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): 2016 Minimal number of generators: 337 Number of equivalence classes of cusps: 96 Genus: 121 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -10/1 -8/1 -20/3 -13/2 -6/1 -16/3 -24/5 -14/3 -13/3 -4/1 -18/5 -13/4 -39/14 -13/5 -12/5 -13/6 -2/1 -13/7 -13/8 -39/25 -26/17 -13/9 -13/10 -13/11 -26/23 0/1 1/1 13/11 26/21 13/10 26/19 13/9 3/2 39/25 13/8 130/79 26/15 13/7 2/1 13/6 104/47 26/11 208/87 12/5 5/2 130/51 13/5 208/79 52/19 39/14 26/9 3/1 13/4 104/31 52/15 7/2 104/29 18/5 26/7 208/55 4/1 25/6 21/5 13/3 22/5 9/2 23/5 14/3 52/11 19/4 24/5 5/1 26/5 21/4 16/3 27/5 11/2 17/3 23/4 52/9 6/1 19/3 13/2 20/3 7/1 22/3 37/5 52/7 15/2 8/1 17/2 26/3 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -10/1 -2/1 0/1 -9/1 1/1 -8/1 -2/1 -15/2 -5/2 -7/1 -3/1 -20/3 0/1 -13/2 1/0 -32/5 -2/1 -19/3 -3/1 -6/1 -2/1 0/1 -17/3 -1/1 -11/2 1/0 -16/3 -2/1 -37/7 -1/1 -21/4 -5/4 -26/5 -1/1 -5/1 -1/1 -24/5 -2/3 -43/9 -3/5 -19/4 -1/2 -14/3 -2/1 0/1 -51/11 -1/1 -37/8 -1/2 -23/5 -1/1 -9/2 1/0 -31/7 -1/1 -53/12 1/0 -22/5 -2/1 0/1 -13/3 -1/1 -17/4 -1/2 -21/5 -1/1 -25/6 -1/6 -4/1 0/1 -27/7 -1/5 -23/6 1/2 -19/5 1/1 -53/14 1/0 -87/23 -1/1 -34/9 0/1 2/1 -15/4 1/0 -26/7 1/0 -11/3 -1/1 -29/8 -3/2 -18/5 -2/3 0/1 -25/7 3/1 -32/9 -2/1 -7/2 -1/2 -31/9 1/3 -24/7 2/3 -41/12 1/0 -17/5 1/1 -27/8 5/2 -64/19 -2/1 -37/11 1/1 -47/14 1/0 -10/3 0/1 2/1 -43/13 -1/1 -33/10 1/0 -23/7 3/1 -13/4 1/0 -16/5 -2/1 -51/16 1/0 -35/11 -1/1 -19/6 1/0 -3/1 1/1 -20/7 -4/1 -37/13 -3/1 -17/6 1/0 -31/11 -3/1 -45/16 -13/6 -14/5 -2/1 -4/3 -53/19 -1/1 -39/14 -1/1 -64/23 -6/7 -25/9 -3/5 -11/4 -1/2 -30/11 0/1 2/5 -49/18 3/4 -19/7 1/1 -46/17 -2/1 0/1 -73/27 -1/1 -27/10 1/4 -35/13 1/1 -8/3 2/1 -37/14 5/2 -29/11 3/1 -79/30 31/8 -50/19 4/1 22/5 -21/8 1/0 -13/5 1/0 -31/12 1/0 -49/19 -19/3 -67/26 1/0 -18/7 -6/1 -4/1 -23/9 -1/1 -51/20 1/0 -130/51 1/0 -79/31 -15/1 -28/11 -4/1 -5/2 1/0 -37/15 -1/1 -32/13 -2/1 -27/11 3/1 -49/20 -7/2 -22/9 -2/1 0/1 -17/7 -1/1 -46/19 -2/3 0/1 -29/12 1/2 -41/17 1/1 -53/22 1/0 -12/5 0/1 -55/23 9/5 -98/41 2/1 16/7 -43/18 1/0 -31/13 3/1 -50/21 4/1 14/3 -69/29 5/1 -19/8 1/0 -26/11 1/0 -7/3 -5/1 -37/16 -9/2 -30/13 -4/1 -10/3 -53/23 -3/1 -23/10 1/0 -16/7 -2/1 -41/18 -5/2 -25/11 -13/5 -34/15 -16/7 -2/1 -9/4 -3/2 -29/13 -1/1 -20/9 0/1 -51/23 -1/1 -31/14 -1/2 -42/19 0/1 2/1 -53/24 1/0 -11/5 -1/1 -24/11 2/1 -13/6 1/0 -28/13 -4/1 -15/7 -3/1 -17/8 1/0 -2/1 -2/1 0/1 -17/9 -1/1 -15/8 -3/2 -13/7 -1/1 -37/20 -3/4 -61/33 -3/5 -24/13 -2/3 -11/6 1/0 -42/23 -2/3 0/1 -73/40 -1/4 -104/57 0/1 -31/17 1/1 -51/28 1/0 -71/39 -1/1 -20/11 0/1 -9/5 -3/1 -25/14 -13/8 -16/9 -2/1 -39/22 -3/2 -23/13 -1/1 -53/30 -3/2 -30/17 -10/7 -4/3 -7/4 -5/4 -26/15 -1/1 -19/11 -1/1 -69/40 -5/6 -50/29 -14/17 -4/5 -31/18 -3/4 -43/25 -1/1 -98/57 -16/23 -2/3 -153/89 -25/37 -208/121 -2/3 -55/32 -9/14 -12/7 0/1 -29/17 -1/3 -17/10 1/0 -39/23 -1/1 -22/13 -2/1 0/1 -27/16 -3/4 -5/3 -1/1 -28/17 -4/3 -79/48 -15/14 -130/79 -1/1 -51/31 -1/1 -23/14 1/0 -18/11 -4/3 -6/5 -13/8 -1/1 -34/21 -10/11 -8/9 -55/34 -23/26 -131/81 -57/65 -76/47 -20/23 -21/13 -1/1 -50/31 -22/27 -4/5 -129/80 -53/66 -208/129 -4/5 -79/49 -31/39 -29/18 -3/4 -37/23 -5/7 -8/5 -2/3 -27/17 -1/5 -73/46 1/0 -119/75 -1/1 -46/29 -2/1 0/1 -19/12 -1/2 -49/31 -3/7 -79/50 -5/16 -30/19 -2/7 0/1 -41/26 -1/8 -52/33 0/1 -11/7 1/1 -25/16 3/2 -64/41 6/1 -39/25 1/0 -92/59 -8/1 -53/34 1/0 -14/9 -4/1 -2/1 -31/20 -3/2 -17/11 -1/1 -37/24 -3/2 -20/13 -4/3 -23/15 -1/1 -26/17 -1/1 -3/2 -1/2 -19/13 -1/1 -35/24 1/0 -51/35 -1/1 -16/11 -2/1 -13/9 -1/1 -36/25 -4/5 -23/16 -3/4 -33/23 -1/1 -43/30 1/0 -10/7 -2/3 0/1 -57/40 -1/2 -104/73 0/1 -47/33 -1/1 -37/26 -1/2 -101/71 -1/5 -64/45 -2/1 -27/19 -5/7 -44/31 -4/7 -61/43 -7/13 -78/55 -1/2 -17/12 -1/2 -24/17 -2/5 -79/56 -9/28 -55/39 -5/17 -31/22 -1/4 -38/27 -2/13 0/1 -45/32 -1/14 -52/37 0/1 -7/5 1/1 -32/23 -2/1 -89/64 1/0 -57/41 -1/1 -25/18 -3/4 -43/31 -1/5 -104/75 0/1 -61/44 1/6 -18/13 0/1 2/1 -29/21 -3/1 -40/29 -2/1 -91/66 -1/1 -51/37 -1/1 -11/8 1/0 -26/19 -1/1 -15/11 -1/1 -64/47 -2/5 -49/36 1/2 -34/25 -2/3 0/1 -121/89 -1/3 -208/153 0/1 -87/64 1/0 -53/39 -1/1 -19/14 -1/2 -23/17 -1/3 -27/20 1/4 -4/3 0/1 -25/19 1/5 -21/16 1/0 -17/13 1/1 -13/10 1/0 -35/27 -1/1 -22/17 -2/1 0/1 -53/41 -1/1 -31/24 1/0 -9/7 -1/1 -32/25 2/1 -55/43 7/1 -78/61 1/0 -23/18 1/0 -37/29 1/1 -88/69 2/1 -51/40 1/0 -14/11 -2/1 0/1 -33/26 -1/2 -52/41 0/1 -19/15 1/1 -43/34 3/2 -110/87 2/1 8/3 -67/53 3/1 -24/19 2/1 -5/4 1/0 -26/21 1/0 -21/17 -5/1 -58/47 -6/1 -4/1 -95/77 -11/3 -37/30 1/0 -53/43 -3/1 -16/13 -2/1 -27/22 -1/2 -11/9 -1/1 -28/23 -4/1 -17/14 1/0 -23/19 -7/3 -52/43 -2/1 -29/24 -7/4 -6/5 -2/1 0/1 -19/16 -3/2 -13/11 -1/1 -33/28 1/0 -53/45 -1/1 -20/17 0/1 -7/6 -3/2 -22/19 -4/1 -2/1 -37/32 -9/4 -52/45 -2/1 -15/13 -5/3 -8/7 -2/1 -17/15 -1/1 -26/23 -1/1 -9/8 -1/2 -10/9 -2/1 0/1 -11/10 -3/2 -1/1 -1/1 0/1 0/1 1/1 1/1 10/9 0/1 2/1 9/8 1/2 8/7 2/1 15/13 5/3 7/6 3/2 20/17 0/1 13/11 1/1 32/27 2/1 19/16 3/2 6/5 0/1 2/1 17/14 1/0 11/9 1/1 16/13 2/1 37/30 1/0 21/17 5/1 26/21 1/0 5/4 1/0 24/19 -2/1 43/34 -3/2 19/15 -1/1 14/11 0/1 2/1 51/40 1/0 37/29 -1/1 23/18 1/0 9/7 1/1 31/24 1/0 53/41 1/1 22/17 0/1 2/1 13/10 1/0 17/13 -1/1 21/16 1/0 25/19 -1/5 4/3 0/1 27/20 -1/4 23/17 1/3 19/14 1/2 53/39 1/1 87/64 1/0 34/25 0/1 2/3 15/11 1/1 26/19 1/1 11/8 1/0 29/21 3/1 18/13 -2/1 0/1 25/18 3/4 32/23 2/1 7/5 -1/1 31/22 1/4 24/17 2/5 41/29 1/1 17/12 1/2 27/19 5/7 64/45 2/1 37/26 1/2 47/33 1/1 10/7 0/1 2/3 43/30 1/0 33/23 1/1 23/16 3/4 13/9 1/1 16/11 2/1 51/35 1/1 35/24 1/0 19/13 1/1 3/2 1/2 20/13 4/3 37/24 3/2 17/11 1/1 31/20 3/2 45/29 13/7 14/9 2/1 4/1 53/34 1/0 39/25 1/0 64/41 -6/1 25/16 -3/2 11/7 -1/1 30/19 0/1 2/7 49/31 3/7 19/12 1/2 46/29 0/1 2/1 73/46 1/0 27/17 1/5 35/22 1/2 8/5 2/3 37/23 5/7 29/18 3/4 79/49 31/39 50/31 4/5 22/27 21/13 1/1 13/8 1/1 31/19 1/1 49/30 19/16 67/41 1/1 18/11 6/5 4/3 23/14 1/0 51/31 1/1 130/79 1/1 79/48 15/14 28/17 4/3 5/3 1/1 37/22 1/0 32/19 2/1 27/16 3/4 49/29 7/5 22/13 0/1 2/1 17/10 1/0 46/27 -2/1 0/1 29/17 1/3 41/24 1/2 53/31 1/1 12/7 0/1 55/32 9/14 98/57 2/3 16/23 43/25 1/1 31/18 3/4 50/29 4/5 14/17 69/40 5/6 19/11 1/1 26/15 1/1 7/4 5/4 37/21 9/7 30/17 4/3 10/7 53/30 3/2 23/13 1/1 16/9 2/1 41/23 5/3 25/14 13/8 34/19 16/9 2/1 9/5 3/1 29/16 1/0 20/11 0/1 51/28 1/0 31/17 -1/1 42/23 0/1 2/3 53/29 1/1 11/6 1/0 24/13 2/3 13/7 1/1 28/15 4/3 15/8 3/2 17/9 1/1 2/1 0/1 2/1 17/8 1/0 15/7 3/1 13/6 1/0 37/17 -3/1 61/28 -3/2 24/11 -2/1 11/5 1/1 42/19 -2/1 0/1 73/33 -1/3 104/47 0/1 31/14 1/2 51/23 1/1 71/32 1/0 20/9 0/1 9/4 3/2 25/11 13/5 16/7 2/1 39/17 3/1 23/10 1/0 53/23 3/1 30/13 10/3 4/1 7/3 5/1 26/11 1/0 19/8 1/0 69/29 -5/1 50/21 -14/3 -4/1 31/13 -3/1 43/18 1/0 98/41 -16/7 -2/1 153/64 -25/12 208/87 -2/1 55/23 -9/5 12/5 0/1 29/12 -1/2 17/7 1/1 39/16 1/0 22/9 0/1 2/1 27/11 -3/1 5/2 1/0 28/11 4/1 79/31 15/1 130/51 1/0 51/20 1/0 23/9 1/1 18/7 4/1 6/1 13/5 1/0 34/13 -10/1 -8/1 55/21 -23/3 131/50 -57/8 76/29 -20/3 21/8 1/0 50/19 -22/5 -4/1 129/49 -53/13 208/79 -4/1 79/30 -31/8 29/11 -3/1 37/14 -5/2 8/3 -2/1 27/10 -1/4 73/27 1/1 119/44 1/0 46/17 0/1 2/1 19/7 -1/1 49/18 -3/4 79/29 -5/11 30/11 -2/5 0/1 41/15 -1/7 52/19 0/1 11/4 1/2 25/9 3/5 64/23 6/7 39/14 1/1 92/33 8/7 53/19 1/1 14/5 4/3 2/1 31/11 3/1 17/6 1/0 37/13 3/1 20/7 4/1 23/8 1/0 26/9 1/0 3/1 -1/1 19/6 1/0 35/11 1/1 51/16 1/0 16/5 2/1 13/4 1/0 36/11 -4/1 23/7 -3/1 33/10 1/0 43/13 1/1 10/3 -2/1 0/1 57/17 -1/1 104/31 0/1 47/14 1/0 37/11 -1/1 101/30 -1/4 64/19 2/1 27/8 -5/2 44/13 -4/3 61/18 -7/6 78/23 -1/1 17/5 -1/1 24/7 -2/3 79/23 -9/19 55/16 -5/12 31/9 -1/3 38/11 -2/11 0/1 45/13 -1/13 52/15 0/1 7/2 1/2 32/9 2/1 89/25 1/1 57/16 1/0 25/7 -3/1 43/12 -1/4 104/29 0/1 61/17 1/7 18/5 0/1 2/3 29/8 3/2 40/11 2/1 91/25 1/0 51/14 1/0 11/3 1/1 26/7 1/0 15/4 1/0 64/17 -2/3 49/13 1/3 34/9 -2/1 0/1 121/32 -1/2 208/55 0/1 87/23 1/1 53/14 1/0 19/5 -1/1 23/6 -1/2 27/7 1/5 4/1 0/1 25/6 1/6 21/5 1/1 17/4 1/2 13/3 1/1 35/8 1/0 22/5 0/1 2/1 53/12 1/0 31/7 1/1 9/2 1/0 32/7 2/3 55/12 7/8 78/17 1/1 23/5 1/1 37/8 1/2 88/19 2/3 51/11 1/1 14/3 0/1 2/1 33/7 -1/1 52/11 0/1 19/4 1/2 43/9 3/5 110/23 2/3 8/11 67/14 3/4 24/5 2/3 5/1 1/1 26/5 1/1 21/4 5/4 58/11 6/5 4/3 95/18 11/8 37/7 1/1 53/10 3/2 16/3 2/1 27/5 -1/1 11/2 1/0 28/5 4/3 17/3 1/1 23/4 7/4 52/9 2/1 29/5 7/3 6/1 0/1 2/1 19/3 3/1 13/2 1/0 33/5 1/1 53/8 1/0 20/3 0/1 7/1 3/1 22/3 4/3 2/1 37/5 9/5 52/7 2/1 15/2 5/2 8/1 2/1 17/2 1/0 26/3 1/0 9/1 -1/1 10/1 0/1 2/1 11/1 3/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(53,572,-24,-259) (-10/1,1/0) -> (-42/19,-53/24) Hyperbolic Matrix(53,520,16,157) (-10/1,-9/1) -> (43/13,10/3) Hyperbolic Matrix(105,884,-74,-623) (-9/1,-8/1) -> (-44/31,-61/43) Hyperbolic Matrix(53,416,20,157) (-8/1,-15/2) -> (37/14,8/3) Hyperbolic Matrix(51,364,-22,-157) (-15/2,-7/1) -> (-7/3,-37/16) Hyperbolic Matrix(53,364,38,261) (-7/1,-20/3) -> (32/23,7/5) Hyperbolic Matrix(103,676,-16,-105) (-20/3,-13/2) -> (-13/2,-32/5) Parabolic Matrix(415,2652,-228,-1457) (-32/5,-19/3) -> (-71/39,-20/11) Hyperbolic Matrix(157,988,58,365) (-19/3,-6/1) -> (46/17,19/7) Hyperbolic Matrix(155,884,-64,-365) (-6/1,-17/3) -> (-17/7,-46/19) Hyperbolic Matrix(157,884,-46,-259) (-17/3,-11/2) -> (-41/12,-17/5) Hyperbolic Matrix(155,832,-68,-365) (-11/2,-16/3) -> (-16/7,-41/18) Hyperbolic Matrix(727,3848,-570,-3017) (-16/3,-37/7) -> (-37/29,-88/69) Hyperbolic Matrix(987,5200,-622,-3277) (-37/7,-21/4) -> (-73/46,-119/75) Hyperbolic Matrix(209,1092,40,209) (-21/4,-26/5) -> (26/5,21/4) Hyperbolic Matrix(51,260,10,51) (-26/5,-5/1) -> (5/1,26/5) Hyperbolic Matrix(53,260,32,157) (-5/1,-24/5) -> (28/17,5/3) Hyperbolic Matrix(521,2496,-282,-1351) (-24/5,-43/9) -> (-61/33,-24/13) Hyperbolic Matrix(469,2236,142,677) (-43/9,-19/4) -> (33/10,43/13) Hyperbolic Matrix(155,728,-122,-573) (-19/4,-14/3) -> (-14/11,-33/26) Hyperbolic Matrix(313,1456,112,521) (-14/3,-51/11) -> (53/19,14/5) Hyperbolic Matrix(831,3848,-674,-3121) (-51/11,-37/8) -> (-37/30,-53/43) Hyperbolic Matrix(417,1924,158,729) (-37/8,-23/5) -> (29/11,37/14) Hyperbolic Matrix(103,468,-46,-209) (-23/5,-9/2) -> (-9/4,-29/13) Hyperbolic Matrix(363,1612,152,675) (-9/2,-31/7) -> (31/13,43/18) Hyperbolic Matrix(729,3224,400,1769) (-31/7,-53/12) -> (51/28,31/17) Hyperbolic Matrix(625,2756,354,1561) (-53/12,-22/5) -> (30/17,53/30) Hyperbolic Matrix(261,1144,-154,-675) (-22/5,-13/3) -> (-39/23,-22/13) Hyperbolic Matrix(207,884,-122,-521) (-13/3,-17/4) -> (-17/10,-39/23) Hyperbolic Matrix(209,884,74,313) (-17/4,-21/5) -> (31/11,17/6) Hyperbolic Matrix(573,2392,212,885) (-21/5,-25/6) -> (27/10,73/27) Hyperbolic Matrix(51,208,38,155) (-25/6,-4/1) -> (4/3,27/20) Hyperbolic Matrix(53,208,40,157) (-4/1,-27/7) -> (25/19,4/3) Hyperbolic Matrix(677,2600,420,1613) (-27/7,-23/6) -> (29/18,79/49) Hyperbolic Matrix(313,1196,218,833) (-23/6,-19/5) -> (33/23,23/16) Hyperbolic Matrix(1249,4732,-686,-2599) (-19/5,-53/14) -> (-51/28,-71/39) Hyperbolic Matrix(1663,6292,522,1975) (-53/14,-87/23) -> (35/11,51/16) Hyperbolic Matrix(1871,7072,-1376,-5201) (-87/23,-34/9) -> (-34/25,-121/89) Hyperbolic Matrix(675,2548,-262,-989) (-34/9,-15/4) -> (-67/26,-18/7) Hyperbolic Matrix(209,780,56,209) (-15/4,-26/7) -> (26/7,15/4) Hyperbolic Matrix(155,572,42,155) (-26/7,-11/3) -> (11/3,26/7) Hyperbolic Matrix(415,1508,-172,-625) (-11/3,-29/8) -> (-29/12,-41/17) Hyperbolic Matrix(259,936,158,571) (-29/8,-18/5) -> (18/11,23/14) Hyperbolic Matrix(363,1300,-160,-573) (-18/5,-25/7) -> (-25/11,-34/15) Hyperbolic Matrix(467,1664,-190,-677) (-25/7,-32/9) -> (-32/13,-27/11) Hyperbolic Matrix(103,364,88,311) (-32/9,-7/2) -> (7/6,20/17) Hyperbolic Matrix(467,1612,-166,-573) (-7/2,-31/9) -> (-31/11,-45/16) Hyperbolic Matrix(831,2860,-514,-1769) (-31/9,-24/7) -> (-76/47,-21/13) Hyperbolic Matrix(365,1248,198,677) (-24/7,-41/12) -> (11/6,24/13) Hyperbolic Matrix(415,1404,-154,-521) (-17/5,-27/8) -> (-27/10,-35/13) Hyperbolic Matrix(987,3328,632,2131) (-27/8,-64/19) -> (64/41,25/16) Hyperbolic Matrix(989,3328,-726,-2443) (-64/19,-37/11) -> (-15/11,-64/47) Hyperbolic Matrix(573,1924,-232,-779) (-37/11,-47/14) -> (-5/2,-37/15) Hyperbolic Matrix(311,1040,-218,-729) (-47/14,-10/3) -> (-10/7,-57/40) Hyperbolic Matrix(157,520,16,53) (-10/3,-43/13) -> (9/1,10/1) Hyperbolic Matrix(677,2236,142,469) (-43/13,-33/10) -> (19/4,43/9) Hyperbolic Matrix(363,1196,268,883) (-33/10,-23/7) -> (23/17,19/14) Hyperbolic Matrix(365,1196,-206,-675) (-23/7,-13/4) -> (-39/22,-23/13) Hyperbolic Matrix(259,832,-146,-469) (-13/4,-16/5) -> (-16/9,-39/22) Hyperbolic Matrix(521,1664,98,313) (-16/5,-51/16) -> (53/10,16/3) Hyperbolic Matrix(1975,6292,522,1663) (-51/16,-35/11) -> (87/23,53/14) Hyperbolic Matrix(623,1976,262,831) (-35/11,-19/6) -> (19/8,69/29) Hyperbolic Matrix(313,988,198,625) (-19/6,-3/1) -> (49/31,19/12) Hyperbolic Matrix(417,1196,-326,-935) (-3/1,-20/7) -> (-32/25,-55/43) Hyperbolic Matrix(675,1924,-274,-781) (-20/7,-37/13) -> (-37/15,-32/13) Hyperbolic Matrix(311,884,146,415) (-37/13,-17/6) -> (17/8,15/7) Hyperbolic Matrix(313,884,74,209) (-17/6,-31/11) -> (21/5,17/4) Hyperbolic Matrix(833,2340,-592,-1663) (-45/16,-14/5) -> (-38/27,-45/32) Hyperbolic Matrix(521,1456,112,313) (-14/5,-53/19) -> (51/11,14/3) Hyperbolic Matrix(2443,6812,-1772,-4941) (-53/19,-39/14) -> (-91/66,-51/37) Hyperbolic Matrix(2653,7384,-1924,-5355) (-39/14,-64/23) -> (-40/29,-91/66) Hyperbolic Matrix(1197,3328,842,2341) (-64/23,-25/9) -> (27/19,64/45) Hyperbolic Matrix(469,1300,-206,-571) (-25/9,-11/4) -> (-41/18,-25/11) Hyperbolic Matrix(571,1560,-362,-989) (-11/4,-30/11) -> (-30/19,-41/26) Hyperbolic Matrix(935,2548,-382,-1041) (-30/11,-49/18) -> (-49/20,-22/9) Hyperbolic Matrix(363,988,248,675) (-49/18,-19/7) -> (19/13,3/2) Hyperbolic Matrix(365,988,58,157) (-19/7,-46/17) -> (6/1,19/3) Hyperbolic Matrix(1923,5200,-1558,-4213) (-46/17,-73/27) -> (-21/17,-58/47) Hyperbolic Matrix(885,2392,212,573) (-73/27,-27/10) -> (25/6,21/5) Hyperbolic Matrix(155,416,-136,-365) (-35/13,-8/3) -> (-8/7,-17/15) Hyperbolic Matrix(157,416,20,53) (-8/3,-37/14) -> (15/2,8/1) Hyperbolic Matrix(729,1924,158,417) (-37/14,-29/11) -> (23/5,37/8) Hyperbolic Matrix(987,2600,730,1923) (-29/11,-79/30) -> (27/20,23/17) Hyperbolic Matrix(3951,10400,-2450,-6449) (-79/30,-50/19) -> (-50/31,-129/80) Hyperbolic Matrix(989,2600,574,1509) (-50/19,-21/8) -> (31/18,50/29) Hyperbolic Matrix(259,676,-100,-261) (-21/8,-13/5) -> (-13/5,-31/12) Parabolic Matrix(1249,3224,-886,-2287) (-31/12,-49/19) -> (-55/39,-31/22) Hyperbolic Matrix(3329,8580,-2340,-6031) (-49/19,-67/26) -> (-37/26,-101/71) Hyperbolic Matrix(365,936,264,677) (-18/7,-23/9) -> (29/21,18/13) Hyperbolic Matrix(937,2392,530,1353) (-23/9,-51/20) -> (53/30,23/13) Hyperbolic Matrix(5201,13260,2040,5201) (-51/20,-130/51) -> (130/51,51/20) Hyperbolic Matrix(8059,20540,3162,8059) (-130/51,-79/31) -> (79/31,130/51) Hyperbolic Matrix(1613,4108,470,1197) (-79/31,-28/11) -> (24/7,79/23) Hyperbolic Matrix(103,260,82,207) (-28/11,-5/2) -> (5/4,24/19) Hyperbolic Matrix(3225,7904,-1994,-4887) (-27/11,-49/20) -> (-55/34,-131/81) Hyperbolic Matrix(469,1144,-362,-883) (-22/9,-17/7) -> (-35/27,-22/17) Hyperbolic Matrix(623,1508,-516,-1249) (-46/19,-29/12) -> (-29/24,-6/5) Hyperbolic Matrix(1143,2756,-518,-1249) (-41/17,-53/22) -> (-53/24,-11/5) Hyperbolic Matrix(2289,5512,-1468,-3535) (-53/22,-12/5) -> (-92/59,-53/34) Hyperbolic Matrix(1977,4732,-1390,-3327) (-12/5,-55/23) -> (-101/71,-64/45) Hyperbolic Matrix(8527,20384,-4960,-11857) (-55/23,-98/41) -> (-98/57,-153/89) Hyperbolic Matrix(3743,8944,-2960,-7073) (-98/41,-43/18) -> (-43/34,-110/87) Hyperbolic Matrix(675,1612,152,363) (-43/18,-31/13) -> (31/7,9/2) Hyperbolic Matrix(1091,2600,676,1611) (-31/13,-50/21) -> (50/31,21/13) Hyperbolic Matrix(415,988,218,519) (-50/21,-69/29) -> (17/9,2/1) Hyperbolic Matrix(831,1976,262,623) (-69/29,-19/8) -> (19/6,35/11) Hyperbolic Matrix(417,988,176,417) (-19/8,-26/11) -> (26/11,19/8) Hyperbolic Matrix(155,364,66,155) (-26/11,-7/3) -> (7/3,26/11) Hyperbolic Matrix(833,1924,-720,-1663) (-37/16,-30/13) -> (-22/19,-37/32) Hyperbolic Matrix(1195,2756,924,2131) (-30/13,-53/23) -> (53/41,22/17) Hyperbolic Matrix(1039,2392,632,1455) (-53/23,-23/10) -> (23/14,51/31) Hyperbolic Matrix(521,1196,-362,-831) (-23/10,-16/7) -> (-36/25,-23/16) Hyperbolic Matrix(987,2236,-712,-1613) (-34/15,-9/4) -> (-61/44,-18/13) Hyperbolic Matrix(467,1040,-304,-677) (-29/13,-20/9) -> (-20/13,-23/15) Hyperbolic Matrix(937,2080,-796,-1767) (-20/9,-51/23) -> (-53/45,-20/17) Hyperbolic Matrix(1455,3224,1126,2495) (-51/23,-31/14) -> (31/24,53/41) Hyperbolic Matrix(1975,4368,-1082,-2393) (-31/14,-42/19) -> (-42/23,-73/40) Hyperbolic Matrix(571,1248,404,883) (-11/5,-24/11) -> (24/17,41/29) Hyperbolic Matrix(311,676,-144,-313) (-24/11,-13/6) -> (-13/6,-28/13) Parabolic Matrix(1039,2236,-822,-1769) (-28/13,-15/7) -> (-67/53,-24/19) Hyperbolic Matrix(415,884,146,311) (-15/7,-17/8) -> (17/6,37/13) Hyperbolic Matrix(469,988,272,573) (-17/8,-2/1) -> (50/29,69/40) Hyperbolic Matrix(519,988,218,415) (-2/1,-17/9) -> (69/29,50/21) Hyperbolic Matrix(469,884,304,573) (-17/9,-15/8) -> (37/24,17/11) Hyperbolic Matrix(363,676,-196,-365) (-15/8,-13/7) -> (-13/7,-37/20) Parabolic Matrix(3121,5772,-2530,-4679) (-37/20,-61/33) -> (-95/77,-37/30) Hyperbolic Matrix(311,572,56,103) (-24/13,-11/6) -> (11/2,28/5) Hyperbolic Matrix(313,572,-284,-519) (-11/6,-42/23) -> (-10/9,-11/10) Hyperbolic Matrix(5927,10816,2678,4887) (-73/40,-104/57) -> (104/47,31/14) Hyperbolic Matrix(5929,10816,2680,4889) (-104/57,-31/17) -> (73/33,104/47) Hyperbolic Matrix(1769,3224,400,729) (-31/17,-51/28) -> (53/12,31/7) Hyperbolic Matrix(259,468,-202,-365) (-20/11,-9/5) -> (-9/7,-32/25) Hyperbolic Matrix(727,1300,-524,-937) (-9/5,-25/14) -> (-25/18,-43/31) Hyperbolic Matrix(467,832,-380,-677) (-25/14,-16/9) -> (-16/13,-27/22) Hyperbolic Matrix(1353,2392,530,937) (-23/13,-53/30) -> (51/20,23/9) Hyperbolic Matrix(1561,2756,354,625) (-53/30,-30/17) -> (22/5,53/12) Hyperbolic Matrix(207,364,-178,-313) (-30/17,-7/4) -> (-7/6,-22/19) Hyperbolic Matrix(209,364,120,209) (-7/4,-26/15) -> (26/15,7/4) Hyperbolic Matrix(571,988,330,571) (-26/15,-19/11) -> (19/11,26/15) Hyperbolic Matrix(1145,1976,784,1353) (-19/11,-69/40) -> (35/24,19/13) Hyperbolic Matrix(573,988,272,469) (-69/40,-50/29) -> (2/1,17/8) Hyperbolic Matrix(1509,2600,574,989) (-50/29,-31/18) -> (21/8,50/19) Hyperbolic Matrix(937,1612,726,1249) (-31/18,-43/25) -> (9/7,31/24) Hyperbolic Matrix(6865,11804,-5564,-9567) (-43/25,-98/57) -> (-58/47,-95/77) Hyperbolic Matrix(25167,43264,10526,18095) (-153/89,-208/121) -> (208/87,55/23) Hyperbolic Matrix(25169,43264,10528,18097) (-208/121,-55/32) -> (153/64,208/87) Hyperbolic Matrix(2391,4108,-1756,-3017) (-55/32,-12/7) -> (-64/47,-49/36) Hyperbolic Matrix(883,1508,-640,-1093) (-12/7,-29/17) -> (-29/21,-40/29) Hyperbolic Matrix(519,884,-428,-729) (-29/17,-17/10) -> (-17/14,-23/19) Hyperbolic Matrix(1507,2548,-954,-1613) (-22/13,-27/16) -> (-79/50,-30/19) Hyperbolic Matrix(987,1664,-710,-1197) (-27/16,-5/3) -> (-57/41,-25/18) Hyperbolic Matrix(157,260,32,53) (-5/3,-28/17) -> (24/5,5/1) Hyperbolic Matrix(5875,9672,2242,3691) (-28/17,-79/48) -> (131/50,76/29) Hyperbolic Matrix(12481,20540,7584,12481) (-79/48,-130/79) -> (130/79,79/48) Hyperbolic Matrix(8059,13260,4898,8059) (-130/79,-51/31) -> (51/31,130/79) Hyperbolic Matrix(1455,2392,632,1039) (-51/31,-23/14) -> (23/10,53/23) Hyperbolic Matrix(571,936,158,259) (-23/14,-18/11) -> (18/5,29/8) Hyperbolic Matrix(415,676,-256,-417) (-18/11,-13/8) -> (-13/8,-34/21) Parabolic Matrix(2185,3536,-1606,-2599) (-34/21,-55/34) -> (-49/36,-34/25) Hyperbolic Matrix(5981,9672,2348,3797) (-131/81,-76/47) -> (28/11,79/31) Hyperbolic Matrix(1611,2600,676,1091) (-21/13,-50/31) -> (50/21,31/13) Hyperbolic Matrix(26831,43264,10190,16431) (-129/80,-208/129) -> (208/79,79/30) Hyperbolic Matrix(26833,43264,10192,16433) (-208/129,-79/49) -> (129/49,208/79) Hyperbolic Matrix(1613,2600,420,677) (-79/49,-29/18) -> (23/6,27/7) Hyperbolic Matrix(1195,1924,936,1507) (-29/18,-37/23) -> (37/29,23/18) Hyperbolic Matrix(259,416,226,363) (-37/23,-8/5) -> (8/7,15/13) Hyperbolic Matrix(883,1404,-622,-989) (-8/5,-27/17) -> (-27/19,-44/31) Hyperbolic Matrix(1507,2392,1146,1819) (-27/17,-73/46) -> (21/16,25/19) Hyperbolic Matrix(10193,16172,-8062,-12791) (-119/75,-46/29) -> (-110/87,-67/53) Hyperbolic Matrix(623,988,524,831) (-46/29,-19/12) -> (19/16,6/5) Hyperbolic Matrix(625,988,198,313) (-19/12,-49/31) -> (3/1,19/6) Hyperbolic Matrix(5199,8216,-3686,-5825) (-49/31,-79/50) -> (-79/56,-55/39) Hyperbolic Matrix(1715,2704,626,987) (-41/26,-52/33) -> (52/19,11/4) Hyperbolic Matrix(1717,2704,628,989) (-52/33,-11/7) -> (41/15,52/19) Hyperbolic Matrix(365,572,-298,-467) (-11/7,-25/16) -> (-27/22,-11/9) Hyperbolic Matrix(2131,3328,632,987) (-25/16,-64/41) -> (64/19,27/8) Hyperbolic Matrix(3899,6084,-2500,-3901) (-64/41,-39/25) -> (-39/25,-92/59) Parabolic Matrix(935,1456,734,1143) (-53/34,-14/9) -> (14/11,51/40) Hyperbolic Matrix(1039,1612,-738,-1145) (-14/9,-31/20) -> (-31/22,-38/27) Hyperbolic Matrix(571,884,436,675) (-31/20,-17/11) -> (17/13,21/16) Hyperbolic Matrix(573,884,304,469) (-17/11,-37/24) -> (15/8,17/9) Hyperbolic Matrix(1925,2964,-1384,-2131) (-37/24,-20/13) -> (-32/23,-89/64) Hyperbolic Matrix(1561,2392,340,521) (-23/15,-26/17) -> (78/17,23/5) Hyperbolic Matrix(1091,1664,238,363) (-26/17,-3/2) -> (55/12,78/17) Hyperbolic Matrix(675,988,248,363) (-3/2,-19/13) -> (19/7,49/18) Hyperbolic Matrix(1353,1976,784,1145) (-19/13,-35/24) -> (69/40,19/11) Hyperbolic Matrix(4317,6292,3176,4629) (-35/24,-51/35) -> (53/39,87/64) Hyperbolic Matrix(3641,5304,786,1145) (-51/35,-16/11) -> (88/19,51/11) Hyperbolic Matrix(467,676,-324,-469) (-16/11,-13/9) -> (-13/9,-36/25) Parabolic Matrix(833,1196,218,313) (-23/16,-33/23) -> (19/5,23/6) Hyperbolic Matrix(1559,2236,1232,1767) (-33/23,-43/30) -> (43/34,19/15) Hyperbolic Matrix(363,520,326,467) (-43/30,-10/7) -> (10/9,9/8) Hyperbolic Matrix(7591,10816,2262,3223) (-57/40,-104/73) -> (104/31,47/14) Hyperbolic Matrix(7593,10816,2264,3225) (-104/73,-47/33) -> (57/17,104/31) Hyperbolic Matrix(4419,6292,-3178,-4525) (-47/33,-37/26) -> (-89/64,-57/41) Hyperbolic Matrix(2341,3328,842,1197) (-64/45,-27/19) -> (25/9,64/23) Hyperbolic Matrix(1613,2288,184,261) (-61/43,-78/55) -> (26/3,9/1) Hyperbolic Matrix(1247,1768,146,207) (-78/55,-17/12) -> (17/2,26/3) Hyperbolic Matrix(625,884,-514,-727) (-17/12,-24/17) -> (-28/23,-17/14) Hyperbolic Matrix(2911,4108,1768,2495) (-24/17,-79/56) -> (79/48,28/17) Hyperbolic Matrix(1923,2704,554,779) (-45/32,-52/37) -> (52/15,7/2) Hyperbolic Matrix(1925,2704,556,781) (-52/37,-7/5) -> (45/13,52/15) Hyperbolic Matrix(261,364,38,53) (-7/5,-32/23) -> (20/3,7/1) Hyperbolic Matrix(7799,10816,2174,3015) (-43/31,-104/75) -> (104/29,61/17) Hyperbolic Matrix(7801,10816,2176,3017) (-104/75,-61/44) -> (43/12,104/29) Hyperbolic Matrix(677,936,264,365) (-18/13,-29/21) -> (23/9,18/7) Hyperbolic Matrix(415,572,-378,-521) (-51/37,-11/8) -> (-11/10,-1/1) Hyperbolic Matrix(417,572,304,417) (-11/8,-26/19) -> (26/19,11/8) Hyperbolic Matrix(571,780,418,571) (-26/19,-15/11) -> (15/11,26/19) Hyperbolic Matrix(31823,43264,8414,11439) (-121/89,-208/153) -> (208/55,87/23) Hyperbolic Matrix(31825,43264,8416,11441) (-208/153,-87/64) -> (121/32,208/55) Hyperbolic Matrix(4629,6292,3176,4317) (-87/64,-53/39) -> (51/35,35/24) Hyperbolic Matrix(2029,2756,-1722,-2339) (-53/39,-19/14) -> (-33/28,-53/45) Hyperbolic Matrix(883,1196,268,363) (-19/14,-23/17) -> (23/7,33/10) Hyperbolic Matrix(1923,2600,730,987) (-23/17,-27/20) -> (79/30,29/11) Hyperbolic Matrix(155,208,38,51) (-27/20,-4/3) -> (4/1,25/6) Hyperbolic Matrix(157,208,40,53) (-4/3,-25/19) -> (27/7,4/1) Hyperbolic Matrix(1819,2392,1146,1507) (-25/19,-21/16) -> (73/46,27/17) Hyperbolic Matrix(675,884,436,571) (-21/16,-17/13) -> (17/11,31/20) Hyperbolic Matrix(519,676,-400,-521) (-17/13,-13/10) -> (-13/10,-35/27) Parabolic Matrix(2131,2756,924,1195) (-22/17,-53/41) -> (53/23,30/13) Hyperbolic Matrix(2495,3224,1126,1455) (-53/41,-31/24) -> (31/14,51/23) Hyperbolic Matrix(1249,1612,726,937) (-31/24,-9/7) -> (43/25,31/18) Hyperbolic Matrix(1301,1664,448,573) (-55/43,-78/61) -> (26/9,3/1) Hyperbolic Matrix(1871,2392,650,831) (-78/61,-23/18) -> (23/8,26/9) Hyperbolic Matrix(1507,1924,936,1195) (-23/18,-37/29) -> (37/23,29/18) Hyperbolic Matrix(4159,5304,1304,1663) (-88/69,-51/40) -> (51/16,16/5) Hyperbolic Matrix(1143,1456,734,935) (-51/40,-14/11) -> (14/9,53/34) Hyperbolic Matrix(2131,2704,450,571) (-33/26,-52/41) -> (52/11,19/4) Hyperbolic Matrix(2133,2704,452,573) (-52/41,-19/15) -> (33/7,52/11) Hyperbolic Matrix(1767,2236,1232,1559) (-19/15,-43/34) -> (43/30,33/23) Hyperbolic Matrix(207,260,82,103) (-24/19,-5/4) -> (5/2,28/11) Hyperbolic Matrix(209,260,168,209) (-5/4,-26/21) -> (26/21,5/4) Hyperbolic Matrix(883,1092,714,883) (-26/21,-21/17) -> (21/17,26/21) Hyperbolic Matrix(1351,1664,928,1143) (-53/43,-16/13) -> (16/11,51/35) Hyperbolic Matrix(469,572,214,261) (-11/9,-28/23) -> (24/11,11/5) Hyperbolic Matrix(2235,2704,386,467) (-23/19,-52/43) -> (52/9,29/5) Hyperbolic Matrix(2237,2704,388,469) (-52/43,-29/24) -> (23/4,52/9) Hyperbolic Matrix(831,988,524,623) (-6/5,-19/16) -> (19/12,46/29) Hyperbolic Matrix(571,676,-484,-573) (-19/16,-13/11) -> (-13/11,-33/28) Parabolic Matrix(311,364,88,103) (-20/17,-7/6) -> (7/2,32/9) Hyperbolic Matrix(2339,2704,314,363) (-37/32,-52/45) -> (52/7,15/2) Hyperbolic Matrix(2341,2704,316,365) (-52/45,-15/13) -> (37/5,52/7) Hyperbolic Matrix(363,416,226,259) (-15/13,-8/7) -> (8/5,37/23) Hyperbolic Matrix(1561,1768,460,521) (-17/15,-26/23) -> (78/23,17/5) Hyperbolic Matrix(2027,2288,598,675) (-26/23,-9/8) -> (61/18,78/23) Hyperbolic Matrix(467,520,326,363) (-9/8,-10/9) -> (10/7,43/30) Hyperbolic Matrix(1,0,2,1) (-1/1,0/1) -> (0/1,1/1) Parabolic Matrix(519,-572,284,-313) (1/1,10/9) -> (42/23,53/29) Hyperbolic Matrix(779,-884,230,-261) (9/8,8/7) -> (44/13,61/18) Hyperbolic Matrix(313,-364,178,-207) (15/13,7/6) -> (7/4,37/21) Hyperbolic Matrix(573,-676,484,-571) (20/17,13/11) -> (13/11,32/27) Parabolic Matrix(2237,-2652,1008,-1195) (32/27,19/16) -> (71/32,20/9) Hyperbolic Matrix(729,-884,428,-519) (6/5,17/14) -> (17/10,46/27) Hyperbolic Matrix(727,-884,514,-625) (17/14,11/9) -> (41/29,17/12) Hyperbolic Matrix(677,-832,380,-467) (11/9,16/13) -> (16/9,41/23) Hyperbolic Matrix(3121,-3848,674,-831) (16/13,37/30) -> (37/8,88/19) Hyperbolic Matrix(4213,-5200,1558,-1923) (37/30,21/17) -> (73/27,119/44) Hyperbolic Matrix(1975,-2496,906,-1145) (24/19,43/34) -> (61/28,24/11) Hyperbolic Matrix(573,-728,122,-155) (19/15,14/11) -> (14/3,33/7) Hyperbolic Matrix(3017,-3848,570,-727) (51/40,37/29) -> (37/7,53/10) Hyperbolic Matrix(365,-468,202,-259) (23/18,9/7) -> (9/5,29/16) Hyperbolic Matrix(883,-1144,362,-469) (22/17,13/10) -> (39/16,22/9) Hyperbolic Matrix(677,-884,278,-363) (13/10,17/13) -> (17/7,39/16) Hyperbolic Matrix(3483,-4732,1570,-2133) (19/14,53/39) -> (51/23,71/32) Hyperbolic Matrix(5201,-7072,1376,-1871) (87/64,34/25) -> (34/9,121/32) Hyperbolic Matrix(1873,-2548,1146,-1559) (34/25,15/11) -> (67/41,18/11) Hyperbolic Matrix(1093,-1508,640,-883) (11/8,29/21) -> (29/17,41/24) Hyperbolic Matrix(937,-1300,524,-727) (18/13,25/18) -> (25/14,34/19) Hyperbolic Matrix(1197,-1664,710,-987) (25/18,32/23) -> (32/19,27/16) Hyperbolic Matrix(1145,-1612,738,-1039) (7/5,31/22) -> (31/20,45/29) Hyperbolic Matrix(2029,-2860,774,-1091) (31/22,24/17) -> (76/29,21/8) Hyperbolic Matrix(989,-1404,622,-883) (17/12,27/19) -> (27/17,35/22) Hyperbolic Matrix(2339,-3328,622,-885) (64/45,37/26) -> (15/4,64/17) Hyperbolic Matrix(1351,-1924,804,-1145) (37/26,47/33) -> (5/3,37/22) Hyperbolic Matrix(729,-1040,218,-311) (47/33,10/7) -> (10/3,57/17) Hyperbolic Matrix(831,-1196,362,-521) (23/16,13/9) -> (39/17,23/10) Hyperbolic Matrix(573,-832,250,-363) (13/9,16/11) -> (16/7,39/17) Hyperbolic Matrix(779,-1196,170,-261) (3/2,20/13) -> (32/7,55/12) Hyperbolic Matrix(1249,-1924,742,-1143) (20/13,37/24) -> (37/22,32/19) Hyperbolic Matrix(1507,-2340,436,-677) (45/29,14/9) -> (38/11,45/13) Hyperbolic Matrix(4369,-6812,1200,-1871) (53/34,39/25) -> (91/25,51/14) Hyperbolic Matrix(4731,-7384,1300,-2029) (39/25,64/41) -> (40/11,91/25) Hyperbolic Matrix(831,-1300,466,-729) (25/16,11/7) -> (41/23,25/14) Hyperbolic Matrix(989,-1560,362,-571) (11/7,30/19) -> (30/11,41/15) Hyperbolic Matrix(1613,-2548,954,-1507) (30/19,49/31) -> (49/29,22/13) Hyperbolic Matrix(3277,-5200,622,-987) (46/29,73/46) -> (21/4,58/11) Hyperbolic Matrix(261,-416,32,-51) (35/22,8/5) -> (8/1,17/2) Hyperbolic Matrix(6449,-10400,2450,-3951) (79/49,50/31) -> (50/19,129/49) Hyperbolic Matrix(417,-676,256,-415) (21/13,13/8) -> (13/8,31/19) Parabolic Matrix(1975,-3224,574,-937) (31/19,49/30) -> (55/16,31/9) Hyperbolic Matrix(5251,-8580,1560,-2549) (49/30,67/41) -> (37/11,101/30) Hyperbolic Matrix(4679,-7904,1786,-3017) (27/16,49/29) -> (55/21,131/50) Hyperbolic Matrix(675,-1144,154,-261) (22/13,17/10) -> (35/8,22/5) Hyperbolic Matrix(885,-1508,152,-259) (46/27,29/17) -> (29/5,6/1) Hyperbolic Matrix(1613,-2756,882,-1507) (41/24,53/31) -> (53/29,11/6) Hyperbolic Matrix(3223,-5512,1156,-1977) (53/31,12/7) -> (92/33,53/19) Hyperbolic Matrix(2755,-4732,818,-1405) (12/7,55/32) -> (101/30,64/19) Hyperbolic Matrix(11857,-20384,4960,-8527) (55/32,98/57) -> (98/41,153/64) Hyperbolic Matrix(5201,-8944,1088,-1871) (98/57,43/25) -> (43/9,110/23) Hyperbolic Matrix(1091,-1924,148,-261) (37/21,30/17) -> (22/3,37/5) Hyperbolic Matrix(675,-1196,206,-365) (23/13,16/9) -> (36/11,23/7) Hyperbolic Matrix(1249,-2236,348,-623) (34/19,9/5) -> (61/17,18/5) Hyperbolic Matrix(573,-1040,200,-363) (29/16,20/11) -> (20/7,23/8) Hyperbolic Matrix(1143,-2080,172,-313) (20/11,51/28) -> (53/8,20/3) Hyperbolic Matrix(2393,-4368,1082,-1975) (31/17,42/23) -> (42/19,73/33) Hyperbolic Matrix(365,-676,196,-363) (24/13,13/7) -> (13/7,28/15) Parabolic Matrix(1197,-2236,250,-467) (28/15,15/8) -> (67/14,24/5) Hyperbolic Matrix(313,-676,144,-311) (15/7,13/6) -> (13/6,37/17) Parabolic Matrix(2651,-5772,502,-1093) (37/17,61/28) -> (95/18,37/7) Hyperbolic Matrix(259,-572,24,-53) (11/5,42/19) -> (10/1,11/1) Hyperbolic Matrix(209,-468,46,-103) (20/9,9/4) -> (9/2,32/7) Hyperbolic Matrix(573,-1300,160,-363) (9/4,25/11) -> (25/7,43/12) Hyperbolic Matrix(365,-832,68,-155) (25/11,16/7) -> (16/3,27/5) Hyperbolic Matrix(157,-364,22,-51) (30/13,7/3) -> (7/1,22/3) Hyperbolic Matrix(4939,-11804,936,-2237) (43/18,98/41) -> (58/11,95/18) Hyperbolic Matrix(1717,-4108,456,-1091) (55/23,12/5) -> (64/17,49/13) Hyperbolic Matrix(625,-1508,172,-415) (12/5,29/12) -> (29/8,40/11) Hyperbolic Matrix(365,-884,64,-155) (29/12,17/7) -> (17/3,23/4) Hyperbolic Matrix(1041,-2548,382,-935) (22/9,27/11) -> (79/29,30/11) Hyperbolic Matrix(677,-1664,190,-467) (27/11,5/2) -> (57/16,25/7) Hyperbolic Matrix(261,-676,100,-259) (18/7,13/5) -> (13/5,34/13) Parabolic Matrix(1351,-3536,358,-937) (34/13,55/21) -> (49/13,34/9) Hyperbolic Matrix(521,-1404,154,-415) (8/3,27/10) -> (27/8,44/13) Hyperbolic Matrix(5979,-16172,1250,-3381) (119/44,46/17) -> (110/23,67/14) Hyperbolic Matrix(3017,-8216,878,-2391) (49/18,79/29) -> (79/23,55/16) Hyperbolic Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(2185,-6084,784,-2183) (64/23,39/14) -> (39/14,92/33) Parabolic Matrix(573,-1612,166,-467) (14/5,31/11) -> (31/9,38/11) Hyperbolic Matrix(1039,-2964,292,-833) (37/13,20/7) -> (32/9,89/25) Hyperbolic Matrix(209,-676,64,-207) (16/5,13/4) -> (13/4,36/11) Parabolic Matrix(1873,-6292,526,-1767) (47/14,37/11) -> (89/25,57/16) Hyperbolic Matrix(259,-884,46,-157) (17/5,24/7) -> (28/5,17/3) Hyperbolic Matrix(157,-572,14,-51) (51/14,11/3) -> (11/1,1/0) Hyperbolic Matrix(727,-2756,110,-417) (53/14,19/5) -> (33/5,53/8) Hyperbolic Matrix(157,-676,36,-155) (17/4,13/3) -> (13/3,35/8) Parabolic Matrix(105,-676,16,-103) (19/3,13/2) -> (13/2,33/5) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(53,572,-24,-259) -> Matrix(1,2,0,1) Matrix(53,520,16,157) -> Matrix(1,0,0,1) Matrix(105,884,-74,-623) -> Matrix(1,6,-2,-11) Matrix(53,416,20,157) -> Matrix(1,0,0,1) Matrix(51,364,-22,-157) -> Matrix(1,-2,0,1) Matrix(53,364,38,261) -> Matrix(1,2,0,1) Matrix(103,676,-16,-105) -> Matrix(1,-2,0,1) Matrix(415,2652,-228,-1457) -> Matrix(1,2,0,1) Matrix(157,988,58,365) -> Matrix(1,2,0,1) Matrix(155,884,-64,-365) -> Matrix(1,2,-2,-3) Matrix(157,884,-46,-259) -> Matrix(1,2,0,1) Matrix(155,832,-68,-365) -> Matrix(5,8,-2,-3) Matrix(727,3848,-570,-3017) -> Matrix(3,4,2,3) Matrix(987,5200,-622,-3277) -> Matrix(3,4,-4,-5) Matrix(209,1092,40,209) -> Matrix(9,10,8,9) Matrix(51,260,10,51) -> Matrix(1,2,0,1) Matrix(53,260,32,157) -> Matrix(1,2,0,1) Matrix(521,2496,-282,-1351) -> Matrix(1,0,0,1) Matrix(469,2236,142,677) -> Matrix(3,2,-2,-1) Matrix(155,728,-122,-573) -> Matrix(1,0,0,1) Matrix(313,1456,112,521) -> Matrix(3,4,2,3) Matrix(831,3848,-674,-3121) -> Matrix(7,4,-2,-1) Matrix(417,1924,158,729) -> Matrix(1,-2,0,1) Matrix(103,468,-46,-209) -> Matrix(3,2,-2,-1) Matrix(363,1612,152,675) -> Matrix(1,-2,0,1) Matrix(729,3224,400,1769) -> Matrix(1,0,0,1) Matrix(625,2756,354,1561) -> Matrix(3,10,2,7) Matrix(261,1144,-154,-675) -> Matrix(1,0,0,1) Matrix(207,884,-122,-521) -> Matrix(3,2,-2,-1) Matrix(209,884,74,313) -> Matrix(5,2,2,1) Matrix(573,2392,212,885) -> Matrix(1,0,2,1) Matrix(51,208,38,155) -> Matrix(1,0,2,1) Matrix(53,208,40,157) -> Matrix(1,0,0,1) Matrix(677,2600,420,1613) -> Matrix(11,-4,14,-5) Matrix(313,1196,218,833) -> Matrix(1,-2,2,-3) Matrix(1249,4732,-686,-2599) -> Matrix(1,-2,0,1) Matrix(1663,6292,522,1975) -> Matrix(1,2,0,1) Matrix(1871,7072,-1376,-5201) -> Matrix(1,0,-2,1) Matrix(675,2548,-262,-989) -> Matrix(1,-6,0,1) Matrix(209,780,56,209) -> Matrix(1,-2,0,1) Matrix(155,572,42,155) -> Matrix(1,2,0,1) Matrix(415,1508,-172,-625) -> Matrix(1,2,0,1) Matrix(259,936,158,571) -> Matrix(3,4,2,3) Matrix(363,1300,-160,-573) -> Matrix(5,-2,-2,1) Matrix(467,1664,-190,-677) -> Matrix(1,0,0,1) Matrix(103,364,88,311) -> Matrix(1,2,0,1) Matrix(467,1612,-166,-573) -> Matrix(9,-2,-4,1) Matrix(831,2860,-514,-1769) -> Matrix(19,-6,-22,7) Matrix(365,1248,198,677) -> Matrix(1,0,0,1) Matrix(415,1404,-154,-521) -> Matrix(1,-2,2,-3) Matrix(987,3328,632,2131) -> Matrix(1,-4,0,1) Matrix(989,3328,-726,-2443) -> Matrix(1,0,-2,1) Matrix(573,1924,-232,-779) -> Matrix(1,-2,0,1) Matrix(311,1040,-218,-729) -> Matrix(1,0,-2,1) Matrix(157,520,16,53) -> Matrix(1,0,0,1) Matrix(677,2236,142,469) -> Matrix(1,-2,2,-3) Matrix(363,1196,268,883) -> Matrix(1,-2,2,-3) Matrix(365,1196,-206,-675) -> Matrix(3,-10,-2,7) Matrix(259,832,-146,-469) -> Matrix(3,8,-2,-5) Matrix(521,1664,98,313) -> Matrix(3,4,2,3) Matrix(1975,6292,522,1663) -> Matrix(1,2,0,1) Matrix(623,1976,262,831) -> Matrix(1,-4,0,1) Matrix(313,988,198,625) -> Matrix(1,2,2,5) Matrix(417,1196,-326,-935) -> Matrix(1,6,0,1) Matrix(675,1924,-274,-781) -> Matrix(1,2,0,1) Matrix(311,884,146,415) -> Matrix(1,6,0,1) Matrix(313,884,74,209) -> Matrix(1,2,2,5) Matrix(833,2340,-592,-1663) -> Matrix(1,2,-8,-15) Matrix(521,1456,112,313) -> Matrix(3,4,2,3) Matrix(2443,6812,-1772,-4941) -> Matrix(5,6,-6,-7) Matrix(2653,7384,-1924,-5355) -> Matrix(9,8,-8,-7) Matrix(1197,3328,842,2341) -> Matrix(5,4,6,5) Matrix(469,1300,-206,-571) -> Matrix(1,-2,0,1) Matrix(571,1560,-362,-989) -> Matrix(1,0,-6,1) Matrix(935,2548,-382,-1041) -> Matrix(5,-2,-2,1) Matrix(363,988,248,675) -> Matrix(3,-2,2,-1) Matrix(365,988,58,157) -> Matrix(1,2,0,1) Matrix(1923,5200,-1558,-4213) -> Matrix(1,-4,0,1) Matrix(885,2392,212,573) -> Matrix(1,0,2,1) Matrix(155,416,-136,-365) -> Matrix(3,-4,-2,3) Matrix(157,416,20,53) -> Matrix(1,0,0,1) Matrix(729,1924,158,417) -> Matrix(1,-2,0,1) Matrix(987,2600,730,1923) -> Matrix(1,-4,4,-15) Matrix(3951,10400,-2450,-6449) -> Matrix(21,-88,-26,109) Matrix(989,2600,574,1509) -> Matrix(3,-16,4,-21) Matrix(259,676,-100,-261) -> Matrix(1,-14,0,1) Matrix(1249,3224,-886,-2287) -> Matrix(1,8,-4,-31) Matrix(3329,8580,-2340,-6031) -> Matrix(1,6,-2,-11) Matrix(365,936,264,677) -> Matrix(1,4,0,1) Matrix(937,2392,530,1353) -> Matrix(3,4,2,3) Matrix(5201,13260,2040,5201) -> Matrix(1,-10,0,1) Matrix(8059,20540,3162,8059) -> Matrix(1,30,0,1) Matrix(1613,4108,470,1197) -> Matrix(1,6,-2,-11) Matrix(103,260,82,207) -> Matrix(1,2,0,1) Matrix(3225,7904,-1994,-4887) -> Matrix(7,36,-8,-41) Matrix(469,1144,-362,-883) -> Matrix(1,0,0,1) Matrix(623,1508,-516,-1249) -> Matrix(3,2,-2,-1) Matrix(1143,2756,-518,-1249) -> Matrix(1,-2,0,1) Matrix(2289,5512,-1468,-3535) -> Matrix(1,-8,0,1) Matrix(1977,4732,-1390,-3327) -> Matrix(1,-2,0,1) Matrix(8527,20384,-4960,-11857) -> Matrix(15,-32,-22,47) Matrix(3743,8944,-2960,-7073) -> Matrix(3,-8,2,-5) Matrix(675,1612,152,363) -> Matrix(1,-2,0,1) Matrix(1091,2600,676,1611) -> Matrix(5,-16,6,-19) Matrix(415,988,218,519) -> Matrix(3,-14,2,-9) Matrix(831,1976,262,623) -> Matrix(1,-4,0,1) Matrix(417,988,176,417) -> Matrix(1,-14,0,1) Matrix(155,364,66,155) -> Matrix(1,10,0,1) Matrix(833,1924,-720,-1663) -> Matrix(5,18,-2,-7) Matrix(1195,2756,924,2131) -> Matrix(3,10,2,7) Matrix(1039,2392,632,1455) -> Matrix(1,4,0,1) Matrix(521,1196,-362,-831) -> Matrix(3,10,-4,-13) Matrix(987,2236,-712,-1613) -> Matrix(1,2,4,9) Matrix(467,1040,-304,-677) -> Matrix(5,4,-4,-3) Matrix(937,2080,-796,-1767) -> Matrix(1,0,0,1) Matrix(1455,3224,1126,2495) -> Matrix(1,0,2,1) Matrix(1975,4368,-1082,-2393) -> Matrix(1,0,-2,1) Matrix(571,1248,404,883) -> Matrix(1,0,2,1) Matrix(311,676,-144,-313) -> Matrix(1,-6,0,1) Matrix(1039,2236,-822,-1769) -> Matrix(1,6,0,1) Matrix(415,884,146,311) -> Matrix(1,6,0,1) Matrix(469,988,272,573) -> Matrix(5,14,6,17) Matrix(519,988,218,415) -> Matrix(9,14,-2,-3) Matrix(469,884,304,573) -> Matrix(5,6,4,5) Matrix(363,676,-196,-365) -> Matrix(5,6,-6,-7) Matrix(3121,5772,-2530,-4679) -> Matrix(13,10,-4,-3) Matrix(311,572,56,103) -> Matrix(1,2,0,1) Matrix(313,572,-284,-519) -> Matrix(3,2,-2,-1) Matrix(5927,10816,2678,4887) -> Matrix(1,0,6,1) Matrix(5929,10816,2680,4889) -> Matrix(1,0,-4,1) Matrix(1769,3224,400,729) -> Matrix(1,0,0,1) Matrix(259,468,-202,-365) -> Matrix(1,2,0,1) Matrix(727,1300,-524,-937) -> Matrix(1,2,-4,-7) Matrix(467,832,-380,-677) -> Matrix(5,8,-2,-3) Matrix(1353,2392,530,937) -> Matrix(3,4,2,3) Matrix(1561,2756,354,625) -> Matrix(7,10,2,3) Matrix(207,364,-178,-313) -> Matrix(1,2,-2,-3) Matrix(209,364,120,209) -> Matrix(9,10,8,9) Matrix(571,988,330,571) -> Matrix(15,14,16,15) Matrix(1145,1976,784,1353) -> Matrix(5,4,6,5) Matrix(573,988,272,469) -> Matrix(17,14,6,5) Matrix(1509,2600,574,989) -> Matrix(21,16,-4,-3) Matrix(937,1612,726,1249) -> Matrix(3,2,4,3) Matrix(6865,11804,-5564,-9567) -> Matrix(37,26,-10,-7) Matrix(25167,43264,10526,18095) -> Matrix(101,68,-52,-35) Matrix(25169,43264,10528,18097) -> Matrix(103,68,-50,-33) Matrix(2391,4108,-1756,-3017) -> Matrix(3,2,-8,-5) Matrix(883,1508,-640,-1093) -> Matrix(3,2,-2,-1) Matrix(519,884,-428,-729) -> Matrix(1,-2,0,1) Matrix(1507,2548,-954,-1613) -> Matrix(1,2,-4,-7) Matrix(987,1664,-710,-1197) -> Matrix(1,0,0,1) Matrix(157,260,32,53) -> Matrix(1,2,0,1) Matrix(5875,9672,2242,3691) -> Matrix(41,48,-6,-7) Matrix(12481,20540,7584,12481) -> Matrix(29,30,28,29) Matrix(8059,13260,4898,8059) -> Matrix(11,10,12,11) Matrix(1455,2392,632,1039) -> Matrix(1,4,0,1) Matrix(571,936,158,259) -> Matrix(3,4,2,3) Matrix(415,676,-256,-417) -> Matrix(13,14,-14,-15) Matrix(2185,3536,-1606,-2599) -> Matrix(9,8,-8,-7) Matrix(5981,9672,2348,3797) -> Matrix(55,48,8,7) Matrix(1611,2600,676,1091) -> Matrix(19,16,-6,-5) Matrix(26831,43264,10190,16431) -> Matrix(419,336,-106,-85) Matrix(26833,43264,10192,16433) -> Matrix(421,336,-104,-83) Matrix(1613,2600,420,677) -> Matrix(5,4,-14,-11) Matrix(1195,1924,936,1507) -> Matrix(3,2,4,3) Matrix(259,416,226,363) -> Matrix(1,0,2,1) Matrix(883,1404,-622,-989) -> Matrix(5,2,-8,-3) Matrix(1507,2392,1146,1819) -> Matrix(1,0,0,1) Matrix(10193,16172,-8062,-12791) -> Matrix(5,2,2,1) Matrix(623,988,524,831) -> Matrix(1,2,0,1) Matrix(625,988,198,313) -> Matrix(5,2,2,1) Matrix(5199,8216,-3686,-5825) -> Matrix(11,4,-36,-13) Matrix(1715,2704,626,987) -> Matrix(1,0,10,1) Matrix(1717,2704,628,989) -> Matrix(1,0,-8,1) Matrix(365,572,-298,-467) -> Matrix(1,-2,0,1) Matrix(2131,3328,632,987) -> Matrix(1,-4,0,1) Matrix(3899,6084,-2500,-3901) -> Matrix(1,-14,0,1) Matrix(935,1456,734,1143) -> Matrix(1,4,0,1) Matrix(1039,1612,-738,-1145) -> Matrix(1,2,-6,-11) Matrix(571,884,436,675) -> Matrix(1,2,-2,-3) Matrix(573,884,304,469) -> Matrix(5,6,4,5) Matrix(1925,2964,-1384,-2131) -> Matrix(1,2,-2,-3) Matrix(1561,2392,340,521) -> Matrix(11,12,10,11) Matrix(1091,1664,238,363) -> Matrix(9,8,10,9) Matrix(675,988,248,363) -> Matrix(1,2,-2,-3) Matrix(1353,1976,784,1145) -> Matrix(5,4,6,5) Matrix(4317,6292,3176,4629) -> Matrix(1,2,0,1) Matrix(3641,5304,786,1145) -> Matrix(1,0,2,1) Matrix(467,676,-324,-469) -> Matrix(5,6,-6,-7) Matrix(833,1196,218,313) -> Matrix(3,2,-2,-1) Matrix(1559,2236,1232,1767) -> Matrix(3,2,-2,-1) Matrix(363,520,326,467) -> Matrix(1,0,2,1) Matrix(7591,10816,2262,3223) -> Matrix(1,0,2,1) Matrix(7593,10816,2264,3225) -> Matrix(1,0,0,1) Matrix(4419,6292,-3178,-4525) -> Matrix(3,2,-2,-1) Matrix(2341,3328,842,1197) -> Matrix(5,4,6,5) Matrix(1613,2288,184,261) -> Matrix(15,8,-2,-1) Matrix(1247,1768,146,207) -> Matrix(17,8,2,1) Matrix(625,884,-514,-727) -> Matrix(3,2,-2,-1) Matrix(2911,4108,1768,2495) -> Matrix(17,6,14,5) Matrix(1923,2704,554,779) -> Matrix(1,0,16,1) Matrix(1925,2704,556,781) -> Matrix(1,0,-14,1) Matrix(261,364,38,53) -> Matrix(1,2,0,1) Matrix(7799,10816,2174,3015) -> Matrix(1,0,12,1) Matrix(7801,10816,2176,3017) -> Matrix(1,0,-10,1) Matrix(677,936,264,365) -> Matrix(1,4,0,1) Matrix(415,572,-378,-521) -> Matrix(3,2,-2,-1) Matrix(417,572,304,417) -> Matrix(1,2,0,1) Matrix(571,780,418,571) -> Matrix(3,2,4,3) Matrix(31823,43264,8414,11439) -> Matrix(1,0,4,1) Matrix(31825,43264,8416,11441) -> Matrix(1,0,-2,1) Matrix(4629,6292,3176,4317) -> Matrix(1,2,0,1) Matrix(2029,2756,-1722,-2339) -> Matrix(3,2,-2,-1) Matrix(883,1196,268,363) -> Matrix(3,2,-2,-1) Matrix(1923,2600,730,987) -> Matrix(15,4,-4,-1) Matrix(155,208,38,51) -> Matrix(1,0,2,1) Matrix(157,208,40,53) -> Matrix(1,0,0,1) Matrix(1819,2392,1146,1507) -> Matrix(1,0,0,1) Matrix(675,884,436,571) -> Matrix(3,-2,2,-1) Matrix(519,676,-400,-521) -> Matrix(1,-2,0,1) Matrix(2131,2756,924,1195) -> Matrix(7,10,2,3) Matrix(2495,3224,1126,1455) -> Matrix(1,0,2,1) Matrix(1249,1612,726,937) -> Matrix(3,2,4,3) Matrix(1301,1664,448,573) -> Matrix(1,-8,0,1) Matrix(1871,2392,650,831) -> Matrix(1,12,0,1) Matrix(1507,1924,936,1195) -> Matrix(3,2,4,3) Matrix(4159,5304,1304,1663) -> Matrix(1,0,0,1) Matrix(1143,1456,734,935) -> Matrix(1,4,0,1) Matrix(2131,2704,450,571) -> Matrix(1,0,4,1) Matrix(2133,2704,452,573) -> Matrix(1,0,-2,1) Matrix(1767,2236,1232,1559) -> Matrix(1,-2,2,-3) Matrix(207,260,82,103) -> Matrix(1,2,0,1) Matrix(209,260,168,209) -> Matrix(1,2,0,1) Matrix(883,1092,714,883) -> Matrix(1,10,0,1) Matrix(1351,1664,928,1143) -> Matrix(1,4,0,1) Matrix(469,572,214,261) -> Matrix(1,2,0,1) Matrix(2235,2704,386,467) -> Matrix(13,28,6,13) Matrix(2237,2704,388,469) -> Matrix(15,28,8,15) Matrix(831,988,524,623) -> Matrix(1,2,0,1) Matrix(571,676,-484,-573) -> Matrix(1,2,-2,-3) Matrix(311,364,88,103) -> Matrix(1,2,0,1) Matrix(2339,2704,314,363) -> Matrix(13,28,6,13) Matrix(2341,2704,316,365) -> Matrix(15,28,8,15) Matrix(363,416,226,259) -> Matrix(1,0,2,1) Matrix(1561,1768,460,521) -> Matrix(7,8,-8,-9) Matrix(2027,2288,598,675) -> Matrix(9,8,-8,-7) Matrix(467,520,326,363) -> Matrix(1,0,2,1) Matrix(1,0,2,1) -> Matrix(1,0,2,1) Matrix(519,-572,284,-313) -> Matrix(1,-2,2,-3) Matrix(779,-884,230,-261) -> Matrix(5,-6,-4,5) Matrix(313,-364,178,-207) -> Matrix(3,-2,2,-1) Matrix(573,-676,484,-571) -> Matrix(3,-2,2,-1) Matrix(2237,-2652,1008,-1195) -> Matrix(1,-2,2,-3) Matrix(729,-884,428,-519) -> Matrix(1,-2,0,1) Matrix(727,-884,514,-625) -> Matrix(1,-2,2,-3) Matrix(677,-832,380,-467) -> Matrix(3,-8,2,-5) Matrix(3121,-3848,674,-831) -> Matrix(1,-4,2,-7) Matrix(4213,-5200,1558,-1923) -> Matrix(1,-4,0,1) Matrix(1975,-2496,906,-1145) -> Matrix(1,0,0,1) Matrix(573,-728,122,-155) -> Matrix(1,0,0,1) Matrix(3017,-3848,570,-727) -> Matrix(3,4,2,3) Matrix(365,-468,202,-259) -> Matrix(1,2,0,1) Matrix(883,-1144,362,-469) -> Matrix(1,0,0,1) Matrix(677,-884,278,-363) -> Matrix(1,2,0,1) Matrix(3483,-4732,1570,-2133) -> Matrix(3,-2,2,-1) Matrix(5201,-7072,1376,-1871) -> Matrix(1,0,-2,1) Matrix(1873,-2548,1146,-1559) -> Matrix(7,-6,6,-5) Matrix(1093,-1508,640,-883) -> Matrix(1,-2,2,-3) Matrix(937,-1300,524,-727) -> Matrix(7,-2,4,-1) Matrix(1197,-1664,710,-987) -> Matrix(1,0,0,1) Matrix(1145,-1612,738,-1039) -> Matrix(11,-2,6,-1) Matrix(2029,-2860,774,-1091) -> Matrix(25,-6,-4,1) Matrix(989,-1404,622,-883) -> Matrix(3,-2,8,-5) Matrix(2339,-3328,622,-885) -> Matrix(1,0,-2,1) Matrix(1351,-1924,804,-1145) -> Matrix(3,-2,2,-1) Matrix(729,-1040,218,-311) -> Matrix(1,0,-2,1) Matrix(831,-1196,362,-521) -> Matrix(13,-10,4,-3) Matrix(573,-832,250,-363) -> Matrix(5,-8,2,-3) Matrix(779,-1196,170,-261) -> Matrix(5,-6,6,-7) Matrix(1249,-1924,742,-1143) -> Matrix(1,-2,2,-3) Matrix(1507,-2340,436,-677) -> Matrix(1,-2,-6,13) Matrix(4369,-6812,1200,-1871) -> Matrix(1,-6,0,1) Matrix(4731,-7384,1300,-2029) -> Matrix(1,8,0,1) Matrix(831,-1300,466,-729) -> Matrix(3,-2,2,-1) Matrix(989,-1560,362,-571) -> Matrix(1,0,-6,1) Matrix(1613,-2548,954,-1507) -> Matrix(7,-2,4,-1) Matrix(3277,-5200,622,-987) -> Matrix(5,-4,4,-3) Matrix(261,-416,32,-51) -> Matrix(7,-4,2,-1) Matrix(6449,-10400,2450,-3951) -> Matrix(109,-88,-26,21) Matrix(417,-676,256,-415) -> Matrix(15,-14,14,-13) Matrix(1975,-3224,574,-937) -> Matrix(7,-8,-20,23) Matrix(5251,-8580,1560,-2549) -> Matrix(5,-6,-4,5) Matrix(4679,-7904,1786,-3017) -> Matrix(29,-36,-4,5) Matrix(675,-1144,154,-261) -> Matrix(1,0,0,1) Matrix(885,-1508,152,-259) -> Matrix(1,2,0,1) Matrix(1613,-2756,882,-1507) -> Matrix(3,-2,2,-1) Matrix(3223,-5512,1156,-1977) -> Matrix(9,-8,8,-7) Matrix(2755,-4732,818,-1405) -> Matrix(3,-2,2,-1) Matrix(11857,-20384,4960,-8527) -> Matrix(47,-32,-22,15) Matrix(5201,-8944,1088,-1871) -> Matrix(11,-8,18,-13) Matrix(1091,-1924,148,-261) -> Matrix(13,-18,8,-11) Matrix(675,-1196,206,-365) -> Matrix(7,-10,-2,3) Matrix(1249,-2236,348,-623) -> Matrix(1,-2,6,-11) Matrix(573,-1040,200,-363) -> Matrix(1,4,0,1) Matrix(1143,-2080,172,-313) -> Matrix(1,0,0,1) Matrix(2393,-4368,1082,-1975) -> Matrix(1,0,-2,1) Matrix(365,-676,196,-363) -> Matrix(7,-6,6,-5) Matrix(1197,-2236,250,-467) -> Matrix(5,-6,6,-7) Matrix(313,-676,144,-311) -> Matrix(1,-6,0,1) Matrix(2651,-5772,502,-1093) -> Matrix(3,10,2,7) Matrix(259,-572,24,-53) -> Matrix(1,2,0,1) Matrix(209,-468,46,-103) -> Matrix(1,-2,2,-3) Matrix(573,-1300,160,-363) -> Matrix(1,-2,-2,5) Matrix(365,-832,68,-155) -> Matrix(3,-8,2,-5) Matrix(157,-364,22,-51) -> Matrix(1,-2,0,1) Matrix(4939,-11804,936,-2237) -> Matrix(11,26,8,19) Matrix(1717,-4108,456,-1091) -> Matrix(1,2,-2,-3) Matrix(625,-1508,172,-415) -> Matrix(1,2,0,1) Matrix(365,-884,64,-155) -> Matrix(3,-2,2,-1) Matrix(1041,-2548,382,-935) -> Matrix(1,-2,-2,5) Matrix(677,-1664,190,-467) -> Matrix(1,0,0,1) Matrix(261,-676,100,-259) -> Matrix(1,-14,0,1) Matrix(1351,-3536,358,-937) -> Matrix(1,8,0,1) Matrix(521,-1404,154,-415) -> Matrix(3,2,-2,-1) Matrix(5979,-16172,1250,-3381) -> Matrix(3,2,4,3) Matrix(3017,-8216,878,-2391) -> Matrix(7,4,-16,-9) Matrix(207,-572,38,-105) -> Matrix(3,-2,2,-1) Matrix(2185,-6084,784,-2183) -> Matrix(15,-14,14,-13) Matrix(573,-1612,166,-467) -> Matrix(1,-2,-4,9) Matrix(1039,-2964,292,-833) -> Matrix(1,-2,0,1) Matrix(209,-676,64,-207) -> Matrix(1,-6,0,1) Matrix(1873,-6292,526,-1767) -> Matrix(1,2,0,1) Matrix(259,-884,46,-157) -> Matrix(1,2,0,1) Matrix(157,-572,14,-51) -> Matrix(1,2,0,1) Matrix(727,-2756,110,-417) -> Matrix(1,2,0,1) Matrix(157,-676,36,-155) -> Matrix(3,-2,2,-1) Matrix(105,-676,16,-103) -> Matrix(1,-2,0,1) 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): 112 Degree of the the map X: 112 Degree of the the map Y: 336 ----------------------------------------------------------------------- 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. ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF 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 elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 60 Genus: 55 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES 0/1 13/11 13/10 4/3 13/9 39/25 13/8 12/7 13/7 2/1 13/6 104/47 26/11 208/87 12/5 130/51 13/5 208/79 8/3 52/19 39/14 26/9 3/1 16/5 13/4 104/31 52/15 104/29 18/5 26/7 208/55 4/1 13/3 32/7 14/3 52/11 24/5 5/1 26/5 21/4 16/3 27/5 28/5 23/4 52/9 6/1 19/3 13/2 20/3 7/1 22/3 52/7 15/2 8/1 17/2 26/3 9/1 10/1 11/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES 0/1 0/1 1/1 1/1 10/9 0/1 2/1 9/8 1/2 8/7 2/1 15/13 5/3 7/6 3/2 20/17 0/1 13/11 1/1 32/27 2/1 19/16 3/2 6/5 0/1 2/1 17/14 1/0 11/9 1/1 16/13 2/1 37/30 1/0 21/17 5/1 26/21 1/0 5/4 1/0 24/19 -2/1 43/34 -3/2 19/15 -1/1 14/11 0/1 2/1 51/40 1/0 37/29 -1/1 23/18 1/0 9/7 1/1 31/24 1/0 53/41 1/1 22/17 0/1 2/1 13/10 1/0 17/13 -1/1 21/16 1/0 25/19 -1/5 4/3 0/1 27/20 -1/4 23/17 1/3 19/14 1/2 53/39 1/1 87/64 1/0 34/25 0/1 2/3 15/11 1/1 26/19 1/1 11/8 1/0 29/21 3/1 18/13 -2/1 0/1 25/18 3/4 32/23 2/1 7/5 -1/1 31/22 1/4 24/17 2/5 41/29 1/1 17/12 1/2 27/19 5/7 64/45 2/1 37/26 1/2 47/33 1/1 10/7 0/1 2/3 43/30 1/0 33/23 1/1 23/16 3/4 13/9 1/1 16/11 2/1 51/35 1/1 35/24 1/0 19/13 1/1 3/2 1/2 20/13 4/3 37/24 3/2 17/11 1/1 31/20 3/2 45/29 13/7 14/9 2/1 4/1 53/34 1/0 39/25 1/0 64/41 -6/1 25/16 -3/2 11/7 -1/1 30/19 0/1 2/7 49/31 3/7 19/12 1/2 46/29 0/1 2/1 73/46 1/0 27/17 1/5 35/22 1/2 8/5 2/3 37/23 5/7 29/18 3/4 79/49 31/39 50/31 4/5 22/27 21/13 1/1 13/8 1/1 31/19 1/1 49/30 19/16 67/41 1/1 18/11 6/5 4/3 23/14 1/0 51/31 1/1 130/79 1/1 79/48 15/14 28/17 4/3 5/3 1/1 37/22 1/0 32/19 2/1 27/16 3/4 49/29 7/5 22/13 0/1 2/1 17/10 1/0 46/27 -2/1 0/1 29/17 1/3 41/24 1/2 53/31 1/1 12/7 0/1 55/32 9/14 98/57 2/3 16/23 43/25 1/1 31/18 3/4 50/29 4/5 14/17 69/40 5/6 19/11 1/1 26/15 1/1 7/4 5/4 37/21 9/7 30/17 4/3 10/7 53/30 3/2 23/13 1/1 16/9 2/1 41/23 5/3 25/14 13/8 34/19 16/9 2/1 9/5 3/1 29/16 1/0 20/11 0/1 51/28 1/0 31/17 -1/1 42/23 0/1 2/3 53/29 1/1 11/6 1/0 24/13 2/3 13/7 1/1 28/15 4/3 15/8 3/2 17/9 1/1 2/1 0/1 2/1 17/8 1/0 15/7 3/1 13/6 1/0 37/17 -3/1 61/28 -3/2 24/11 -2/1 11/5 1/1 42/19 -2/1 0/1 73/33 -1/3 104/47 0/1 31/14 1/2 51/23 1/1 71/32 1/0 20/9 0/1 9/4 3/2 25/11 13/5 16/7 2/1 39/17 3/1 23/10 1/0 53/23 3/1 30/13 10/3 4/1 7/3 5/1 26/11 1/0 19/8 1/0 69/29 -5/1 50/21 -14/3 -4/1 31/13 -3/1 43/18 1/0 98/41 -16/7 -2/1 153/64 -25/12 208/87 -2/1 55/23 -9/5 12/5 0/1 29/12 -1/2 17/7 1/1 39/16 1/0 22/9 0/1 2/1 27/11 -3/1 5/2 1/0 28/11 4/1 79/31 15/1 130/51 1/0 51/20 1/0 23/9 1/1 18/7 4/1 6/1 13/5 1/0 34/13 -10/1 -8/1 55/21 -23/3 131/50 -57/8 76/29 -20/3 21/8 1/0 50/19 -22/5 -4/1 129/49 -53/13 208/79 -4/1 79/30 -31/8 29/11 -3/1 37/14 -5/2 8/3 -2/1 27/10 -1/4 73/27 1/1 119/44 1/0 46/17 0/1 2/1 19/7 -1/1 49/18 -3/4 79/29 -5/11 30/11 -2/5 0/1 41/15 -1/7 52/19 0/1 11/4 1/2 25/9 3/5 64/23 6/7 39/14 1/1 92/33 8/7 53/19 1/1 14/5 4/3 2/1 31/11 3/1 17/6 1/0 37/13 3/1 20/7 4/1 23/8 1/0 26/9 1/0 3/1 -1/1 19/6 1/0 35/11 1/1 51/16 1/0 16/5 2/1 13/4 1/0 36/11 -4/1 23/7 -3/1 33/10 1/0 43/13 1/1 10/3 -2/1 0/1 57/17 -1/1 104/31 0/1 47/14 1/0 37/11 -1/1 101/30 -1/4 64/19 2/1 27/8 -5/2 44/13 -4/3 61/18 -7/6 78/23 -1/1 17/5 -1/1 24/7 -2/3 79/23 -9/19 55/16 -5/12 31/9 -1/3 38/11 -2/11 0/1 45/13 -1/13 52/15 0/1 7/2 1/2 32/9 2/1 89/25 1/1 57/16 1/0 25/7 -3/1 43/12 -1/4 104/29 0/1 61/17 1/7 18/5 0/1 2/3 29/8 3/2 40/11 2/1 91/25 1/0 51/14 1/0 11/3 1/1 26/7 1/0 15/4 1/0 64/17 -2/3 49/13 1/3 34/9 -2/1 0/1 121/32 -1/2 208/55 0/1 87/23 1/1 53/14 1/0 19/5 -1/1 23/6 -1/2 27/7 1/5 4/1 0/1 25/6 1/6 21/5 1/1 17/4 1/2 13/3 1/1 35/8 1/0 22/5 0/1 2/1 53/12 1/0 31/7 1/1 9/2 1/0 32/7 2/3 55/12 7/8 78/17 1/1 23/5 1/1 37/8 1/2 88/19 2/3 51/11 1/1 14/3 0/1 2/1 33/7 -1/1 52/11 0/1 19/4 1/2 43/9 3/5 110/23 2/3 8/11 67/14 3/4 24/5 2/3 5/1 1/1 26/5 1/1 21/4 5/4 58/11 6/5 4/3 95/18 11/8 37/7 1/1 53/10 3/2 16/3 2/1 27/5 -1/1 11/2 1/0 28/5 4/3 17/3 1/1 23/4 7/4 52/9 2/1 29/5 7/3 6/1 0/1 2/1 19/3 3/1 13/2 1/0 33/5 1/1 53/8 1/0 20/3 0/1 7/1 3/1 22/3 4/3 2/1 37/5 9/5 52/7 2/1 15/2 5/2 8/1 2/1 17/2 1/0 26/3 1/0 9/1 -1/1 10/1 0/1 2/1 11/1 3/1 1/0 1/0 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,1,1) (0/1,1/0) -> (0/1,1/1) Parabolic Matrix(519,-572,284,-313) (1/1,10/9) -> (42/23,53/29) Hyperbolic Matrix(467,-520,141,-157) (10/9,9/8) -> (43/13,10/3) Hyperbolic Matrix(779,-884,230,-261) (9/8,8/7) -> (44/13,61/18) Hyperbolic Matrix(363,-416,137,-157) (8/7,15/13) -> (37/14,8/3) Hyperbolic Matrix(313,-364,178,-207) (15/13,7/6) -> (7/4,37/21) Hyperbolic Matrix(311,-364,223,-261) (7/6,20/17) -> (32/23,7/5) Hyperbolic Matrix(573,-676,484,-571) (20/17,13/11) -> (13/11,32/27) Parabolic Matrix(2237,-2652,1008,-1195) (32/27,19/16) -> (71/32,20/9) Hyperbolic Matrix(831,-988,307,-365) (19/16,6/5) -> (46/17,19/7) Hyperbolic Matrix(729,-884,428,-519) (6/5,17/14) -> (17/10,46/27) Hyperbolic Matrix(727,-884,514,-625) (17/14,11/9) -> (41/29,17/12) Hyperbolic Matrix(677,-832,380,-467) (11/9,16/13) -> (16/9,41/23) Hyperbolic Matrix(3121,-3848,674,-831) (16/13,37/30) -> (37/8,88/19) Hyperbolic Matrix(4213,-5200,1558,-1923) (37/30,21/17) -> (73/27,119/44) Hyperbolic Matrix(883,-1092,169,-209) (21/17,26/21) -> (26/5,21/4) Hyperbolic Matrix(209,-260,41,-51) (26/21,5/4) -> (5/1,26/5) Hyperbolic Matrix(207,-260,125,-157) (5/4,24/19) -> (28/17,5/3) Hyperbolic Matrix(1975,-2496,906,-1145) (24/19,43/34) -> (61/28,24/11) Hyperbolic Matrix(1767,-2236,535,-677) (43/34,19/15) -> (33/10,43/13) Hyperbolic Matrix(573,-728,122,-155) (19/15,14/11) -> (14/3,33/7) Hyperbolic Matrix(1143,-1456,409,-521) (14/11,51/40) -> (53/19,14/5) Hyperbolic Matrix(3017,-3848,570,-727) (51/40,37/29) -> (37/7,53/10) Hyperbolic Matrix(1507,-1924,571,-729) (37/29,23/18) -> (29/11,37/14) Hyperbolic Matrix(365,-468,202,-259) (23/18,9/7) -> (9/5,29/16) Hyperbolic Matrix(1249,-1612,523,-675) (9/7,31/24) -> (31/13,43/18) Hyperbolic Matrix(2495,-3224,1369,-1769) (31/24,53/41) -> (51/28,31/17) Hyperbolic Matrix(2131,-2756,1207,-1561) (53/41,22/17) -> (30/17,53/30) Hyperbolic Matrix(883,-1144,362,-469) (22/17,13/10) -> (39/16,22/9) Hyperbolic Matrix(677,-884,278,-363) (13/10,17/13) -> (17/7,39/16) Hyperbolic Matrix(675,-884,239,-313) (17/13,21/16) -> (31/11,17/6) Hyperbolic Matrix(1819,-2392,673,-885) (21/16,25/19) -> (27/10,73/27) Hyperbolic Matrix(157,-208,117,-155) (25/19,4/3) -> (4/3,27/20) Parabolic Matrix(1923,-2600,1193,-1613) (27/20,23/17) -> (29/18,79/49) Hyperbolic Matrix(883,-1196,615,-833) (23/17,19/14) -> (33/23,23/16) Hyperbolic Matrix(3483,-4732,1570,-2133) (19/14,53/39) -> (51/23,71/32) Hyperbolic Matrix(4629,-6292,1453,-1975) (53/39,87/64) -> (35/11,51/16) Hyperbolic Matrix(5201,-7072,1376,-1871) (87/64,34/25) -> (34/9,121/32) Hyperbolic Matrix(1873,-2548,1146,-1559) (34/25,15/11) -> (67/41,18/11) Hyperbolic Matrix(571,-780,153,-209) (15/11,26/19) -> (26/7,15/4) Hyperbolic Matrix(417,-572,113,-155) (26/19,11/8) -> (11/3,26/7) Hyperbolic Matrix(1093,-1508,640,-883) (11/8,29/21) -> (29/17,41/24) Hyperbolic Matrix(677,-936,413,-571) (29/21,18/13) -> (18/11,23/14) Hyperbolic Matrix(937,-1300,524,-727) (18/13,25/18) -> (25/14,34/19) Hyperbolic Matrix(1197,-1664,710,-987) (25/18,32/23) -> (32/19,27/16) Hyperbolic Matrix(1145,-1612,738,-1039) (7/5,31/22) -> (31/20,45/29) Hyperbolic Matrix(2029,-2860,774,-1091) (31/22,24/17) -> (76/29,21/8) Hyperbolic Matrix(883,-1248,479,-677) (24/17,41/29) -> (11/6,24/13) Hyperbolic Matrix(989,-1404,622,-883) (17/12,27/19) -> (27/17,35/22) Hyperbolic Matrix(2341,-3328,1499,-2131) (27/19,64/45) -> (64/41,25/16) Hyperbolic Matrix(2339,-3328,622,-885) (64/45,37/26) -> (15/4,64/17) Hyperbolic Matrix(1351,-1924,804,-1145) (37/26,47/33) -> (5/3,37/22) Hyperbolic Matrix(729,-1040,218,-311) (47/33,10/7) -> (10/3,57/17) Hyperbolic Matrix(363,-520,37,-53) (10/7,43/30) -> (9/1,10/1) Hyperbolic Matrix(1559,-2236,327,-469) (43/30,33/23) -> (19/4,43/9) Hyperbolic Matrix(831,-1196,362,-521) (23/16,13/9) -> (39/17,23/10) Hyperbolic Matrix(573,-832,250,-363) (13/9,16/11) -> (16/7,39/17) Hyperbolic Matrix(1143,-1664,215,-313) (16/11,51/35) -> (53/10,16/3) Hyperbolic Matrix(4317,-6292,1141,-1663) (51/35,35/24) -> (87/23,53/14) Hyperbolic Matrix(1353,-1976,569,-831) (35/24,19/13) -> (19/8,69/29) Hyperbolic Matrix(675,-988,427,-625) (19/13,3/2) -> (49/31,19/12) Hyperbolic Matrix(779,-1196,170,-261) (3/2,20/13) -> (32/7,55/12) Hyperbolic Matrix(1249,-1924,742,-1143) (20/13,37/24) -> (37/22,32/19) Hyperbolic Matrix(573,-884,269,-415) (37/24,17/11) -> (17/8,15/7) Hyperbolic Matrix(571,-884,135,-209) (17/11,31/20) -> (21/5,17/4) Hyperbolic Matrix(1507,-2340,436,-677) (45/29,14/9) -> (38/11,45/13) Hyperbolic Matrix(935,-1456,201,-313) (14/9,53/34) -> (51/11,14/3) Hyperbolic Matrix(4369,-6812,1200,-1871) (53/34,39/25) -> (91/25,51/14) Hyperbolic Matrix(4731,-7384,1300,-2029) (39/25,64/41) -> (40/11,91/25) Hyperbolic Matrix(831,-1300,466,-729) (25/16,11/7) -> (41/23,25/14) Hyperbolic Matrix(989,-1560,362,-571) (11/7,30/19) -> (30/11,41/15) Hyperbolic Matrix(1613,-2548,954,-1507) (30/19,49/31) -> (49/29,22/13) Hyperbolic Matrix(623,-988,99,-157) (19/12,46/29) -> (6/1,19/3) Hyperbolic Matrix(3277,-5200,622,-987) (46/29,73/46) -> (21/4,58/11) Hyperbolic Matrix(1507,-2392,361,-573) (73/46,27/17) -> (25/6,21/5) Hyperbolic Matrix(261,-416,32,-51) (35/22,8/5) -> (8/1,17/2) Hyperbolic Matrix(259,-416,33,-53) (8/5,37/23) -> (15/2,8/1) Hyperbolic Matrix(1195,-1924,259,-417) (37/23,29/18) -> (23/5,37/8) Hyperbolic Matrix(6449,-10400,2450,-3951) (79/49,50/31) -> (50/19,129/49) Hyperbolic Matrix(1611,-2600,935,-1509) (50/31,21/13) -> (31/18,50/29) Hyperbolic Matrix(417,-676,256,-415) (21/13,13/8) -> (13/8,31/19) Parabolic Matrix(1975,-3224,574,-937) (31/19,49/30) -> (55/16,31/9) Hyperbolic Matrix(5251,-8580,1560,-2549) (49/30,67/41) -> (37/11,101/30) Hyperbolic Matrix(1455,-2392,823,-1353) (23/14,51/31) -> (53/30,23/13) Hyperbolic Matrix(8059,-13260,3161,-5201) (51/31,130/79) -> (130/51,51/20) Hyperbolic Matrix(12481,-20540,4897,-8059) (130/79,79/48) -> (79/31,130/51) Hyperbolic Matrix(2495,-4108,727,-1197) (79/48,28/17) -> (24/7,79/23) Hyperbolic Matrix(4679,-7904,1786,-3017) (27/16,49/29) -> (55/21,131/50) Hyperbolic Matrix(675,-1144,154,-261) (22/13,17/10) -> (35/8,22/5) Hyperbolic Matrix(885,-1508,152,-259) (46/27,29/17) -> (29/5,6/1) Hyperbolic Matrix(1613,-2756,882,-1507) (41/24,53/31) -> (53/29,11/6) Hyperbolic Matrix(3223,-5512,1156,-1977) (53/31,12/7) -> (92/33,53/19) Hyperbolic Matrix(2755,-4732,818,-1405) (12/7,55/32) -> (101/30,64/19) Hyperbolic Matrix(11857,-20384,4960,-8527) (55/32,98/57) -> (98/41,153/64) Hyperbolic Matrix(5201,-8944,1088,-1871) (98/57,43/25) -> (43/9,110/23) Hyperbolic Matrix(937,-1612,211,-363) (43/25,31/18) -> (31/7,9/2) Hyperbolic Matrix(573,-988,301,-519) (50/29,69/40) -> (17/9,2/1) Hyperbolic Matrix(1145,-1976,361,-623) (69/40,19/11) -> (19/6,35/11) Hyperbolic Matrix(571,-988,241,-417) (19/11,26/15) -> (26/11,19/8) Hyperbolic Matrix(209,-364,89,-155) (26/15,7/4) -> (7/3,26/11) Hyperbolic Matrix(1091,-1924,148,-261) (37/21,30/17) -> (22/3,37/5) Hyperbolic Matrix(675,-1196,206,-365) (23/13,16/9) -> (36/11,23/7) Hyperbolic Matrix(1249,-2236,348,-623) (34/19,9/5) -> (61/17,18/5) Hyperbolic Matrix(573,-1040,200,-363) (29/16,20/11) -> (20/7,23/8) Hyperbolic Matrix(1143,-2080,172,-313) (20/11,51/28) -> (53/8,20/3) Hyperbolic Matrix(2393,-4368,1082,-1975) (31/17,42/23) -> (42/19,73/33) Hyperbolic Matrix(365,-676,196,-363) (24/13,13/7) -> (13/7,28/15) Parabolic Matrix(1197,-2236,250,-467) (28/15,15/8) -> (67/14,24/5) Hyperbolic Matrix(469,-884,165,-311) (15/8,17/9) -> (17/6,37/13) Hyperbolic Matrix(469,-988,197,-415) (2/1,17/8) -> (69/29,50/21) Hyperbolic Matrix(313,-676,144,-311) (15/7,13/6) -> (13/6,37/17) Parabolic Matrix(2651,-5772,502,-1093) (37/17,61/28) -> (95/18,37/7) Hyperbolic Matrix(261,-572,47,-103) (24/11,11/5) -> (11/2,28/5) Hyperbolic Matrix(259,-572,24,-53) (11/5,42/19) -> (10/1,11/1) Hyperbolic Matrix(4889,-10816,2209,-4887) (73/33,104/47) -> (104/47,31/14) Parabolic Matrix(1455,-3224,329,-729) (31/14,51/23) -> (53/12,31/7) Hyperbolic Matrix(209,-468,46,-103) (20/9,9/4) -> (9/2,32/7) Hyperbolic Matrix(573,-1300,160,-363) (9/4,25/11) -> (25/7,43/12) Hyperbolic Matrix(365,-832,68,-155) (25/11,16/7) -> (16/3,27/5) Hyperbolic Matrix(1039,-2392,407,-937) (23/10,53/23) -> (51/20,23/9) Hyperbolic Matrix(1195,-2756,271,-625) (53/23,30/13) -> (22/5,53/12) Hyperbolic Matrix(157,-364,22,-51) (30/13,7/3) -> (7/1,22/3) Hyperbolic Matrix(1091,-2600,415,-989) (50/21,31/13) -> (21/8,50/19) Hyperbolic Matrix(4939,-11804,936,-2237) (43/18,98/41) -> (58/11,95/18) Hyperbolic Matrix(18097,-43264,7569,-18095) (153/64,208/87) -> (208/87,55/23) Parabolic Matrix(1717,-4108,456,-1091) (55/23,12/5) -> (64/17,49/13) Hyperbolic Matrix(625,-1508,172,-415) (12/5,29/12) -> (29/8,40/11) Hyperbolic Matrix(365,-884,64,-155) (29/12,17/7) -> (17/3,23/4) Hyperbolic Matrix(1041,-2548,382,-935) (22/9,27/11) -> (79/29,30/11) Hyperbolic Matrix(677,-1664,190,-467) (27/11,5/2) -> (57/16,25/7) Hyperbolic Matrix(103,-260,21,-53) (5/2,28/11) -> (24/5,5/1) Hyperbolic Matrix(3797,-9672,1449,-3691) (28/11,79/31) -> (131/50,76/29) Hyperbolic Matrix(365,-936,101,-259) (23/9,18/7) -> (18/5,29/8) Hyperbolic Matrix(261,-676,100,-259) (18/7,13/5) -> (13/5,34/13) Parabolic Matrix(1351,-3536,358,-937) (34/13,55/21) -> (49/13,34/9) Hyperbolic Matrix(16433,-43264,6241,-16431) (129/49,208/79) -> (208/79,79/30) Parabolic Matrix(987,-2600,257,-677) (79/30,29/11) -> (23/6,27/7) Hyperbolic Matrix(521,-1404,154,-415) (8/3,27/10) -> (27/8,44/13) Hyperbolic Matrix(5979,-16172,1250,-3381) (119/44,46/17) -> (110/23,67/14) Hyperbolic Matrix(363,-988,115,-313) (19/7,49/18) -> (3/1,19/6) Hyperbolic Matrix(3017,-8216,878,-2391) (49/18,79/29) -> (79/23,55/16) Hyperbolic Matrix(989,-2704,361,-987) (41/15,52/19) -> (52/19,11/4) Parabolic Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(1197,-3328,355,-987) (25/9,64/23) -> (64/19,27/8) Hyperbolic Matrix(2185,-6084,784,-2183) (64/23,39/14) -> (39/14,92/33) Parabolic Matrix(573,-1612,166,-467) (14/5,31/11) -> (31/9,38/11) Hyperbolic Matrix(1039,-2964,292,-833) (37/13,20/7) -> (32/9,89/25) Hyperbolic Matrix(831,-2392,181,-521) (23/8,26/9) -> (78/17,23/5) Hyperbolic Matrix(573,-1664,125,-363) (26/9,3/1) -> (55/12,78/17) Hyperbolic Matrix(1663,-5304,359,-1145) (51/16,16/5) -> (88/19,51/11) Hyperbolic Matrix(209,-676,64,-207) (16/5,13/4) -> (13/4,36/11) Parabolic Matrix(363,-1196,95,-313) (23/7,33/10) -> (19/5,23/6) Hyperbolic Matrix(3225,-10816,961,-3223) (57/17,104/31) -> (104/31,47/14) Parabolic Matrix(1873,-6292,526,-1767) (47/14,37/11) -> (89/25,57/16) Hyperbolic Matrix(675,-2288,77,-261) (61/18,78/23) -> (26/3,9/1) Hyperbolic Matrix(521,-1768,61,-207) (78/23,17/5) -> (17/2,26/3) Hyperbolic Matrix(259,-884,46,-157) (17/5,24/7) -> (28/5,17/3) Hyperbolic Matrix(781,-2704,225,-779) (45/13,52/15) -> (52/15,7/2) Parabolic Matrix(103,-364,15,-53) (7/2,32/9) -> (20/3,7/1) Hyperbolic Matrix(3017,-10816,841,-3015) (43/12,104/29) -> (104/29,61/17) Parabolic Matrix(157,-572,14,-51) (51/14,11/3) -> (11/1,1/0) Hyperbolic Matrix(11441,-43264,3025,-11439) (121/32,208/55) -> (208/55,87/23) Parabolic Matrix(727,-2756,110,-417) (53/14,19/5) -> (33/5,53/8) Hyperbolic Matrix(53,-208,13,-51) (27/7,4/1) -> (4/1,25/6) Parabolic Matrix(157,-676,36,-155) (17/4,13/3) -> (13/3,35/8) Parabolic Matrix(573,-2704,121,-571) (33/7,52/11) -> (52/11,19/4) Parabolic Matrix(469,-2704,81,-467) (23/4,52/9) -> (52/9,29/5) Parabolic Matrix(105,-676,16,-103) (19/3,13/2) -> (13/2,33/5) Parabolic Matrix(365,-2704,49,-363) (37/5,52/7) -> (52/7,15/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,0,1,1) -> Matrix(1,0,1,1) Matrix(519,-572,284,-313) -> Matrix(1,-2,2,-3) Matrix(467,-520,141,-157) -> Matrix(1,0,-1,1) Matrix(779,-884,230,-261) -> Matrix(5,-6,-4,5) Matrix(363,-416,137,-157) -> Matrix(1,0,-1,1) Matrix(313,-364,178,-207) -> Matrix(3,-2,2,-1) Matrix(311,-364,223,-261) -> Matrix(1,-2,1,-1) Matrix(573,-676,484,-571) -> Matrix(3,-2,2,-1) Matrix(2237,-2652,1008,-1195) -> Matrix(1,-2,2,-3) Matrix(831,-988,307,-365) -> Matrix(1,-2,1,-1) Matrix(729,-884,428,-519) -> Matrix(1,-2,0,1) Matrix(727,-884,514,-625) -> Matrix(1,-2,2,-3) Matrix(677,-832,380,-467) -> Matrix(3,-8,2,-5) Matrix(3121,-3848,674,-831) -> Matrix(1,-4,2,-7) Matrix(4213,-5200,1558,-1923) -> Matrix(1,-4,0,1) Matrix(883,-1092,169,-209) -> Matrix(1,-10,1,-9) Matrix(209,-260,41,-51) -> Matrix(1,-2,1,-1) Matrix(207,-260,125,-157) -> Matrix(1,-2,1,-1) Matrix(1975,-2496,906,-1145) -> Matrix(1,0,0,1) Matrix(1767,-2236,535,-677) -> Matrix(1,2,-1,-1) Matrix(573,-728,122,-155) -> Matrix(1,0,0,1) Matrix(1143,-1456,409,-521) -> Matrix(1,-4,1,-3) Matrix(3017,-3848,570,-727) -> Matrix(3,4,2,3) Matrix(1507,-1924,571,-729) -> Matrix(3,-2,-1,1) Matrix(365,-468,202,-259) -> Matrix(1,2,0,1) Matrix(1249,-1612,523,-675) -> Matrix(3,-2,-1,1) Matrix(2495,-3224,1369,-1769) -> Matrix(1,0,-1,1) Matrix(2131,-2756,1207,-1561) -> Matrix(7,-10,5,-7) Matrix(883,-1144,362,-469) -> Matrix(1,0,0,1) Matrix(677,-884,278,-363) -> Matrix(1,2,0,1) Matrix(675,-884,239,-313) -> Matrix(3,2,1,1) Matrix(1819,-2392,673,-885) -> Matrix(1,0,1,1) Matrix(157,-208,117,-155) -> Matrix(1,0,1,1) Matrix(1923,-2600,1193,-1613) -> Matrix(15,-4,19,-5) Matrix(883,-1196,615,-833) -> Matrix(3,-2,5,-3) Matrix(3483,-4732,1570,-2133) -> Matrix(3,-2,2,-1) Matrix(4629,-6292,1453,-1975) -> Matrix(1,-2,1,-1) Matrix(5201,-7072,1376,-1871) -> Matrix(1,0,-2,1) Matrix(1873,-2548,1146,-1559) -> Matrix(7,-6,6,-5) Matrix(571,-780,153,-209) -> Matrix(3,-2,-1,1) Matrix(417,-572,113,-155) -> Matrix(1,-2,1,-1) Matrix(1093,-1508,640,-883) -> Matrix(1,-2,2,-3) Matrix(677,-936,413,-571) -> Matrix(1,-4,1,-3) Matrix(937,-1300,524,-727) -> Matrix(7,-2,4,-1) Matrix(1197,-1664,710,-987) -> Matrix(1,0,0,1) Matrix(1145,-1612,738,-1039) -> Matrix(11,-2,6,-1) Matrix(2029,-2860,774,-1091) -> Matrix(25,-6,-4,1) Matrix(883,-1248,479,-677) -> Matrix(1,0,-1,1) Matrix(989,-1404,622,-883) -> Matrix(3,-2,8,-5) Matrix(2341,-3328,1499,-2131) -> Matrix(5,-4,-1,1) Matrix(2339,-3328,622,-885) -> Matrix(1,0,-2,1) Matrix(1351,-1924,804,-1145) -> Matrix(3,-2,2,-1) Matrix(729,-1040,218,-311) -> Matrix(1,0,-2,1) Matrix(363,-520,37,-53) -> Matrix(1,0,-1,1) Matrix(1559,-2236,327,-469) -> Matrix(3,-2,5,-3) Matrix(831,-1196,362,-521) -> Matrix(13,-10,4,-3) Matrix(573,-832,250,-363) -> Matrix(5,-8,2,-3) Matrix(1143,-1664,215,-313) -> Matrix(1,-4,1,-3) Matrix(4317,-6292,1141,-1663) -> Matrix(1,-2,1,-1) Matrix(1353,-1976,569,-831) -> Matrix(5,-4,-1,1) Matrix(675,-988,427,-625) -> Matrix(1,-2,3,-5) Matrix(779,-1196,170,-261) -> Matrix(5,-6,6,-7) Matrix(1249,-1924,742,-1143) -> Matrix(1,-2,2,-3) Matrix(573,-884,269,-415) -> Matrix(5,-6,1,-1) Matrix(571,-884,135,-209) -> Matrix(1,-2,3,-5) Matrix(1507,-2340,436,-677) -> Matrix(1,-2,-6,13) Matrix(935,-1456,201,-313) -> Matrix(1,-4,1,-3) Matrix(4369,-6812,1200,-1871) -> Matrix(1,-6,0,1) Matrix(4731,-7384,1300,-2029) -> Matrix(1,8,0,1) Matrix(831,-1300,466,-729) -> Matrix(3,-2,2,-1) Matrix(989,-1560,362,-571) -> Matrix(1,0,-6,1) Matrix(1613,-2548,954,-1507) -> Matrix(7,-2,4,-1) Matrix(623,-988,99,-157) -> Matrix(1,-2,1,-1) Matrix(3277,-5200,622,-987) -> Matrix(5,-4,4,-3) Matrix(1507,-2392,361,-573) -> Matrix(1,0,1,1) Matrix(261,-416,32,-51) -> Matrix(7,-4,2,-1) Matrix(259,-416,33,-53) -> Matrix(1,0,-1,1) Matrix(1195,-1924,259,-417) -> Matrix(3,-2,-1,1) Matrix(6449,-10400,2450,-3951) -> Matrix(109,-88,-26,21) Matrix(1611,-2600,935,-1509) -> Matrix(19,-16,25,-21) Matrix(417,-676,256,-415) -> Matrix(15,-14,14,-13) Matrix(1975,-3224,574,-937) -> Matrix(7,-8,-20,23) Matrix(5251,-8580,1560,-2549) -> Matrix(5,-6,-4,5) Matrix(1455,-2392,823,-1353) -> Matrix(1,-4,1,-3) Matrix(8059,-13260,3161,-5201) -> Matrix(11,-10,-1,1) Matrix(12481,-20540,4897,-8059) -> Matrix(29,-30,1,-1) Matrix(2495,-4108,727,-1197) -> Matrix(5,-6,-9,11) Matrix(4679,-7904,1786,-3017) -> Matrix(29,-36,-4,5) Matrix(675,-1144,154,-261) -> Matrix(1,0,0,1) Matrix(885,-1508,152,-259) -> Matrix(1,2,0,1) Matrix(1613,-2756,882,-1507) -> Matrix(3,-2,2,-1) Matrix(3223,-5512,1156,-1977) -> Matrix(9,-8,8,-7) Matrix(2755,-4732,818,-1405) -> Matrix(3,-2,2,-1) Matrix(11857,-20384,4960,-8527) -> Matrix(47,-32,-22,15) Matrix(5201,-8944,1088,-1871) -> Matrix(11,-8,18,-13) Matrix(937,-1612,211,-363) -> Matrix(3,-2,-1,1) Matrix(573,-988,301,-519) -> Matrix(17,-14,11,-9) Matrix(1145,-1976,361,-623) -> Matrix(5,-4,-1,1) Matrix(571,-988,241,-417) -> Matrix(15,-14,-1,1) Matrix(209,-364,89,-155) -> Matrix(9,-10,1,-1) Matrix(1091,-1924,148,-261) -> Matrix(13,-18,8,-11) Matrix(675,-1196,206,-365) -> Matrix(7,-10,-2,3) Matrix(1249,-2236,348,-623) -> Matrix(1,-2,6,-11) Matrix(573,-1040,200,-363) -> Matrix(1,4,0,1) Matrix(1143,-2080,172,-313) -> Matrix(1,0,0,1) Matrix(2393,-4368,1082,-1975) -> Matrix(1,0,-2,1) Matrix(365,-676,196,-363) -> Matrix(7,-6,6,-5) Matrix(1197,-2236,250,-467) -> Matrix(5,-6,6,-7) Matrix(469,-884,165,-311) -> Matrix(5,-6,1,-1) Matrix(469,-988,197,-415) -> Matrix(5,-14,-1,3) Matrix(313,-676,144,-311) -> Matrix(1,-6,0,1) Matrix(2651,-5772,502,-1093) -> Matrix(3,10,2,7) Matrix(261,-572,47,-103) -> Matrix(1,-2,1,-1) Matrix(259,-572,24,-53) -> Matrix(1,2,0,1) Matrix(4889,-10816,2209,-4887) -> Matrix(1,0,5,1) Matrix(1455,-3224,329,-729) -> Matrix(1,0,-1,1) Matrix(209,-468,46,-103) -> Matrix(1,-2,2,-3) Matrix(573,-1300,160,-363) -> Matrix(1,-2,-2,5) Matrix(365,-832,68,-155) -> Matrix(3,-8,2,-5) Matrix(1039,-2392,407,-937) -> Matrix(1,-4,1,-3) Matrix(1195,-2756,271,-625) -> Matrix(3,-10,1,-3) Matrix(157,-364,22,-51) -> Matrix(1,-2,0,1) Matrix(1091,-2600,415,-989) -> Matrix(5,16,-1,-3) Matrix(4939,-11804,936,-2237) -> Matrix(11,26,8,19) Matrix(18097,-43264,7569,-18095) -> Matrix(33,68,-17,-35) Matrix(1717,-4108,456,-1091) -> Matrix(1,2,-2,-3) Matrix(625,-1508,172,-415) -> Matrix(1,2,0,1) Matrix(365,-884,64,-155) -> Matrix(3,-2,2,-1) Matrix(1041,-2548,382,-935) -> Matrix(1,-2,-2,5) Matrix(677,-1664,190,-467) -> Matrix(1,0,0,1) Matrix(103,-260,21,-53) -> Matrix(1,-2,1,-1) Matrix(3797,-9672,1449,-3691) -> Matrix(7,-48,-1,7) Matrix(365,-936,101,-259) -> Matrix(1,-4,1,-3) Matrix(261,-676,100,-259) -> Matrix(1,-14,0,1) Matrix(1351,-3536,358,-937) -> Matrix(1,8,0,1) Matrix(16433,-43264,6241,-16431) -> Matrix(83,336,-21,-85) Matrix(987,-2600,257,-677) -> Matrix(1,4,-3,-11) Matrix(521,-1404,154,-415) -> Matrix(3,2,-2,-1) Matrix(5979,-16172,1250,-3381) -> Matrix(3,2,4,3) Matrix(363,-988,115,-313) -> Matrix(3,2,1,1) Matrix(3017,-8216,878,-2391) -> Matrix(7,4,-16,-9) Matrix(989,-2704,361,-987) -> Matrix(1,0,9,1) Matrix(207,-572,38,-105) -> Matrix(3,-2,2,-1) Matrix(1197,-3328,355,-987) -> Matrix(5,-4,-1,1) Matrix(2185,-6084,784,-2183) -> Matrix(15,-14,14,-13) Matrix(573,-1612,166,-467) -> Matrix(1,-2,-4,9) Matrix(1039,-2964,292,-833) -> Matrix(1,-2,0,1) Matrix(831,-2392,181,-521) -> Matrix(1,-12,1,-11) Matrix(573,-1664,125,-363) -> Matrix(1,8,1,9) Matrix(1663,-5304,359,-1145) -> Matrix(1,0,1,1) Matrix(209,-676,64,-207) -> Matrix(1,-6,0,1) Matrix(363,-1196,95,-313) -> Matrix(1,2,-1,-1) Matrix(3225,-10816,961,-3223) -> Matrix(1,0,1,1) Matrix(1873,-6292,526,-1767) -> Matrix(1,2,0,1) Matrix(675,-2288,77,-261) -> Matrix(7,8,-1,-1) Matrix(521,-1768,61,-207) -> Matrix(9,8,1,1) Matrix(259,-884,46,-157) -> Matrix(1,2,0,1) Matrix(781,-2704,225,-779) -> Matrix(1,0,15,1) Matrix(103,-364,15,-53) -> Matrix(1,-2,1,-1) Matrix(3017,-10816,841,-3015) -> Matrix(1,0,11,1) Matrix(157,-572,14,-51) -> Matrix(1,2,0,1) Matrix(11441,-43264,3025,-11439) -> Matrix(1,0,3,1) Matrix(727,-2756,110,-417) -> Matrix(1,2,0,1) Matrix(53,-208,13,-51) -> Matrix(1,0,1,1) Matrix(157,-676,36,-155) -> Matrix(3,-2,2,-1) Matrix(573,-2704,121,-571) -> Matrix(1,0,3,1) Matrix(469,-2704,81,-467) -> Matrix(15,-28,7,-13) Matrix(105,-676,16,-103) -> Matrix(1,-2,0,1) Matrix(365,-2704,49,-363) -> Matrix(15,-28,7,-13) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 3 Minimal number of generators: 2 Number of equivalence classes of elliptic points of order 2: 1 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 2 Genus: 0 Degree of H/liftables -> H/(image of liftables): 112 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d 0/1 0/1 1 1 2/1 (0/1,2/1) 0 13 17/8 1/0 1 26 15/7 3/1 1 26 13/6 1/0 3 2 37/17 -3/1 1 26 24/11 -2/1 1 13 11/5 1/1 1 26 42/19 (-2/1,0/1) 0 13 104/47 0/1 5 1 31/14 1/2 1 26 51/23 1/1 1 26 20/9 0/1 1 13 9/4 3/2 1 26 25/11 13/5 1 26 16/7 2/1 1 13 23/10 1/0 1 26 53/23 3/1 1 26 30/13 (10/3,4/1) 0 13 7/3 5/1 1 26 26/11 1/0 12 1 19/8 1/0 1 26 69/29 -5/1 1 26 50/21 (-14/3,-4/1) 0 13 31/13 -3/1 1 26 43/18 1/0 1 26 98/41 (-16/7,-2/1) 0 13 208/87 -2/1 17 1 55/23 -9/5 1 26 12/5 0/1 1 13 29/12 -1/2 1 26 17/7 1/1 1 26 22/9 (0/1,2/1) 0 13 27/11 -3/1 1 26 5/2 1/0 1 26 28/11 4/1 1 13 79/31 15/1 1 26 130/51 1/0 20 1 51/20 1/0 1 26 23/9 1/1 1 26 18/7 (4/1,6/1) 0 13 13/5 1/0 7 2 34/13 (-10/1,-8/1) 0 13 55/21 -23/3 1 26 21/8 1/0 1 26 50/19 (-22/5,-4/1) 0 13 208/79 -4/1 21 1 79/30 -31/8 1 26 29/11 -3/1 1 26 37/14 -5/2 1 26 8/3 -2/1 1 13 27/10 -1/4 1 26 73/27 1/1 1 26 46/17 (0/1,2/1) 0 13 19/7 -1/1 1 26 49/18 -3/4 1 26 79/29 -5/11 1 26 30/11 (-2/5,0/1) 0 13 52/19 0/1 9 1 11/4 1/2 1 26 25/9 3/5 1 26 64/23 6/7 1 13 39/14 1/1 7 2 53/19 1/1 1 26 14/5 (4/3,2/1) 0 13 31/11 3/1 1 26 17/6 1/0 1 26 37/13 3/1 1 26 20/7 4/1 1 13 3/1 -1/1 1 26 19/6 1/0 1 26 35/11 1/1 1 26 51/16 1/0 1 26 16/5 2/1 1 13 13/4 1/0 3 2 36/11 -4/1 1 13 23/7 -3/1 1 26 33/10 1/0 1 26 43/13 1/1 1 26 10/3 (-2/1,0/1) 0 13 104/31 0/1 1 1 47/14 1/0 1 26 37/11 -1/1 1 26 64/19 2/1 1 13 27/8 -5/2 1 26 44/13 -4/3 1 13 17/5 -1/1 1 26 24/7 -2/3 1 13 79/23 -9/19 1 26 55/16 -5/12 1 26 31/9 -1/3 1 26 38/11 (-2/11,0/1) 0 13 52/15 0/1 15 1 7/2 1/2 1 26 32/9 2/1 1 13 89/25 1/1 1 26 57/16 1/0 1 26 25/7 -3/1 1 26 43/12 -1/4 1 26 104/29 0/1 11 1 18/5 (0/1,2/3) 0 13 29/8 3/2 1 26 40/11 2/1 1 13 91/25 1/0 7 2 51/14 1/0 1 26 11/3 1/1 1 26 26/7 1/0 2 1 15/4 1/0 1 26 64/17 -2/3 1 13 49/13 1/3 1 26 34/9 (-2/1,0/1) 0 13 208/55 0/1 3 1 87/23 1/1 1 26 53/14 1/0 1 26 19/5 -1/1 1 26 23/6 -1/2 1 26 27/7 1/5 1 26 4/1 0/1 1 13 25/6 1/6 1 26 21/5 1/1 1 26 17/4 1/2 1 26 13/3 1/1 1 2 35/8 1/0 1 26 22/5 (0/1,2/1) 0 13 53/12 1/0 1 26 31/7 1/1 1 26 9/2 1/0 1 26 32/7 2/3 1 13 55/12 7/8 1 26 78/17 1/1 10 1 23/5 1/1 1 26 37/8 1/2 1 26 51/11 1/1 1 26 14/3 (0/1,2/1) 0 13 52/11 0/1 3 1 19/4 1/2 1 26 43/9 3/5 1 26 67/14 3/4 1 26 24/5 2/3 1 13 5/1 1/1 1 26 26/5 1/1 4 1 21/4 5/4 1 26 58/11 (6/5,4/3) 0 13 95/18 11/8 1 26 37/7 1/1 1 26 53/10 3/2 1 26 16/3 2/1 1 13 27/5 -1/1 1 26 11/2 1/0 1 26 28/5 4/3 1 13 17/3 1/1 1 26 23/4 7/4 1 26 52/9 2/1 7 1 6/1 (0/1,2/1) 0 13 19/3 3/1 1 26 13/2 1/0 1 2 33/5 1/1 1 26 53/8 1/0 1 26 20/3 0/1 1 13 7/1 3/1 1 26 22/3 (4/3,2/1) 0 13 52/7 2/1 7 1 15/2 5/2 1 26 8/1 2/1 1 13 17/2 1/0 1 26 26/3 1/0 8 1 9/1 -1/1 1 26 10/1 (0/1,2/1) 0 13 11/1 3/1 1 26 1/0 1/0 1 26 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Reflection Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Reflection Matrix(469,-988,197,-415) (2/1,17/8) -> (69/29,50/21) Hyperbolic Matrix(415,-884,146,-311) (17/8,15/7) -> (17/6,37/13) Glide Reflection Matrix(313,-676,144,-311) (15/7,13/6) -> (13/6,37/17) Parabolic Matrix(1145,-2496,239,-521) (37/17,24/11) -> (67/14,24/5) Glide Reflection Matrix(261,-572,47,-103) (24/11,11/5) -> (11/2,28/5) Hyperbolic Matrix(259,-572,24,-53) (11/5,42/19) -> (10/1,11/1) Hyperbolic Matrix(1975,-4368,893,-1975) (42/19,104/47) -> (42/19,104/47) Reflection Matrix(2913,-6448,1316,-2913) (104/47,31/14) -> (104/47,31/14) Reflection Matrix(1455,-3224,329,-729) (31/14,51/23) -> (53/12,31/7) Hyperbolic Matrix(937,-2080,141,-313) (51/23,20/9) -> (53/8,20/3) Glide Reflection Matrix(209,-468,46,-103) (20/9,9/4) -> (9/2,32/7) Hyperbolic Matrix(573,-1300,160,-363) (9/4,25/11) -> (25/7,43/12) Hyperbolic Matrix(365,-832,68,-155) (25/11,16/7) -> (16/3,27/5) Hyperbolic Matrix(521,-1196,159,-365) (16/7,23/10) -> (36/11,23/7) Glide Reflection Matrix(1039,-2392,407,-937) (23/10,53/23) -> (51/20,23/9) Hyperbolic Matrix(1195,-2756,271,-625) (53/23,30/13) -> (22/5,53/12) Hyperbolic Matrix(157,-364,22,-51) (30/13,7/3) -> (7/1,22/3) Hyperbolic Matrix(155,-364,66,-155) (7/3,26/11) -> (7/3,26/11) Reflection Matrix(417,-988,176,-417) (26/11,19/8) -> (26/11,19/8) Reflection Matrix(831,-1976,262,-623) (19/8,69/29) -> (19/6,35/11) Glide Reflection Matrix(1091,-2600,415,-989) (50/21,31/13) -> (21/8,50/19) Hyperbolic Matrix(675,-1612,152,-363) (31/13,43/18) -> (31/7,9/2) Glide Reflection Matrix(4939,-11804,936,-2237) (43/18,98/41) -> (58/11,95/18) Hyperbolic Matrix(8527,-20384,3567,-8527) (98/41,208/87) -> (98/41,208/87) Reflection Matrix(9569,-22880,4002,-9569) (208/87,55/23) -> (208/87,55/23) Reflection Matrix(1717,-4108,456,-1091) (55/23,12/5) -> (64/17,49/13) Hyperbolic Matrix(625,-1508,172,-415) (12/5,29/12) -> (29/8,40/11) Hyperbolic Matrix(365,-884,64,-155) (29/12,17/7) -> (17/3,23/4) Hyperbolic Matrix(469,-1144,107,-261) (17/7,22/9) -> (35/8,22/5) Glide Reflection Matrix(1041,-2548,382,-935) (22/9,27/11) -> (79/29,30/11) Hyperbolic Matrix(677,-1664,190,-467) (27/11,5/2) -> (57/16,25/7) Hyperbolic Matrix(103,-260,21,-53) (5/2,28/11) -> (24/5,5/1) Hyperbolic Matrix(1613,-4108,470,-1197) (28/11,79/31) -> (24/7,79/23) Glide Reflection Matrix(8059,-20540,3162,-8059) (79/31,130/51) -> (79/31,130/51) Reflection Matrix(5201,-13260,2040,-5201) (130/51,51/20) -> (130/51,51/20) Reflection Matrix(365,-936,101,-259) (23/9,18/7) -> (18/5,29/8) Hyperbolic Matrix(261,-676,100,-259) (18/7,13/5) -> (13/5,34/13) Parabolic Matrix(1351,-3536,358,-937) (34/13,55/21) -> (49/13,34/9) Hyperbolic Matrix(1091,-2860,317,-831) (55/21,21/8) -> (55/16,31/9) Glide Reflection Matrix(3951,-10400,1501,-3951) (50/19,208/79) -> (50/19,208/79) Reflection Matrix(12481,-32864,4740,-12481) (208/79,79/30) -> (208/79,79/30) Reflection Matrix(987,-2600,257,-677) (79/30,29/11) -> (23/6,27/7) Hyperbolic Matrix(729,-1924,158,-417) (29/11,37/14) -> (23/5,37/8) Glide Reflection Matrix(157,-416,20,-53) (37/14,8/3) -> (15/2,8/1) Glide Reflection Matrix(521,-1404,154,-415) (8/3,27/10) -> (27/8,44/13) Hyperbolic Matrix(885,-2392,212,-573) (27/10,73/27) -> (25/6,21/5) Glide Reflection Matrix(1923,-5200,365,-987) (73/27,46/17) -> (21/4,58/11) Glide Reflection Matrix(365,-988,58,-157) (46/17,19/7) -> (6/1,19/3) Glide Reflection Matrix(363,-988,115,-313) (19/7,49/18) -> (3/1,19/6) Hyperbolic Matrix(3017,-8216,878,-2391) (49/18,79/29) -> (79/23,55/16) Hyperbolic Matrix(571,-1560,209,-571) (30/11,52/19) -> (30/11,52/19) Reflection Matrix(417,-1144,152,-417) (52/19,11/4) -> (52/19,11/4) Reflection Matrix(207,-572,38,-105) (11/4,25/9) -> (27/5,11/2) Hyperbolic Matrix(1197,-3328,355,-987) (25/9,64/23) -> (64/19,27/8) Hyperbolic Matrix(2653,-7384,729,-2029) (64/23,39/14) -> (40/11,91/25) Glide Reflection Matrix(2443,-6812,671,-1871) (39/14,53/19) -> (91/25,51/14) Glide Reflection Matrix(521,-1456,112,-313) (53/19,14/5) -> (51/11,14/3) Glide Reflection Matrix(573,-1612,166,-467) (14/5,31/11) -> (31/9,38/11) Hyperbolic Matrix(313,-884,74,-209) (31/11,17/6) -> (21/5,17/4) Glide Reflection Matrix(1039,-2964,292,-833) (37/13,20/7) -> (32/9,89/25) Hyperbolic Matrix(417,-1196,91,-261) (20/7,3/1) -> (32/7,55/12) Glide Reflection Matrix(1975,-6292,522,-1663) (35/11,51/16) -> (87/23,53/14) Glide Reflection Matrix(521,-1664,98,-313) (51/16,16/5) -> (53/10,16/3) Glide Reflection Matrix(209,-676,64,-207) (16/5,13/4) -> (13/4,36/11) Parabolic Matrix(363,-1196,95,-313) (23/7,33/10) -> (19/5,23/6) Hyperbolic Matrix(677,-2236,142,-469) (33/10,43/13) -> (19/4,43/9) Glide Reflection Matrix(157,-520,16,-53) (43/13,10/3) -> (9/1,10/1) Glide Reflection Matrix(311,-1040,93,-311) (10/3,104/31) -> (10/3,104/31) Reflection Matrix(2913,-9776,868,-2913) (104/31,47/14) -> (104/31,47/14) Reflection Matrix(1873,-6292,526,-1767) (47/14,37/11) -> (89/25,57/16) Hyperbolic Matrix(989,-3328,263,-885) (37/11,64/19) -> (15/4,64/17) Glide Reflection Matrix(261,-884,31,-105) (44/13,17/5) -> (8/1,17/2) Glide Reflection Matrix(259,-884,46,-157) (17/5,24/7) -> (28/5,17/3) Hyperbolic Matrix(571,-1976,165,-571) (38/11,52/15) -> (38/11,52/15) Reflection Matrix(209,-728,60,-209) (52/15,7/2) -> (52/15,7/2) Reflection Matrix(103,-364,15,-53) (7/2,32/9) -> (20/3,7/1) Hyperbolic Matrix(2495,-8944,696,-2495) (43/12,104/29) -> (43/12,104/29) Reflection Matrix(521,-1872,145,-521) (104/29,18/5) -> (104/29,18/5) Reflection Matrix(157,-572,14,-51) (51/14,11/3) -> (11/1,1/0) Hyperbolic Matrix(155,-572,42,-155) (11/3,26/7) -> (11/3,26/7) Reflection Matrix(209,-780,56,-209) (26/7,15/4) -> (26/7,15/4) Reflection Matrix(1871,-7072,495,-1871) (34/9,208/55) -> (34/9,208/55) Reflection Matrix(9569,-36192,2530,-9569) (208/55,87/23) -> (208/55,87/23) Reflection Matrix(727,-2756,110,-417) (53/14,19/5) -> (33/5,53/8) Hyperbolic Matrix(53,-208,13,-51) (27/7,4/1) -> (4/1,25/6) Parabolic Matrix(157,-676,36,-155) (17/4,13/3) -> (13/3,35/8) Parabolic Matrix(1871,-8580,408,-1871) (55/12,78/17) -> (55/12,78/17) Reflection Matrix(781,-3588,170,-781) (78/17,23/5) -> (78/17,23/5) Reflection Matrix(831,-3848,157,-727) (37/8,51/11) -> (37/7,53/10) Glide Reflection Matrix(155,-728,33,-155) (14/3,52/11) -> (14/3,52/11) Reflection Matrix(417,-1976,88,-417) (52/11,19/4) -> (52/11,19/4) Reflection Matrix(1663,-7956,315,-1507) (43/9,67/14) -> (95/18,37/7) Glide Reflection Matrix(51,-260,10,-51) (5/1,26/5) -> (5/1,26/5) Reflection Matrix(209,-1092,40,-209) (26/5,21/4) -> (26/5,21/4) Reflection Matrix(415,-2392,72,-415) (23/4,52/9) -> (23/4,52/9) Reflection Matrix(53,-312,9,-53) (52/9,6/1) -> (52/9,6/1) Reflection Matrix(105,-676,16,-103) (19/3,13/2) -> (13/2,33/5) Parabolic Matrix(155,-1144,21,-155) (22/3,52/7) -> (22/3,52/7) Reflection Matrix(209,-1560,28,-209) (52/7,15/2) -> (52/7,15/2) Reflection Matrix(103,-884,12,-103) (17/2,26/3) -> (17/2,26/3) Reflection Matrix(53,-468,6,-53) (26/3,9/1) -> (26/3,9/1) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,0,-1) (0/1,1/0) -> (0/1,1/0) Matrix(1,0,1,-1) -> Matrix(1,0,1,-1) (0/1,2/1) -> (0/1,2/1) Matrix(469,-988,197,-415) -> Matrix(5,-14,-1,3) Matrix(415,-884,146,-311) -> Matrix(-1,6,0,1) *** -> (3/1,1/0) Matrix(313,-676,144,-311) -> Matrix(1,-6,0,1) 1/0 Matrix(1145,-2496,239,-521) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(261,-572,47,-103) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(259,-572,24,-53) -> Matrix(1,2,0,1) 1/0 Matrix(1975,-4368,893,-1975) -> Matrix(-1,0,1,1) (42/19,104/47) -> (-2/1,0/1) Matrix(2913,-6448,1316,-2913) -> Matrix(1,0,4,-1) (104/47,31/14) -> (0/1,1/2) Matrix(1455,-3224,329,-729) -> Matrix(1,0,-1,1) 0/1 Matrix(937,-2080,141,-313) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(209,-468,46,-103) -> Matrix(1,-2,2,-3) 1/1 Matrix(573,-1300,160,-363) -> Matrix(1,-2,-2,5) Matrix(365,-832,68,-155) -> Matrix(3,-8,2,-5) 2/1 Matrix(521,-1196,159,-365) -> Matrix(3,-10,-1,3) Matrix(1039,-2392,407,-937) -> Matrix(1,-4,1,-3) 2/1 Matrix(1195,-2756,271,-625) -> Matrix(3,-10,1,-3) (2/1,4/1).(3/1,1/0) Matrix(157,-364,22,-51) -> Matrix(1,-2,0,1) 1/0 Matrix(155,-364,66,-155) -> Matrix(-1,10,0,1) (7/3,26/11) -> (5/1,1/0) Matrix(417,-988,176,-417) -> Matrix(1,14,0,-1) (26/11,19/8) -> (-7/1,1/0) Matrix(831,-1976,262,-623) -> Matrix(1,4,0,-1) *** -> (-2/1,1/0) Matrix(1091,-2600,415,-989) -> Matrix(5,16,-1,-3) -4/1 Matrix(675,-1612,152,-363) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(4939,-11804,936,-2237) -> Matrix(11,26,8,19) Matrix(8527,-20384,3567,-8527) -> Matrix(15,32,-7,-15) (98/41,208/87) -> (-16/7,-2/1) Matrix(9569,-22880,4002,-9569) -> Matrix(19,36,-10,-19) (208/87,55/23) -> (-2/1,-9/5) Matrix(1717,-4108,456,-1091) -> Matrix(1,2,-2,-3) -1/1 Matrix(625,-1508,172,-415) -> Matrix(1,2,0,1) 1/0 Matrix(365,-884,64,-155) -> Matrix(3,-2,2,-1) 1/1 Matrix(469,-1144,107,-261) -> Matrix(1,0,1,-1) *** -> (0/1,2/1) Matrix(1041,-2548,382,-935) -> Matrix(1,-2,-2,5) Matrix(677,-1664,190,-467) -> Matrix(1,0,0,1) Matrix(103,-260,21,-53) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(1613,-4108,470,-1197) -> Matrix(1,-6,-2,11) Matrix(8059,-20540,3162,-8059) -> Matrix(-1,30,0,1) (79/31,130/51) -> (15/1,1/0) Matrix(5201,-13260,2040,-5201) -> Matrix(1,10,0,-1) (130/51,51/20) -> (-5/1,1/0) Matrix(365,-936,101,-259) -> Matrix(1,-4,1,-3) 2/1 Matrix(261,-676,100,-259) -> Matrix(1,-14,0,1) 1/0 Matrix(1351,-3536,358,-937) -> Matrix(1,8,0,1) 1/0 Matrix(1091,-2860,317,-831) -> Matrix(1,6,-3,-19) Matrix(3951,-10400,1501,-3951) -> Matrix(21,88,-5,-21) (50/19,208/79) -> (-22/5,-4/1) Matrix(12481,-32864,4740,-12481) -> Matrix(63,248,-16,-63) (208/79,79/30) -> (-4/1,-31/8) Matrix(987,-2600,257,-677) -> Matrix(1,4,-3,-11) Matrix(729,-1924,158,-417) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(157,-416,20,-53) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(521,-1404,154,-415) -> Matrix(3,2,-2,-1) -1/1 Matrix(885,-2392,212,-573) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(1923,-5200,365,-987) -> Matrix(1,4,1,3) Matrix(365,-988,58,-157) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(363,-988,115,-313) -> Matrix(3,2,1,1) Matrix(3017,-8216,878,-2391) -> Matrix(7,4,-16,-9) -1/2 Matrix(571,-1560,209,-571) -> Matrix(-1,0,5,1) (30/11,52/19) -> (-2/5,0/1) Matrix(417,-1144,152,-417) -> Matrix(1,0,4,-1) (52/19,11/4) -> (0/1,1/2) Matrix(207,-572,38,-105) -> Matrix(3,-2,2,-1) 1/1 Matrix(1197,-3328,355,-987) -> Matrix(5,-4,-1,1) Matrix(2653,-7384,729,-2029) -> Matrix(9,-8,1,-1) Matrix(2443,-6812,671,-1871) -> Matrix(5,-6,-1,1) Matrix(521,-1456,112,-313) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(573,-1612,166,-467) -> Matrix(1,-2,-4,9) Matrix(313,-884,74,-209) -> Matrix(1,-2,2,-5) Matrix(1039,-2964,292,-833) -> Matrix(1,-2,0,1) 1/0 Matrix(417,-1196,91,-261) -> Matrix(1,-6,1,-7) Matrix(1975,-6292,522,-1663) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(521,-1664,98,-313) -> Matrix(3,-4,2,-3) *** -> (1/1,2/1) Matrix(209,-676,64,-207) -> Matrix(1,-6,0,1) 1/0 Matrix(363,-1196,95,-313) -> Matrix(1,2,-1,-1) (-2/1,0/1).(-1/1,1/0) Matrix(677,-2236,142,-469) -> Matrix(1,2,2,3) Matrix(157,-520,16,-53) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(311,-1040,93,-311) -> Matrix(-1,0,1,1) (10/3,104/31) -> (-2/1,0/1) Matrix(2913,-9776,868,-2913) -> Matrix(1,0,0,-1) (104/31,47/14) -> (0/1,1/0) Matrix(1873,-6292,526,-1767) -> Matrix(1,2,0,1) 1/0 Matrix(989,-3328,263,-885) -> Matrix(-1,0,1,1) *** -> (-2/1,0/1) Matrix(261,-884,31,-105) -> Matrix(5,6,1,1) Matrix(259,-884,46,-157) -> Matrix(1,2,0,1) 1/0 Matrix(571,-1976,165,-571) -> Matrix(-1,0,11,1) (38/11,52/15) -> (-2/11,0/1) Matrix(209,-728,60,-209) -> Matrix(1,0,4,-1) (52/15,7/2) -> (0/1,1/2) Matrix(103,-364,15,-53) -> Matrix(1,-2,1,-1) (0/1,2/1).(1/1,1/0) Matrix(2495,-8944,696,-2495) -> Matrix(-1,0,8,1) (43/12,104/29) -> (-1/4,0/1) Matrix(521,-1872,145,-521) -> Matrix(1,0,3,-1) (104/29,18/5) -> (0/1,2/3) Matrix(157,-572,14,-51) -> Matrix(1,2,0,1) 1/0 Matrix(155,-572,42,-155) -> Matrix(-1,2,0,1) (11/3,26/7) -> (1/1,1/0) Matrix(209,-780,56,-209) -> Matrix(1,2,0,-1) (26/7,15/4) -> (-1/1,1/0) Matrix(1871,-7072,495,-1871) -> Matrix(-1,0,1,1) (34/9,208/55) -> (-2/1,0/1) Matrix(9569,-36192,2530,-9569) -> Matrix(1,0,2,-1) (208/55,87/23) -> (0/1,1/1) Matrix(727,-2756,110,-417) -> Matrix(1,2,0,1) 1/0 Matrix(53,-208,13,-51) -> Matrix(1,0,1,1) 0/1 Matrix(157,-676,36,-155) -> Matrix(3,-2,2,-1) 1/1 Matrix(1871,-8580,408,-1871) -> Matrix(15,-14,16,-15) (55/12,78/17) -> (7/8,1/1) Matrix(781,-3588,170,-781) -> Matrix(5,-6,4,-5) (78/17,23/5) -> (1/1,3/2) Matrix(831,-3848,157,-727) -> Matrix(7,-4,5,-3) Matrix(155,-728,33,-155) -> Matrix(1,0,1,-1) (14/3,52/11) -> (0/1,2/1) Matrix(417,-1976,88,-417) -> Matrix(1,0,4,-1) (52/11,19/4) -> (0/1,1/2) Matrix(1663,-7956,315,-1507) -> Matrix(13,-10,9,-7) Matrix(51,-260,10,-51) -> Matrix(-1,2,0,1) (5/1,26/5) -> (1/1,1/0) Matrix(209,-1092,40,-209) -> Matrix(9,-10,8,-9) (26/5,21/4) -> (1/1,5/4) Matrix(415,-2392,72,-415) -> Matrix(15,-28,8,-15) (23/4,52/9) -> (7/4,2/1) Matrix(53,-312,9,-53) -> Matrix(1,0,1,-1) (52/9,6/1) -> (0/1,2/1) Matrix(105,-676,16,-103) -> Matrix(1,-2,0,1) 1/0 Matrix(155,-1144,21,-155) -> Matrix(5,-8,3,-5) (22/3,52/7) -> (4/3,2/1) Matrix(209,-1560,28,-209) -> Matrix(9,-20,4,-9) (52/7,15/2) -> (2/1,5/2) Matrix(103,-884,12,-103) -> Matrix(-1,14,0,1) (17/2,26/3) -> (7/1,1/0) Matrix(53,-468,6,-53) -> Matrix(1,2,0,-1) (26/3,9/1) -> (-1/1,1/0) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.