -1/2 0/1 13/17 0/1 10/13 0/1 1/1 37/48 1/1 64/83 1/2 2/3 91/118 1/1 27/35 1/1 44/57 3/1 1/0 105/136 1/0 61/79 -3/1 17/22 -1/1 24/31 -1/2 0/1 79/102 0/1 55/71 1/9 31/40 1/3 7/9 1/1 32/41 3/2 2/1 25/32 1/1 18/23 2/1 1/0 47/60 3/1 29/37 3/1 11/14 1/1 26/33 1/1 1/0 67/85 1/0 41/52 1/1 15/19 1/1 34/43 2/1 3/1 19/24 5/1 42/53 6/1 1/0 23/29 11/1 27/34 1/0 4/5 -2/1 1/0 13/16 -1/1 22/27 0/1 1/0 9/11 -1/1 14/17 -1/1 19/23 -1/1 5/6 -1/1 21/25 1/1 16/19 0/1 1/0 43/51 0/1 27/32 1/1 11/13 1/1 28/33 1/1 1/0 17/20 1/1 40/47 4/1 1/0 23/27 7/1 29/34 1/0 6/7 -3/1 1/0 7/8 -1/1 22/25 -6/5 -1/1 15/17 -1/1 8/9 -1/1 -1/2 17/19 -1/3 9/10 -1/1 1/1 -1/1 1/0 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(203,184,374,339) (-1/1,-9/10) -> (13/24,19/35) Hyperbolic Matrix(1087,974,1972,1767) (-9/10,-17/19) -> (27/49,43/78) Hyperbolic Matrix(137,122,612,545) (-17/19,-8/9) -> (2/9,11/49) Hyperbolic Matrix(271,240,306,271) (-8/9,-15/17) -> (15/17,8/9) Hyperbolic Matrix(203,178,-544,-477) (-15/17,-7/8) -> (-3/8,-19/51) Hyperbolic Matrix(137,118,238,205) (-7/8,-6/7) -> (4/7,15/26) Hyperbolic Matrix(407,348,476,407) (-6/7,-29/34) -> (29/34,6/7) Hyperbolic Matrix(1565,1334,1836,1565) (-29/34,-23/27) -> (23/27,29/34) Hyperbolic Matrix(341,290,-1598,-1359) (-23/27,-17/20) -> (-3/14,-13/61) Hyperbolic Matrix(203,172,-884,-749) (-17/20,-11/13) -> (-3/13,-11/48) Hyperbolic Matrix(613,518,-884,-747) (-11/13,-16/19) -> (-34/49,-9/13) Hyperbolic Matrix(271,228,1292,1087) (-16/19,-21/25) -> (9/43,4/19) Hyperbolic Matrix(817,686,1054,885) (-21/25,-5/6) -> (31/40,7/9) Hyperbolic Matrix(475,392,-578,-477) (-5/6,-14/17) -> (-14/17,-23/28) Parabolic Matrix(205,168,748,613) (-23/28,-9/11) -> (3/11,11/40) Hyperbolic Matrix(67,54,-170,-137) (-9/11,-4/5) -> (-2/5,-9/23) Hyperbolic Matrix(271,216,340,271) (-4/5,-27/34) -> (27/34,4/5) Hyperbolic Matrix(1565,1242,1972,1565) (-27/34,-23/29) -> (23/29,27/34) Hyperbolic Matrix(2311,1832,-3604,-2857) (-23/29,-19/24) -> (-59/92,-25/39) Hyperbolic Matrix(1021,808,1462,1157) (-19/24,-34/43) -> (30/43,7/10) Hyperbolic Matrix(205,162,1292,1021) (-34/43,-15/19) -> (3/19,4/25) Hyperbolic Matrix(885,698,-1292,-1019) (-15/19,-26/33) -> (-24/35,-13/19) Hyperbolic Matrix(475,374,-2074,-1633) (-26/33,-11/14) -> (-11/48,-8/35) Hyperbolic Matrix(339,266,952,747) (-11/14,-29/37) -> (11/31,5/14) Hyperbolic Matrix(1905,1492,-3298,-2583) (-29/37,-18/23) -> (-26/45,-41/71) Hyperbolic Matrix(1087,850,1564,1223) (-18/23,-25/32) -> (25/36,16/23) Hyperbolic Matrix(613,478,-1394,-1087) (-25/32,-7/9) -> (-11/25,-29/66) Hyperbolic Matrix(613,474,-1054,-815) (-7/9,-17/22) -> (-7/12,-25/43) Hyperbolic Matrix(681,526,-2992,-2311) (-17/22,-44/57) -> (-18/79,-5/22) Hyperbolic Matrix(1293,998,2380,1837) (-44/57,-27/35) -> (19/35,6/11) Hyperbolic Matrix(135,104,-884,-681) (-27/35,-10/13) -> (-2/13,-5/33) Hyperbolic Matrix(339,260,442,339) (-10/13,-13/17) -> (13/17,10/13) Hyperbolic Matrix(545,416,714,545) (-13/17,-16/21) -> (16/21,13/17) Hyperbolic Matrix(3671,2794,5270,4011) (-16/21,-35/46) -> (39/56,62/89) Hyperbolic Matrix(1157,880,1700,1293) (-35/46,-19/25) -> (17/25,15/22) Hyperbolic Matrix(545,414,986,749) (-19/25,-3/4) -> (21/38,5/9) Hyperbolic Matrix(409,302,646,477) (-3/4,-14/19) -> (12/19,19/30) Hyperbolic Matrix(951,700,1292,951) (-14/19,-25/34) -> (25/34,14/19) Hyperbolic Matrix(749,550,1020,749) (-25/34,-11/15) -> (11/15,25/34) Hyperbolic Matrix(137,100,374,273) (-11/15,-8/11) -> (4/11,7/19) Hyperbolic Matrix(69,50,-374,-271) (-8/11,-13/18) -> (-3/16,-2/11) Hyperbolic Matrix(477,344,850,613) (-13/18,-18/25) -> (14/25,9/16) Hyperbolic Matrix(1087,782,1700,1223) (-18/25,-23/32) -> (23/36,16/25) Hyperbolic Matrix(747,536,-1802,-1293) (-23/32,-5/7) -> (-17/41,-29/70) Hyperbolic Matrix(407,288,-578,-409) (-5/7,-12/17) -> (-12/17,-19/27) Parabolic Matrix(543,382,-1258,-885) (-19/27,-26/37) -> (-16/37,-3/7) Hyperbolic Matrix(749,526,1938,1361) (-26/37,-7/10) -> (17/44,12/31) Hyperbolic Matrix(1157,808,1462,1021) (-7/10,-30/43) -> (34/43,19/24) Hyperbolic Matrix(1087,758,2924,2039) (-30/43,-23/33) -> (13/35,16/43) Hyperbolic Matrix(953,664,-4488,-3127) (-23/33,-39/56) -> (-17/80,-7/33) Hyperbolic Matrix(135,94,-1564,-1089) (-39/56,-55/79) -> (-1/11,-1/12) Hyperbolic Matrix(11219,7810,16116,11219) (-55/79,-71/102) -> (71/102,55/79) Hyperbolic Matrix(3265,2272,4692,3265) (-71/102,-16/23) -> (16/23,71/102) Hyperbolic Matrix(1223,850,1564,1087) (-16/23,-25/36) -> (25/32,18/23) Hyperbolic Matrix(409,284,-782,-543) (-25/36,-34/49) -> (-10/19,-1/2) Hyperbolic Matrix(273,188,-986,-679) (-9/13,-11/16) -> (-5/18,-13/47) Hyperbolic Matrix(2583,1774,4454,3059) (-11/16,-35/51) -> (69/119,29/50) Hyperbolic Matrix(3671,2518,4658,3195) (-35/51,-24/35) -> (26/33,67/85) Hyperbolic Matrix(477,326,-1292,-883) (-13/19,-2/3) -> (-24/65,-7/19) Hyperbolic Matrix(67,44,102,67) (-2/3,-11/17) -> (11/17,2/3) Hyperbolic Matrix(681,440,1054,681) (-11/17,-20/31) -> (20/31,11/17) Hyperbolic Matrix(475,306,1054,679) (-20/31,-9/14) -> (9/20,14/31) Hyperbolic Matrix(271,174,-1802,-1157) (-9/14,-34/53) -> (-8/53,-3/20) Hyperbolic Matrix(1631,1046,5406,3467) (-34/53,-59/92) -> (3/10,16/53) Hyperbolic Matrix(1089,698,-1802,-1155) (-25/39,-41/64) -> (-23/38,-3/5) Hyperbolic Matrix(409,262,1700,1089) (-41/64,-16/25) -> (6/25,1/4) Hyperbolic Matrix(1223,782,1700,1087) (-16/25,-23/36) -> (23/32,18/25) Hyperbolic Matrix(407,260,850,543) (-23/36,-53/83) -> (9/19,1/2) Hyperbolic Matrix(2177,1390,-9690,-6187) (-53/83,-30/47) -> (-20/89,-11/49) Hyperbolic Matrix(953,608,-3196,-2039) (-30/47,-7/11) -> (-17/57,-14/47) Hyperbolic Matrix(611,388,748,475) (-7/11,-26/41) -> (22/27,9/11) Hyperbolic Matrix(1019,646,-3434,-2177) (-26/41,-19/30) -> (-19/64,-8/27) Hyperbolic Matrix(477,302,646,409) (-19/30,-12/19) -> (14/19,3/4) Hyperbolic Matrix(273,172,-646,-407) (-12/19,-5/8) -> (-11/26,-8/19) Hyperbolic Matrix(883,550,-1530,-953) (-5/8,-23/37) -> (-41/71,-15/26) Hyperbolic Matrix(7003,4352,11050,6867) (-23/37,-64/103) -> (64/101,45/71) Hyperbolic Matrix(6799,4224,-17952,-11153) (-64/103,-41/66) -> (-25/66,-64/169) Hyperbolic Matrix(2515,1562,3502,2175) (-41/66,-18/29) -> (28/39,23/32) Hyperbolic Matrix(545,338,-1972,-1223) (-18/29,-13/21) -> (-13/47,-8/29) Hyperbolic Matrix(883,546,1428,883) (-13/21,-21/34) -> (21/34,13/21) Hyperbolic Matrix(545,336,884,545) (-21/34,-8/13) -> (8/13,21/34) Hyperbolic Matrix(137,84,-442,-271) (-8/13,-11/18) -> (-5/16,-4/13) Hyperbolic Matrix(341,208,782,477) (-11/18,-14/23) -> (10/23,7/16) Hyperbolic Matrix(135,82,782,475) (-14/23,-17/28) -> (1/6,4/23) Hyperbolic Matrix(1903,1154,3026,1835) (-17/28,-20/33) -> (22/35,39/62) Hyperbolic Matrix(3059,1852,4828,2923) (-20/33,-23/38) -> (19/30,64/101) Hyperbolic Matrix(339,200,-578,-341) (-3/5,-10/17) -> (-10/17,-17/29) Parabolic Matrix(1495,876,3944,2311) (-17/29,-41/70) -> (25/66,11/29) Hyperbolic Matrix(3265,1912,4182,2449) (-41/70,-24/41) -> (32/41,25/32) Hyperbolic Matrix(817,478,2210,1293) (-24/41,-7/12) -> (17/46,10/27) Hyperbolic Matrix(1769,1028,2108,1225) (-25/43,-43/74) -> (5/6,21/25) Hyperbolic Matrix(4217,2450,-10064,-5847) (-43/74,-18/31) -> (-44/105,-31/74) Hyperbolic Matrix(817,474,-2108,-1223) (-18/31,-11/19) -> (-19/49,-12/31) Hyperbolic Matrix(339,196,1292,747) (-11/19,-26/45) -> (6/23,5/19) Hyperbolic Matrix(205,118,238,137) (-15/26,-4/7) -> (6/7,7/8) Hyperbolic Matrix(67,38,238,135) (-4/7,-9/16) -> (5/18,2/7) Hyperbolic Matrix(613,344,850,477) (-9/16,-14/25) -> (18/25,13/18) Hyperbolic Matrix(951,532,1700,951) (-14/25,-19/34) -> (19/34,14/25) Hyperbolic Matrix(341,190,612,341) (-19/34,-5/9) -> (5/9,19/34) Hyperbolic Matrix(135,74,-374,-205) (-5/9,-6/11) -> (-4/11,-9/25) Hyperbolic Matrix(1837,998,2380,1293) (-6/11,-19/35) -> (27/35,44/57) Hyperbolic Matrix(339,184,374,203) (-19/35,-13/24) -> (9/10,1/1) Hyperbolic Matrix(341,184,884,477) (-13/24,-7/13) -> (5/13,17/44) Hyperbolic Matrix(1223,656,-3298,-1769) (-7/13,-15/28) -> (-23/62,-33/89) Hyperbolic Matrix(1087,582,-4828,-2585) (-15/28,-23/43) -> (-25/111,-9/40) Hyperbolic Matrix(883,472,2924,1563) (-23/43,-8/15) -> (16/53,13/43) Hyperbolic Matrix(271,144,510,271) (-8/15,-9/17) -> (9/17,8/15) Hyperbolic Matrix(1089,574,1292,681) (-9/17,-10/19) -> (16/19,43/51) Hyperbolic Matrix(271,128,-578,-273) (-1/2,-8/17) -> (-8/17,-15/32) Parabolic Matrix(2041,956,3196,1497) (-15/32,-7/15) -> (53/83,23/36) Hyperbolic Matrix(69,32,442,205) (-7/15,-6/13) -> (2/13,3/19) Hyperbolic Matrix(135,62,442,203) (-6/13,-5/11) -> (7/23,4/13) Hyperbolic Matrix(67,30,-306,-137) (-5/11,-4/9) -> (-2/9,-5/23) Hyperbolic Matrix(271,120,612,271) (-4/9,-15/34) -> (15/34,4/9) Hyperbolic Matrix(749,330,1700,749) (-15/34,-11/25) -> (11/25,15/34) Hyperbolic Matrix(1835,806,3094,1359) (-29/66,-18/41) -> (16/27,19/32) Hyperbolic Matrix(885,388,1088,477) (-18/41,-7/16) -> (13/16,22/27) Hyperbolic Matrix(477,208,782,341) (-7/16,-10/23) -> (14/23,11/18) Hyperbolic Matrix(203,88,782,339) (-10/23,-13/30) -> (1/4,6/23) Hyperbolic Matrix(2517,1090,4556,1973) (-13/30,-29/67) -> (37/67,21/38) Hyperbolic Matrix(2381,1030,6290,2721) (-29/67,-16/37) -> (14/37,39/103) Hyperbolic Matrix(1361,580,1598,681) (-3/7,-20/47) -> (40/47,23/27) Hyperbolic Matrix(1223,520,-5440,-2313) (-20/47,-17/40) -> (-9/40,-20/89) Hyperbolic Matrix(1361,578,2244,953) (-17/40,-14/33) -> (20/33,17/28) Hyperbolic Matrix(1019,432,3366,1427) (-14/33,-25/59) -> (13/43,10/33) Hyperbolic Matrix(203,86,-1768,-749) (-25/59,-11/26) -> (-3/26,-1/9) Hyperbolic Matrix(205,86,-646,-271) (-8/19,-13/31) -> (-1/3,-6/19) Hyperbolic Matrix(9929,4162,12818,5373) (-13/31,-57/136) -> (79/102,55/71) Hyperbolic Matrix(11559,4844,14926,6255) (-57/136,-44/105) -> (24/31,79/102) Hyperbolic Matrix(339,142,2108,883) (-31/74,-18/43) -> (4/25,1/6) Hyperbolic Matrix(545,228,2278,953) (-18/43,-23/55) -> (5/21,6/25) Hyperbolic Matrix(1019,426,-6834,-2857) (-23/55,-28/67) -> (-10/67,-7/47) Hyperbolic Matrix(67,28,-816,-341) (-28/67,-5/12) -> (-1/12,0/1) Hyperbolic Matrix(135,56,-986,-409) (-5/12,-17/41) -> (-1/7,-3/22) Hyperbolic Matrix(2449,1014,3944,1633) (-29/70,-12/29) -> (18/29,41/66) Hyperbolic Matrix(407,168,986,407) (-12/29,-7/17) -> (7/17,12/29) Hyperbolic Matrix(69,28,170,69) (-7/17,-2/5) -> (2/5,7/17) Hyperbolic Matrix(885,346,1394,545) (-9/23,-16/41) -> (26/41,7/11) Hyperbolic Matrix(611,238,1394,543) (-16/41,-7/18) -> (7/16,18/41) Hyperbolic Matrix(4691,1822,5950,2311) (-7/18,-33/85) -> (67/85,41/52) Hyperbolic Matrix(8023,3114,13838,5371) (-33/85,-26/67) -> (40/69,69/119) Hyperbolic Matrix(2449,950,-6834,-2651) (-26/67,-19/49) -> (-19/53,-24/67) Hyperbolic Matrix(1495,578,2108,815) (-12/31,-17/44) -> (17/24,22/31) Hyperbolic Matrix(477,184,884,341) (-17/44,-5/13) -> (7/13,13/24) Hyperbolic Matrix(339,130,884,339) (-5/13,-13/34) -> (13/34,5/13) Hyperbolic Matrix(545,208,1428,545) (-13/34,-8/21) -> (8/21,13/34) Hyperbolic Matrix(137,52,-714,-271) (-8/21,-11/29) -> (-1/5,-4/21) Hyperbolic Matrix(749,284,1258,477) (-11/29,-25/66) -> (19/32,3/5) Hyperbolic Matrix(45969,17408,73984,28017) (-64/169,-103/272) -> (169/272,64/103) Hyperbolic Matrix(45967,17406,73984,28015) (-103/272,-39/103) -> (105/169,169/272) Hyperbolic Matrix(4079,1544,5746,2175) (-39/103,-14/37) -> (22/31,49/69) Hyperbolic Matrix(339,128,1258,475) (-14/37,-3/8) -> (7/26,10/37) Hyperbolic Matrix(1767,658,2006,747) (-19/51,-16/43) -> (22/25,15/17) Hyperbolic Matrix(2039,758,2924,1087) (-16/43,-13/35) -> (23/33,30/43) Hyperbolic Matrix(1563,580,5678,2107) (-13/35,-23/62) -> (11/40,19/69) Hyperbolic Matrix(545,202,3672,1361) (-33/89,-10/27) -> (4/27,7/47) Hyperbolic Matrix(1087,402,1836,679) (-10/27,-17/46) -> (13/22,16/27) Hyperbolic Matrix(4759,1758,6256,2311) (-17/46,-41/111) -> (19/25,35/46) Hyperbolic Matrix(3401,1256,-15096,-5575) (-41/111,-24/65) -> (-16/71,-25/111) Hyperbolic Matrix(273,100,374,137) (-7/19,-4/11) -> (8/11,11/15) Hyperbolic Matrix(1291,464,1700,611) (-9/25,-23/64) -> (3/4,19/25) Hyperbolic Matrix(1565,562,-5678,-2039) (-23/64,-14/39) -> (-8/29,-27/98) Hyperbolic Matrix(747,268,-3604,-1293) (-14/39,-19/53) -> (-11/53,-6/29) Hyperbolic Matrix(341,122,-2278,-815) (-24/67,-5/14) -> (-3/20,-10/67) Hyperbolic Matrix(203,72,-578,-205) (-5/14,-6/17) -> (-6/17,-7/20) Parabolic Matrix(613,214,782,273) (-7/20,-1/3) -> (29/37,11/14) Hyperbolic Matrix(273,86,-1292,-407) (-6/19,-5/16) -> (-11/52,-4/19) Hyperbolic Matrix(203,62,442,135) (-4/13,-7/23) -> (5/11,6/13) Hyperbolic Matrix(613,186,-2686,-815) (-7/23,-10/33) -> (-8/35,-13/57) Hyperbolic Matrix(1837,556,2924,885) (-10/33,-13/43) -> (27/43,22/35) Hyperbolic Matrix(1563,472,2924,883) (-13/43,-16/53) -> (8/15,23/43) Hyperbolic Matrix(1427,430,1802,543) (-16/53,-3/10) -> (19/24,42/53) Hyperbolic Matrix(67,20,680,203) (-3/10,-17/57) -> (1/11,1/10) Hyperbolic Matrix(3467,1032,4794,1427) (-14/47,-11/37) -> (47/65,34/47) Hyperbolic Matrix(4691,1394,7548,2243) (-11/37,-30/101) -> (64/103,23/37) Hyperbolic Matrix(8365,2484,13056,3877) (-30/101,-19/64) -> (41/64,66/103) Hyperbolic Matrix(271,80,918,271) (-8/27,-5/17) -> (5/17,8/27) Hyperbolic Matrix(69,20,238,69) (-5/17,-2/7) -> (2/7,5/17) Hyperbolic Matrix(135,38,238,67) (-2/7,-5/18) -> (9/16,4/7) Hyperbolic Matrix(6665,1836,9384,2585) (-27/98,-19/69) -> (49/69,27/38) Hyperbolic Matrix(2107,580,5678,1563) (-19/69,-11/40) -> (23/62,13/35) Hyperbolic Matrix(815,224,986,271) (-11/40,-3/11) -> (19/23,5/6) Hyperbolic Matrix(339,92,748,203) (-3/11,-10/37) -> (14/31,5/11) Hyperbolic Matrix(475,128,1258,339) (-10/37,-7/26) -> (3/8,14/37) Hyperbolic Matrix(67,18,-510,-137) (-7/26,-4/15) -> (-2/15,-1/8) Hyperbolic Matrix(271,72,1020,271) (-4/15,-9/34) -> (9/34,4/15) Hyperbolic Matrix(341,90,1292,341) (-9/34,-5/19) -> (5/19,9/34) Hyperbolic Matrix(747,196,1292,339) (-5/19,-6/23) -> (26/45,11/19) Hyperbolic Matrix(339,88,782,203) (-6/23,-1/4) -> (13/30,10/23) Hyperbolic Matrix(135,32,-578,-137) (-1/4,-4/17) -> (-4/17,-7/30) Parabolic Matrix(2243,522,3502,815) (-7/30,-10/43) -> (16/25,41/64) Hyperbolic Matrix(1223,284,2924,679) (-10/43,-3/13) -> (23/55,18/43) Hyperbolic Matrix(14281,3256,18496,4217) (-13/57,-31/136) -> (105/136,61/79) Hyperbolic Matrix(14279,3254,18496,4215) (-31/136,-18/79) -> (44/57,105/136) Hyperbolic Matrix(749,170,1802,409) (-5/22,-12/53) -> (22/53,5/12) Hyperbolic Matrix(681,154,-3604,-815) (-12/53,-7/31) -> (-7/37,-10/53) Hyperbolic Matrix(1427,322,6324,1427) (-7/31,-23/102) -> (23/102,7/31) Hyperbolic Matrix(3265,736,14484,3265) (-23/102,-16/71) -> (16/71,23/102) Hyperbolic Matrix(545,122,612,137) (-11/49,-2/9) -> (8/9,17/19) Hyperbolic Matrix(341,74,1258,273) (-5/23,-8/37) -> (10/37,3/11) Hyperbolic Matrix(613,132,952,205) (-8/37,-3/14) -> (9/14,20/31) Hyperbolic Matrix(4215,898,6698,1427) (-13/61,-10/47) -> (56/89,17/27) Hyperbolic Matrix(2925,622,3842,817) (-10/47,-17/80) -> (35/46,16/21) Hyperbolic Matrix(3059,648,-14450,-3061) (-7/33,-18/85) -> (-18/85,-29/137) Parabolic Matrix(13871,2936,17986,3807) (-29/137,-11/52) -> (91/118,27/35) Hyperbolic Matrix(1087,228,1292,271) (-4/19,-9/43) -> (21/25,16/19) Hyperbolic Matrix(67,14,646,135) (-9/43,-5/24) -> (1/10,1/9) Hyperbolic Matrix(885,184,986,205) (-5/24,-11/53) -> (17/19,9/10) Hyperbolic Matrix(407,84,1972,407) (-6/29,-7/34) -> (7/34,6/29) Hyperbolic Matrix(69,14,340,69) (-7/34,-1/5) -> (1/5,7/34) Hyperbolic Matrix(749,142,2516,477) (-4/21,-7/37) -> (11/37,14/47) Hyperbolic Matrix(817,154,-5406,-1019) (-10/53,-3/16) -> (-13/86,-8/53) Hyperbolic Matrix(67,12,374,67) (-2/11,-3/17) -> (3/17,2/11) Hyperbolic Matrix(137,24,782,137) (-3/17,-4/23) -> (4/23,3/17) Hyperbolic Matrix(475,82,782,135) (-4/23,-1/6) -> (17/28,14/23) Hyperbolic Matrix(883,142,2108,339) (-1/6,-4/25) -> (18/43,31/74) Hyperbolic Matrix(1021,162,1292,205) (-4/25,-3/19) -> (15/19,34/43) Hyperbolic Matrix(205,32,442,69) (-3/19,-2/13) -> (6/13,7/15) Hyperbolic Matrix(6595,998,10778,1631) (-5/33,-13/86) -> (93/152,41/67) Hyperbolic Matrix(1223,182,2278,339) (-7/47,-4/27) -> (22/41,7/13) Hyperbolic Matrix(271,40,1836,271) (-4/27,-5/34) -> (5/34,4/27) Hyperbolic Matrix(69,10,476,69) (-5/34,-1/7) -> (1/7,5/34) Hyperbolic Matrix(339,46,1496,203) (-3/22,-2/15) -> (12/53,5/22) Hyperbolic Matrix(67,8,-578,-69) (-1/8,-2/17) -> (-2/17,-3/26) Parabolic Matrix(135,14,646,67) (-1/9,-1/10) -> (5/24,9/43) Hyperbolic Matrix(477,44,748,69) (-1/10,-1/11) -> (7/11,37/58) Hyperbolic Matrix(1089,-94,1564,-135) (0/1,1/11) -> (55/79,94/135) Hyperbolic Matrix(747,-86,1190,-137) (1/9,2/17) -> (32/51,27/43) Hyperbolic Matrix(341,-42,544,-67) (2/17,1/8) -> (5/8,32/51) Hyperbolic Matrix(137,-18,510,-67) (1/8,1/7) -> (11/41,7/26) Hyperbolic Matrix(4217,-630,7276,-1087) (7/47,3/20) -> (51/88,91/157) Hyperbolic Matrix(681,-104,884,-135) (3/20,2/13) -> (10/13,37/48) Hyperbolic Matrix(271,-50,374,-69) (2/11,1/5) -> (21/29,8/11) Hyperbolic Matrix(1631,-338,2958,-613) (6/29,5/24) -> (43/78,16/29) Hyperbolic Matrix(1769,-374,2890,-611) (4/19,7/33) -> (41/67,30/49) Hyperbolic Matrix(3127,-664,4488,-953) (7/33,10/47) -> (62/89,23/33) Hyperbolic Matrix(1359,-290,1598,-341) (10/47,3/14) -> (17/20,40/47) Hyperbolic Matrix(137,-30,306,-67) (3/14,2/9) -> (4/9,9/20) Hyperbolic Matrix(6187,-1390,9690,-2177) (11/49,9/40) -> (83/130,53/83) Hyperbolic Matrix(1429,-322,2108,-475) (9/40,16/71) -> (2/3,19/28) Hyperbolic Matrix(4351,-984,6018,-1361) (7/31,12/53) -> (60/83,47/65) Hyperbolic Matrix(815,-186,2686,-613) (5/22,8/35) -> (10/33,17/56) Hyperbolic Matrix(749,-172,884,-203) (8/35,3/13) -> (11/13,28/33) Hyperbolic Matrix(137,-32,578,-135) (3/13,4/17) -> (4/17,5/21) Parabolic Matrix(1157,-310,2788,-747) (4/15,11/41) -> (17/41,22/53) Hyperbolic Matrix(2177,-600,3944,-1087) (19/69,8/29) -> (16/29,37/67) Hyperbolic Matrix(679,-188,986,-273) (8/29,5/18) -> (11/16,20/29) Hyperbolic Matrix(2177,-646,3434,-1019) (8/27,11/37) -> (45/71,26/41) Hyperbolic Matrix(2039,-608,3196,-953) (14/47,3/10) -> (37/58,30/47) Hyperbolic Matrix(3807,-1156,4930,-1497) (17/56,7/23) -> (61/79,17/22) Hyperbolic Matrix(271,-84,442,-137) (4/13,1/3) -> (19/31,8/13) Hyperbolic Matrix(205,-72,578,-203) (1/3,6/17) -> (6/17,11/31) Parabolic Matrix(205,-74,374,-135) (5/14,4/11) -> (6/11,11/20) Hyperbolic Matrix(883,-326,1292,-477) (7/19,17/46) -> (15/22,13/19) Hyperbolic Matrix(1769,-656,3298,-1223) (10/27,23/62) -> (15/28,22/41) Hyperbolic Matrix(477,-178,544,-203) (16/43,3/8) -> (7/8,22/25) Hyperbolic Matrix(11153,-4224,17952,-6799) (39/103,25/66) -> (41/66,105/169) Hyperbolic Matrix(1427,-542,1972,-749) (11/29,8/21) -> (34/47,21/29) Hyperbolic Matrix(1223,-474,2108,-817) (12/31,7/18) -> (29/50,18/31) Hyperbolic Matrix(137,-54,170,-67) (7/18,2/5) -> (4/5,13/16) Hyperbolic Matrix(1293,-536,1802,-747) (12/29,17/41) -> (5/7,28/39) Hyperbolic Matrix(3741,-1562,5372,-2243) (5/12,28/67) -> (94/135,39/56) Hyperbolic Matrix(8297,-3468,14314,-5983) (28/67,23/55) -> (91/157,40/69) Hyperbolic Matrix(5031,-2108,6494,-2721) (31/74,13/31) -> (55/71,31/40) Hyperbolic Matrix(1291,-542,2108,-885) (13/31,8/19) -> (30/49,19/31) Hyperbolic Matrix(407,-172,646,-273) (8/19,3/7) -> (17/27,12/19) Hyperbolic Matrix(339,-146,476,-205) (3/7,13/30) -> (27/38,5/7) Hyperbolic Matrix(1087,-478,1394,-613) (18/41,11/25) -> (7/9,32/41) Hyperbolic Matrix(273,-128,578,-271) (7/15,8/17) -> (8/17,9/19) Parabolic Matrix(545,-286,646,-339) (1/2,9/17) -> (43/51,27/32) Hyperbolic Matrix(1293,-692,1904,-1019) (23/43,15/28) -> (19/28,17/25) Hyperbolic Matrix(2719,-1498,4692,-2585) (11/20,27/49) -> (11/19,51/88) Hyperbolic Matrix(2583,-1492,3298,-1905) (15/26,26/45) -> (18/23,47/60) Hyperbolic Matrix(815,-474,1054,-613) (18/31,7/12) -> (17/22,24/31) Hyperbolic Matrix(341,-200,578,-339) (7/12,10/17) -> (10/17,13/22) Parabolic Matrix(1155,-698,1802,-1089) (3/5,20/33) -> (66/103,25/39) Hyperbolic Matrix(8841,-5408,14450,-8839) (11/18,52/85) -> (52/85,93/152) Parabolic Matrix(681,-422,986,-611) (13/21,18/29) -> (20/29,9/13) Hyperbolic Matrix(1971,-1226,2516,-1565) (23/37,5/8) -> (47/60,29/37) Hyperbolic Matrix(9247,-5818,14484,-9113) (39/62,56/89) -> (30/47,83/130) Hyperbolic Matrix(2857,-1832,3604,-2311) (25/39,34/53) -> (42/53,23/29) Hyperbolic Matrix(2857,-1834,3706,-2379) (34/53,9/14) -> (37/48,64/83) Hyperbolic Matrix(1019,-698,1292,-885) (13/19,11/16) -> (41/52,15/19) Hyperbolic Matrix(747,-518,884,-613) (9/13,25/36) -> (27/32,11/13) Hyperbolic Matrix(409,-288,578,-407) (7/10,12/17) -> (12/17,17/24) Parabolic Matrix(8705,-6292,11288,-8159) (13/18,60/83) -> (64/83,91/118) Hyperbolic Matrix(953,-750,1122,-883) (11/14,26/33) -> (28/33,17/20) Hyperbolic Matrix(477,-392,578,-475) (9/11,14/17) -> (14/17,19/23) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,0,-2,1) Matrix(203,184,374,339) -> Matrix(1,0,0,1) Matrix(1087,974,1972,1767) -> Matrix(5,-2,-2,1) Matrix(137,122,612,545) -> Matrix(3,-2,2,-1) Matrix(271,240,306,271) -> Matrix(3,-2,-4,3) Matrix(203,178,-544,-477) -> Matrix(1,-2,2,-3) Matrix(137,118,238,205) -> Matrix(1,-2,-2,5) Matrix(407,348,476,407) -> Matrix(1,-6,0,1) Matrix(1565,1334,1836,1565) -> Matrix(1,14,0,1) Matrix(341,290,-1598,-1359) -> Matrix(1,2,0,1) Matrix(203,172,-884,-749) -> Matrix(1,0,0,1) Matrix(613,518,-884,-747) -> Matrix(1,0,2,1) Matrix(271,228,1292,1087) -> Matrix(1,0,2,1) Matrix(817,686,1054,885) -> Matrix(1,0,2,1) Matrix(475,392,-578,-477) -> Matrix(3,-2,2,-1) Matrix(205,168,748,613) -> Matrix(1,-2,2,-3) Matrix(67,54,-170,-137) -> Matrix(1,-2,0,1) Matrix(271,216,340,271) -> Matrix(1,-4,0,1) Matrix(1565,1242,1972,1565) -> Matrix(1,22,0,1) Matrix(2311,1832,-3604,-2857) -> Matrix(1,8,4,33) Matrix(1021,808,1462,1157) -> Matrix(1,4,-2,-7) Matrix(205,162,1292,1021) -> Matrix(1,2,0,1) Matrix(885,698,-1292,-1019) -> Matrix(1,2,0,1) Matrix(475,374,-2074,-1633) -> Matrix(1,0,0,1) Matrix(339,266,952,747) -> Matrix(1,-2,0,1) Matrix(1905,1492,-3298,-2583) -> Matrix(1,2,4,9) Matrix(1087,850,1564,1223) -> Matrix(1,2,-2,-3) Matrix(613,478,-1394,-1087) -> Matrix(5,6,4,5) Matrix(613,474,-1054,-815) -> Matrix(1,0,2,1) Matrix(681,526,-2992,-2311) -> Matrix(1,-2,0,1) Matrix(1293,998,2380,1837) -> Matrix(1,2,0,1) Matrix(135,104,-884,-681) -> Matrix(1,0,0,1) Matrix(339,260,442,339) -> Matrix(1,0,2,1) Matrix(545,416,714,545) -> Matrix(1,0,-4,1) Matrix(3671,2794,5270,4011) -> Matrix(1,0,-2,1) Matrix(1157,880,1700,1293) -> Matrix(1,0,-2,1) Matrix(545,414,986,749) -> Matrix(1,-2,0,1) Matrix(409,302,646,477) -> Matrix(1,-2,-2,5) Matrix(951,700,1292,951) -> Matrix(1,-8,0,1) Matrix(749,550,1020,749) -> Matrix(1,6,0,1) Matrix(137,100,374,273) -> Matrix(1,0,0,1) Matrix(69,50,-374,-271) -> Matrix(1,2,0,1) Matrix(477,344,850,613) -> Matrix(3,4,-4,-5) Matrix(1087,782,1700,1223) -> Matrix(3,2,-8,-5) Matrix(747,536,-1802,-1293) -> Matrix(9,4,2,1) Matrix(407,288,-578,-409) -> Matrix(1,0,8,1) Matrix(543,382,-1258,-885) -> Matrix(11,-2,6,-1) Matrix(749,526,1938,1361) -> Matrix(1,0,-4,1) Matrix(1157,808,1462,1021) -> Matrix(7,-4,2,-1) Matrix(1087,758,2924,2039) -> Matrix(1,-2,0,1) Matrix(953,664,-4488,-3127) -> Matrix(1,-2,0,1) Matrix(135,94,-1564,-1089) -> Matrix(1,0,0,1) Matrix(11219,7810,16116,11219) -> Matrix(1,0,2,1) Matrix(3265,2272,4692,3265) -> Matrix(1,0,-4,1) Matrix(1223,850,1564,1087) -> Matrix(3,-2,2,-1) Matrix(409,284,-782,-543) -> Matrix(1,0,0,1) Matrix(273,188,-986,-679) -> Matrix(1,0,-2,1) Matrix(2583,1774,4454,3059) -> Matrix(1,-2,-2,5) Matrix(3671,2518,4658,3195) -> Matrix(1,0,0,1) Matrix(477,326,-1292,-883) -> Matrix(1,2,0,1) Matrix(67,44,102,67) -> Matrix(1,0,0,1) Matrix(681,440,1054,681) -> Matrix(1,0,-20,1) Matrix(475,306,1054,679) -> Matrix(1,0,-8,1) Matrix(271,174,-1802,-1157) -> Matrix(1,0,-6,1) Matrix(1631,1046,5406,3467) -> Matrix(17,-4,-4,1) Matrix(1089,698,-1802,-1155) -> Matrix(7,-2,4,-1) Matrix(409,262,1700,1089) -> Matrix(1,0,-4,1) Matrix(1223,782,1700,1087) -> Matrix(5,-2,8,-3) Matrix(407,260,850,543) -> Matrix(5,-2,-2,1) Matrix(2177,1390,-9690,-6187) -> Matrix(5,-2,-2,1) Matrix(953,608,-3196,-2039) -> Matrix(3,-2,2,-1) Matrix(611,388,748,475) -> Matrix(5,-2,-2,1) Matrix(1019,646,-3434,-2177) -> Matrix(3,-2,2,-1) Matrix(477,302,646,409) -> Matrix(5,-2,-2,1) Matrix(273,172,-646,-407) -> Matrix(3,-2,2,-1) Matrix(883,550,-1530,-953) -> Matrix(1,0,2,1) Matrix(7003,4352,11050,6867) -> Matrix(1,0,-4,1) Matrix(6799,4224,-17952,-11153) -> Matrix(3,-2,2,-1) Matrix(2515,1562,3502,2175) -> Matrix(1,0,0,1) Matrix(545,338,-1972,-1223) -> Matrix(3,-2,-4,3) Matrix(883,546,1428,883) -> Matrix(7,-6,-8,7) Matrix(545,336,884,545) -> Matrix(3,-4,-2,3) Matrix(137,84,-442,-271) -> Matrix(1,0,0,1) Matrix(341,208,782,477) -> Matrix(3,-4,-2,3) Matrix(135,82,782,475) -> Matrix(1,0,0,1) Matrix(1903,1154,3026,1835) -> Matrix(1,0,-2,1) Matrix(3059,1852,4828,2923) -> Matrix(1,-2,-2,5) Matrix(339,200,-578,-341) -> Matrix(1,0,6,1) Matrix(1495,876,3944,2311) -> Matrix(1,0,-6,1) Matrix(3265,1912,4182,2449) -> Matrix(11,-2,6,-1) Matrix(817,478,2210,1293) -> Matrix(9,-2,-4,1) Matrix(1769,1028,2108,1225) -> Matrix(1,0,0,1) Matrix(4217,2450,-10064,-5847) -> Matrix(9,2,4,1) Matrix(817,474,-2108,-1223) -> Matrix(1,0,-4,1) Matrix(339,196,1292,747) -> Matrix(1,0,-6,1) Matrix(205,118,238,137) -> Matrix(5,-2,-2,1) Matrix(67,38,238,135) -> Matrix(3,-2,2,-1) Matrix(613,344,850,477) -> Matrix(5,-4,4,-3) Matrix(951,532,1700,951) -> Matrix(17,-16,-18,17) Matrix(341,190,612,341) -> Matrix(5,-6,-4,5) Matrix(135,74,-374,-205) -> Matrix(1,0,0,1) Matrix(1837,998,2380,1293) -> Matrix(1,2,0,1) Matrix(339,184,374,203) -> Matrix(1,0,0,1) Matrix(341,184,884,477) -> Matrix(1,0,0,1) Matrix(1223,656,-3298,-1769) -> Matrix(3,-2,2,-1) Matrix(1087,582,-4828,-2585) -> Matrix(1,-2,0,1) Matrix(883,472,2924,1563) -> Matrix(1,-2,0,1) Matrix(271,144,510,271) -> Matrix(1,0,0,1) Matrix(1089,574,1292,681) -> Matrix(1,0,-2,1) Matrix(271,128,-578,-273) -> Matrix(1,-2,0,1) Matrix(2041,956,3196,1497) -> Matrix(1,0,-2,1) Matrix(69,32,442,205) -> Matrix(1,0,0,1) Matrix(135,62,442,203) -> Matrix(1,-2,0,1) Matrix(67,30,-306,-137) -> Matrix(1,0,-2,1) Matrix(271,120,612,271) -> Matrix(3,-2,-4,3) Matrix(749,330,1700,749) -> Matrix(11,-12,-10,11) Matrix(1835,806,3094,1359) -> Matrix(3,-4,4,-5) Matrix(885,388,1088,477) -> Matrix(3,-4,-2,3) Matrix(477,208,782,341) -> Matrix(3,-4,-2,3) Matrix(203,88,782,339) -> Matrix(1,-2,0,1) Matrix(2517,1090,4556,1973) -> Matrix(3,-4,-2,3) Matrix(2381,1030,6290,2721) -> Matrix(1,-2,2,-3) Matrix(1361,580,1598,681) -> Matrix(1,4,0,1) Matrix(1223,520,-5440,-2313) -> Matrix(1,-2,0,1) Matrix(1361,578,2244,953) -> Matrix(1,-2,0,1) Matrix(1019,432,3366,1427) -> Matrix(1,-2,0,1) Matrix(203,86,-1768,-749) -> Matrix(1,-2,0,1) Matrix(205,86,-646,-271) -> Matrix(1,-2,2,-3) Matrix(9929,4162,12818,5373) -> Matrix(1,-2,12,-23) Matrix(11559,4844,14926,6255) -> Matrix(1,-2,-10,21) Matrix(339,142,2108,883) -> Matrix(1,-2,-2,5) Matrix(545,228,2278,953) -> Matrix(1,-4,0,1) Matrix(1019,426,-6834,-2857) -> Matrix(1,-2,-2,5) Matrix(67,28,-816,-341) -> Matrix(1,-2,0,1) Matrix(135,56,-986,-409) -> Matrix(1,-4,0,1) Matrix(2449,1014,3944,1633) -> Matrix(1,-4,-2,9) Matrix(407,168,986,407) -> Matrix(1,-12,0,1) Matrix(69,28,170,69) -> Matrix(1,0,0,1) Matrix(885,346,1394,545) -> Matrix(1,0,-2,1) Matrix(611,238,1394,543) -> Matrix(3,2,-2,-1) Matrix(4691,1822,5950,2311) -> Matrix(1,0,2,1) Matrix(8023,3114,13838,5371) -> Matrix(1,0,0,1) Matrix(2449,950,-6834,-2651) -> Matrix(5,2,2,1) Matrix(1495,578,2108,815) -> Matrix(1,0,4,1) Matrix(477,184,884,341) -> Matrix(1,0,0,1) Matrix(339,130,884,339) -> Matrix(1,0,2,1) Matrix(545,208,1428,545) -> Matrix(1,0,-4,1) Matrix(137,52,-714,-271) -> Matrix(1,0,0,1) Matrix(749,284,1258,477) -> Matrix(1,0,0,1) Matrix(45969,17408,73984,28017) -> Matrix(1,0,-2,1) Matrix(45967,17406,73984,28015) -> Matrix(1,4,-2,-7) Matrix(4079,1544,5746,2175) -> Matrix(1,0,4,1) Matrix(339,128,1258,475) -> Matrix(1,0,0,1) Matrix(1767,658,2006,747) -> Matrix(9,-10,-8,9) Matrix(2039,758,2924,1087) -> Matrix(1,-2,0,1) Matrix(1563,580,5678,2107) -> Matrix(1,-2,2,-3) Matrix(545,202,3672,1361) -> Matrix(1,-2,4,-7) Matrix(1087,402,1836,679) -> Matrix(1,-2,2,-3) Matrix(4759,1758,6256,2311) -> Matrix(1,-2,-2,5) Matrix(3401,1256,-15096,-5575) -> Matrix(1,-4,0,1) Matrix(273,100,374,137) -> Matrix(1,0,0,1) Matrix(1291,464,1700,611) -> Matrix(1,-2,0,1) Matrix(1565,562,-5678,-2039) -> Matrix(1,-2,0,1) Matrix(747,268,-3604,-1293) -> Matrix(1,-2,-4,9) Matrix(341,122,-2278,-815) -> Matrix(1,-2,-2,5) Matrix(203,72,-578,-205) -> Matrix(1,-6,0,1) Matrix(613,214,782,273) -> Matrix(1,4,0,1) Matrix(273,86,-1292,-407) -> Matrix(3,-2,-4,3) Matrix(203,62,442,135) -> Matrix(1,-2,0,1) Matrix(613,186,-2686,-815) -> Matrix(1,-2,0,1) Matrix(1837,556,2924,885) -> Matrix(1,0,-2,1) Matrix(1563,472,2924,883) -> Matrix(1,-2,0,1) Matrix(1427,430,1802,543) -> Matrix(1,4,0,1) Matrix(67,20,680,203) -> Matrix(1,-2,0,1) Matrix(3467,1032,4794,1427) -> Matrix(3,-8,2,-5) Matrix(4691,1394,7548,2243) -> Matrix(1,-2,-2,5) Matrix(8365,2484,13056,3877) -> Matrix(1,-2,-4,9) Matrix(271,80,918,271) -> Matrix(1,-8,0,1) Matrix(69,20,238,69) -> Matrix(1,2,0,1) Matrix(135,38,238,67) -> Matrix(1,2,-2,-3) Matrix(6665,1836,9384,2585) -> Matrix(1,0,4,1) Matrix(2107,580,5678,1563) -> Matrix(3,2,-2,-1) Matrix(815,224,986,271) -> Matrix(1,0,0,1) Matrix(339,92,748,203) -> Matrix(1,0,2,1) Matrix(475,128,1258,339) -> Matrix(1,0,0,1) Matrix(67,18,-510,-137) -> Matrix(1,0,2,1) Matrix(271,72,1020,271) -> Matrix(1,0,8,1) Matrix(341,90,1292,341) -> Matrix(1,0,-10,1) Matrix(747,196,1292,339) -> Matrix(1,0,-6,1) Matrix(339,88,782,203) -> Matrix(1,-2,0,1) Matrix(135,32,-578,-137) -> Matrix(1,-4,0,1) Matrix(2243,522,3502,815) -> Matrix(1,4,-4,-15) Matrix(1223,284,2924,679) -> Matrix(1,0,0,1) Matrix(14281,3256,18496,4217) -> Matrix(1,-4,0,1) Matrix(14279,3254,18496,4215) -> Matrix(1,8,0,1) Matrix(749,170,1802,409) -> Matrix(1,-2,0,1) Matrix(681,154,-3604,-815) -> Matrix(1,0,2,1) Matrix(1427,322,6324,1427) -> Matrix(1,2,0,1) Matrix(3265,736,14484,3265) -> Matrix(1,4,0,1) Matrix(545,122,612,137) -> Matrix(1,2,-2,-3) Matrix(341,74,1258,273) -> Matrix(1,0,4,1) Matrix(613,132,952,205) -> Matrix(1,0,-6,1) Matrix(4215,898,6698,1427) -> Matrix(1,4,-2,-7) Matrix(2925,622,3842,817) -> Matrix(1,2,-2,-3) Matrix(3059,648,-14450,-3061) -> Matrix(11,12,-12,-13) Matrix(13871,2936,17986,3807) -> Matrix(9,8,10,9) Matrix(1087,228,1292,271) -> Matrix(1,0,2,1) Matrix(67,14,646,135) -> Matrix(1,0,2,1) Matrix(885,184,986,205) -> Matrix(1,0,2,1) Matrix(407,84,1972,407) -> Matrix(1,0,12,1) Matrix(69,14,340,69) -> Matrix(1,0,-2,1) Matrix(749,142,2516,477) -> Matrix(5,-2,-2,1) Matrix(817,154,-5406,-1019) -> Matrix(5,-4,-6,5) Matrix(67,12,374,67) -> Matrix(1,-2,0,1) Matrix(137,24,782,137) -> Matrix(1,4,0,1) Matrix(475,82,782,135) -> Matrix(1,0,0,1) Matrix(883,142,2108,339) -> Matrix(5,-2,-2,1) Matrix(1021,162,1292,205) -> Matrix(1,2,0,1) Matrix(205,32,442,69) -> Matrix(1,0,0,1) Matrix(6595,998,10778,1631) -> Matrix(5,6,-6,-7) Matrix(1223,182,2278,339) -> Matrix(1,0,2,1) Matrix(271,40,1836,271) -> Matrix(1,0,8,1) Matrix(69,10,476,69) -> Matrix(1,0,-2,1) Matrix(339,46,1496,203) -> Matrix(1,2,0,1) Matrix(67,8,-578,-69) -> Matrix(1,-2,0,1) Matrix(135,14,646,67) -> Matrix(1,0,2,1) Matrix(477,44,748,69) -> Matrix(1,0,-2,1) Matrix(1089,-94,1564,-135) -> Matrix(1,0,0,1) Matrix(747,-86,1190,-137) -> Matrix(1,0,-2,1) Matrix(341,-42,544,-67) -> Matrix(1,2,-2,-3) Matrix(137,-18,510,-67) -> Matrix(1,0,2,1) Matrix(4217,-630,7276,-1087) -> Matrix(1,0,-4,1) Matrix(681,-104,884,-135) -> Matrix(1,0,0,1) Matrix(271,-50,374,-69) -> Matrix(1,2,0,1) Matrix(1631,-338,2958,-613) -> Matrix(9,-2,-4,1) Matrix(1769,-374,2890,-611) -> Matrix(3,-2,-4,3) Matrix(3127,-664,4488,-953) -> Matrix(1,-2,0,1) Matrix(1359,-290,1598,-341) -> Matrix(1,2,0,1) Matrix(137,-30,306,-67) -> Matrix(1,0,-2,1) Matrix(6187,-1390,9690,-2177) -> Matrix(1,-2,-2,5) Matrix(1429,-322,2108,-475) -> Matrix(1,-2,0,1) Matrix(4351,-984,6018,-1361) -> Matrix(3,-2,2,-1) Matrix(815,-186,2686,-613) -> Matrix(1,-2,0,1) Matrix(749,-172,884,-203) -> Matrix(1,0,0,1) Matrix(137,-32,578,-135) -> Matrix(1,-4,0,1) Matrix(1157,-310,2788,-747) -> Matrix(9,-4,-2,1) Matrix(2177,-600,3944,-1087) -> Matrix(1,-2,0,1) Matrix(679,-188,986,-273) -> Matrix(1,0,-2,1) Matrix(2177,-646,3434,-1019) -> Matrix(1,2,-2,-3) Matrix(2039,-608,3196,-953) -> Matrix(1,2,-2,-3) Matrix(3807,-1156,4930,-1497) -> Matrix(1,0,0,1) Matrix(271,-84,442,-137) -> Matrix(1,0,0,1) Matrix(205,-72,578,-203) -> Matrix(1,-6,0,1) Matrix(205,-74,374,-135) -> Matrix(1,0,0,1) Matrix(883,-326,1292,-477) -> Matrix(1,2,0,1) Matrix(1769,-656,3298,-1223) -> Matrix(1,2,-2,-3) Matrix(477,-178,544,-203) -> Matrix(3,2,-2,-1) Matrix(11153,-4224,17952,-6799) -> Matrix(1,2,-2,-3) Matrix(1427,-542,1972,-749) -> Matrix(1,2,0,1) Matrix(1223,-474,2108,-817) -> Matrix(1,0,-4,1) Matrix(137,-54,170,-67) -> Matrix(1,-2,0,1) Matrix(1293,-536,1802,-747) -> Matrix(1,4,2,9) Matrix(3741,-1562,5372,-2243) -> Matrix(1,2,0,1) Matrix(8297,-3468,14314,-5983) -> Matrix(1,2,-2,-3) Matrix(5031,-2108,6494,-2721) -> Matrix(1,2,6,13) Matrix(1291,-542,2108,-885) -> Matrix(1,2,-2,-3) Matrix(407,-172,646,-273) -> Matrix(1,2,-2,-3) Matrix(339,-146,476,-205) -> Matrix(1,2,2,5) Matrix(1087,-478,1394,-613) -> Matrix(5,6,4,5) Matrix(273,-128,578,-271) -> Matrix(1,-2,0,1) Matrix(545,-286,646,-339) -> Matrix(1,0,2,1) Matrix(1293,-692,1904,-1019) -> Matrix(1,0,0,1) Matrix(2719,-1498,4692,-2585) -> Matrix(1,2,-2,-3) Matrix(2583,-1492,3298,-1905) -> Matrix(9,2,4,1) Matrix(815,-474,1054,-613) -> Matrix(1,0,2,1) Matrix(341,-200,578,-339) -> Matrix(1,0,6,1) Matrix(1155,-698,1802,-1089) -> Matrix(1,2,-4,-7) Matrix(8841,-5408,14450,-8839) -> Matrix(11,12,-12,-13) Matrix(681,-422,986,-611) -> Matrix(3,2,-2,-1) Matrix(1971,-1226,2516,-1565) -> Matrix(5,2,2,1) Matrix(9247,-5818,14484,-9113) -> Matrix(3,2,-8,-5) Matrix(2857,-1832,3604,-2311) -> Matrix(33,8,4,1) Matrix(2857,-1834,3706,-2379) -> Matrix(1,0,6,1) Matrix(1019,-698,1292,-885) -> Matrix(1,2,0,1) Matrix(747,-518,884,-613) -> Matrix(1,0,2,1) Matrix(409,-288,578,-407) -> Matrix(1,0,8,1) Matrix(8705,-6292,11288,-8159) -> Matrix(5,-6,6,-7) Matrix(953,-750,1122,-883) -> Matrix(1,0,0,1) Matrix(477,-392,578,-475) -> Matrix(1,2,-2,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 68 Degree of the the map X: 68 Degree of the the map Y: 288 ----------------------------------------------------------------------- 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.