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): 1536 Minimal number of generators: 257 Number of equivalence classes of cusps: 96 Genus: 81 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 -7/15 -13/29 -3/7 -11/27 -5/13 -7/19 -9/25 -1/3 -7/23 -5/17 -3/11 -1/5 -1/7 -1/9 0/1 1/7 3/13 5/19 1/3 7/17 5/11 1/2 7/13 17/31 3/5 11/17 5/7 7/9 11/13 13/15 1/1 17/15 13/11 11/9 9/7 23/17 37/27 7/5 19/13 3/2 17/11 39/25 11/7 49/31 5/3 41/23 9/5 31/17 13/7 2/1 11/5 7/3 45/19 17/7 5/2 23/9 13/5 35/13 19/7 117/43 3/1 49/15 10/3 37/11 17/5 99/29 7/2 25/7 11/3 63/17 19/5 127/33 27/7 4/1 13/3 31/7 9/2 23/5 14/3 33/7 53/11 5/1 27/5 11/2 17/3 29/5 6/1 19/3 13/2 7/1 8/1 9/1 29/3 10/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/2 1/0 -1/2 -1/1 0/1 -7/15 -1/2 -6/13 -1/1 0/1 -11/24 -4/3 -1/1 -5/11 -1/1 -2/3 -14/31 -9/13 -2/3 -9/20 -3/5 -4/7 -13/29 -1/2 -4/9 -1/1 0/1 -15/34 -1/1 0/1 -11/25 -1/1 0/1 -7/16 -1/1 -2/3 -24/55 -1/1 -4/5 -17/39 -1/1 -2/3 -10/23 -1/1 0/1 -3/7 -1/2 -14/33 -2/5 -1/3 -11/26 -1/3 0/1 -30/71 -1/3 0/1 -19/45 -1/1 0/1 -8/19 -1/3 0/1 -21/50 -1/3 0/1 -13/31 -1/3 0/1 -5/12 -1/1 0/1 -17/41 -1/2 -12/29 0/1 1/1 -19/46 -1/1 0/1 -7/17 -1/1 0/1 -16/39 -1/1 -2/3 -9/22 -2/3 -3/5 -11/27 -1/2 -2/5 -1/3 0/1 -11/28 0/1 1/1 -9/23 -1/1 0/1 -16/41 -1/1 0/1 -7/18 -2/1 -1/1 -5/13 -1/2 -13/34 -4/11 -1/3 -21/55 -1/3 0/1 -29/76 -1/3 0/1 -8/21 -2/5 -1/3 -19/50 -1/3 -2/7 -11/29 -1/3 0/1 -14/37 -1/3 0/1 -3/8 -1/5 0/1 -13/35 0/1 1/5 -10/27 0/1 1/1 -17/46 0/1 1/1 -24/65 0/1 1/1 -7/19 1/0 -25/68 -6/5 -1/1 -18/49 -1/1 0/1 -11/30 -1/1 0/1 -15/41 -1/1 0/1 -4/11 -1/1 0/1 -9/25 -1/2 -14/39 -2/5 -1/3 -5/14 -1/3 0/1 -11/31 -1/2 -6/17 -1/3 0/1 -7/20 -1/5 0/1 -8/23 -1/15 0/1 -1/3 -1/1 0/1 -8/25 -1/15 0/1 -7/22 0/1 1/13 -6/19 0/1 1/3 -5/16 0/1 1/1 -9/29 1/0 -4/13 0/1 1/1 -7/23 1/0 -10/33 -2/1 -1/1 -3/10 -1/1 0/1 -11/37 -1/1 0/1 -19/64 -1/1 0/1 -8/27 -1/1 0/1 -13/44 -1/1 0/1 -18/61 -1/1 -6/7 -5/17 -1/2 -17/58 -1/3 0/1 -12/41 -1/3 0/1 -7/24 -1/3 0/1 -9/31 -1/7 0/1 -11/38 -1/17 0/1 -2/7 0/1 1/3 -9/32 0/1 1/1 -16/57 0/1 1/1 -7/25 0/1 1/1 -12/43 2/3 1/1 -5/18 1/1 2/1 -3/11 1/0 -7/26 -1/1 0/1 -11/41 -2/1 -1/1 -4/15 -1/1 -2/3 -9/34 -1/1 0/1 -14/53 -1/1 0/1 -5/19 -1/1 0/1 -6/23 -1/3 0/1 -1/4 0/1 1/1 -5/21 1/0 -4/17 -3/1 -2/1 -7/30 -2/1 -1/1 -3/13 -1/1 0/1 -11/48 -1/1 0/1 -8/35 -1/1 0/1 -5/22 -1/3 0/1 -7/31 1/0 -2/9 -1/1 0/1 -7/32 0/1 1/3 -5/23 0/1 1/1 -8/37 0/1 1/1 -3/14 0/1 1/1 -7/33 -1/1 0/1 -11/52 0/1 1/1 -4/19 0/1 1/1 -1/5 1/0 -4/21 -2/1 -1/1 -11/58 -2/1 -1/1 -7/37 -2/1 -1/1 -3/16 -1/1 0/1 -5/27 -2/1 -1/1 -7/38 -4/3 -1/1 -2/11 -2/1 -1/1 -5/28 -1/1 -2/3 -3/17 -1/1 0/1 -4/23 -1/1 0/1 -1/6 -1/1 0/1 -3/19 1/0 -2/13 -4/1 -3/1 -3/20 -2/1 -9/5 -1/7 -2/1 -1/1 -3/22 -8/7 -1/1 -2/15 -1/1 -4/5 -1/8 -1/1 0/1 -1/9 1/0 0/1 -1/1 0/1 1/10 -6/5 -1/1 1/9 -1/1 -4/5 1/8 -1/1 -2/3 1/7 -1/2 2/13 -1/3 0/1 3/19 0/1 1/1 1/6 -1/1 0/1 3/17 1/0 2/11 -4/3 -1/1 1/5 -1/1 -2/3 4/19 -1/1 -2/3 7/33 -3/4 3/14 -9/13 -2/3 5/23 -5/8 7/32 -2/3 -3/5 2/9 -3/5 -4/7 3/13 -1/2 4/17 -3/7 -2/5 5/21 -2/5 -1/3 1/4 -1/1 0/1 5/19 -1/2 4/15 -1/1 0/1 3/11 -1/1 0/1 2/7 -1/1 -2/3 7/24 -1/1 -4/5 5/17 -1/1 -2/3 8/27 -3/5 -4/7 11/37 -1/2 3/10 -1/1 0/1 1/3 -1/2 5/14 -2/5 -1/3 4/11 -1/3 0/1 15/41 -1/2 11/30 -1/3 0/1 7/19 -1/1 0/1 10/27 -2/3 -3/5 13/35 -1/2 3/8 -1/3 0/1 14/37 -1/1 0/1 11/29 -1/2 19/50 -2/5 -1/3 8/21 -1/3 0/1 5/13 -1/3 0/1 2/5 -1/1 0/1 11/27 -1/1 0/1 9/22 -1/1 -4/5 7/17 -1/2 19/46 -1/3 -2/7 12/29 -1/3 0/1 29/70 -1/3 0/1 17/41 -1/3 0/1 5/12 0/1 1/1 13/31 1/0 21/50 -1/1 0/1 8/19 -1/1 0/1 3/7 -1/1 0/1 10/23 -1/1 -4/5 17/39 -3/4 7/16 -1/1 -2/3 18/41 -2/3 -3/5 11/25 -3/4 4/9 -2/3 -3/5 5/11 -1/2 6/13 -4/9 -3/7 7/15 -3/7 -2/5 1/2 -1/3 0/1 9/17 0/1 1/3 8/15 0/1 1/1 7/13 1/0 13/24 -1/1 0/1 6/11 0/1 1/1 17/31 1/0 11/20 -1/1 0/1 16/29 -1/1 0/1 5/9 -1/1 0/1 9/16 -1/1 0/1 22/39 -2/1 -1/1 13/23 -1/2 17/30 0/1 1/5 4/7 -2/1 -1/1 3/5 -1/2 8/13 -4/11 -1/3 21/34 -1/3 0/1 34/55 -2/5 -1/3 13/21 -1/3 0/1 18/29 -1/3 0/1 5/8 -2/5 -1/3 22/35 -1/3 -2/7 17/27 -1/4 29/46 -1/3 0/1 41/65 -1/3 0/1 12/19 -1/3 -2/7 31/49 -1/4 19/30 -1/3 0/1 26/41 -1/3 0/1 7/11 -1/3 0/1 9/14 -1/3 0/1 20/31 -1/5 0/1 31/48 0/1 1/5 11/17 -1/2 24/37 -4/11 -1/3 13/20 -1/3 -6/19 2/3 -1/5 0/1 9/13 0/1 1/5 16/23 0/1 1/3 23/33 1/2 7/10 0/1 1/1 26/37 2/3 1/1 19/27 0/1 1/1 12/17 0/1 1/1 17/24 0/1 1/1 5/7 1/0 23/32 -2/1 -1/1 18/25 -6/5 -1/1 13/18 -1/1 0/1 34/47 -1/3 0/1 21/29 -1/1 0/1 8/11 -1/1 0/1 11/15 -1/1 0/1 14/19 -1/1 -4/5 17/23 -1/2 3/4 -1/1 0/1 7/9 -1/2 11/14 -2/5 -1/3 26/33 -2/5 -1/3 15/19 -1/3 0/1 19/24 -4/11 -1/3 23/29 -1/4 4/5 -1/3 0/1 13/16 0/1 1/1 9/11 -1/2 14/17 -2/5 -1/3 5/6 -1/3 0/1 16/19 -1/3 0/1 11/13 -1/4 28/33 -2/9 -1/5 17/20 -1/5 0/1 6/7 -1/5 0/1 13/15 -1/8 7/8 -1/15 0/1 1/1 -1/1 0/1 9/8 -1/15 0/1 17/15 0/1 25/22 0/1 1/41 8/7 0/1 1/13 7/6 0/1 1/3 20/17 0/1 1/3 13/11 1/2 32/27 2/3 1/1 19/16 0/1 1/1 6/5 0/1 1/1 23/19 0/1 1/1 17/14 1/1 2/1 28/23 2/3 1/1 11/9 1/0 27/22 0/1 1/1 16/13 -1/3 0/1 21/17 0/1 1/3 5/4 0/1 1/1 9/7 1/0 13/10 -2/1 -1/1 43/33 -3/2 30/23 -1/1 -2/3 17/13 -2/1 -1/1 55/42 -1/1 -12/13 38/29 -1/1 -2/3 21/16 -1/1 0/1 25/19 1/0 4/3 -1/1 0/1 23/17 1/0 42/31 -2/1 -1/1 19/14 -4/3 -1/1 53/39 -3/4 34/25 -2/3 -3/5 15/11 -1/1 0/1 26/19 -1/1 0/1 37/27 -1/2 1/0 48/35 -1/1 0/1 11/8 -1/1 0/1 18/13 -1/1 0/1 43/31 -4/3 -1/1 25/18 -1/1 -6/7 7/5 -1/2 24/17 -1/3 0/1 41/29 -1/3 0/1 17/12 -1/3 0/1 10/7 -1/3 0/1 43/30 -1/3 0/1 33/23 -1/4 23/16 -1/5 0/1 59/41 -1/4 95/66 -8/39 -1/5 36/25 -1/5 -2/11 13/9 -1/7 0/1 16/11 -1/17 0/1 19/13 0/1 22/15 0/1 1/23 3/2 0/1 1/3 20/13 6/7 1/1 17/11 1/0 31/20 0/1 1/3 14/9 0/1 1/1 39/25 1/2 1/0 64/41 0/1 1/1 25/16 0/1 1/1 11/7 0/1 1/1 41/26 0/1 1/1 30/19 0/1 1/1 49/31 1/2 68/43 3/5 2/3 19/12 2/3 1/1 65/41 0/1 1/1 111/70 0/1 1/1 46/29 0/1 1/1 27/17 1/2 35/22 2/3 1/1 8/5 1/1 2/1 5/3 1/0 12/7 -1/1 0/1 19/11 -2/1 -1/1 83/48 -1/1 -2/3 64/37 -1/1 0/1 45/26 -1/1 0/1 26/15 -2/1 -1/1 33/19 -3/2 7/4 -1/1 -2/3 30/17 -1/7 0/1 53/30 0/1 1/3 23/13 1/0 62/35 -8/7 -1/1 39/22 -1/1 -2/3 16/9 -1/1 0/1 41/23 -1/2 1/0 66/37 -1/1 0/1 25/14 -1/1 0/1 9/5 -1/1 0/1 29/16 -1/1 0/1 20/11 -1/1 0/1 31/17 -1/2 42/23 -2/5 -1/3 11/6 -1/3 0/1 24/13 -1/1 0/1 37/20 -1/1 0/1 13/7 -1/2 15/8 -1/3 0/1 17/9 -1/5 0/1 19/10 -1/11 0/1 2/1 0/1 1/1 11/5 1/0 20/9 -6/1 -5/1 49/22 -5/1 -4/1 29/13 -4/1 -3/1 9/4 -3/1 -2/1 25/11 -3/2 41/18 -3/1 -2/1 16/7 -2/1 -1/1 55/24 -2/1 -1/1 39/17 -3/2 23/10 -4/3 -1/1 30/13 -10/9 -1/1 67/29 -1/1 37/16 -1/1 -10/11 7/3 -1/1 0/1 26/11 -1/1 0/1 45/19 -1/2 1/0 64/27 -1/1 0/1 19/8 -1/1 0/1 31/13 -1/2 43/18 0/1 1/1 12/5 -1/3 0/1 41/17 0/1 1/1 111/46 0/1 1/1 70/29 0/1 1/1 29/12 0/1 1/1 17/7 1/0 22/9 -4/3 -1/1 49/20 -2/3 -3/5 27/11 -1/1 0/1 5/2 -1/1 0/1 23/9 0/1 41/16 0/1 1/7 18/7 0/1 1/3 13/5 0/1 1/1 47/18 1/1 2/1 81/31 1/0 34/13 0/1 1/1 21/8 0/1 1/1 29/11 1/0 8/3 0/1 1/1 35/13 1/0 27/10 -3/1 -2/1 73/27 -3/2 46/17 -1/1 -4/5 19/7 -1/1 0/1 68/25 -1/7 0/1 117/43 0/1 166/61 0/1 1/17 49/18 0/1 1/5 30/11 0/1 1/1 11/4 0/1 1/1 3/1 1/0 13/4 -2/1 -1/1 49/15 -3/2 1/0 85/26 -2/1 -1/1 36/11 -2/1 -1/1 23/7 -2/1 -1/1 10/3 -1/1 0/1 37/11 1/0 27/8 -4/1 -3/1 44/13 -3/1 -2/1 17/5 -2/1 -1/1 58/17 -2/1 -1/1 99/29 -3/2 1/0 140/41 -2/1 -1/1 41/12 -2/1 -1/1 24/7 -4/3 -1/1 31/9 1/0 7/2 -2/1 -1/1 25/7 -1/1 43/12 -1/1 -6/7 18/5 -1/1 -2/3 11/3 -1/1 0/1 37/10 0/1 1/1 63/17 1/0 26/7 -1/1 0/1 15/4 -1/1 0/1 34/9 0/1 1/1 19/5 1/0 23/6 -2/1 -1/1 50/13 -12/11 -1/1 127/33 -1/1 77/20 -1/1 -16/17 27/7 -1/1 -2/3 4/1 -1/1 0/1 13/3 1/0 22/5 -7/1 -6/1 53/12 -5/1 -24/5 31/7 -5/1 -4/1 9/2 -4/1 -3/1 32/7 -3/1 -2/1 55/12 -4/1 -3/1 133/29 -16/5 -3/1 78/17 -3/1 -26/9 23/5 -5/2 37/8 -11/5 -2/1 14/3 -2/1 -9/5 33/7 -3/2 52/11 -1/1 0/1 19/4 -2/1 -1/1 24/5 -2/1 -1/1 53/11 -3/2 1/0 82/17 -2/1 -1/1 29/6 -2/1 -1/1 5/1 -2/1 -1/1 16/3 -8/7 -1/1 27/5 -1/1 38/7 -1/1 -16/17 11/2 -1/1 -4/5 28/5 -1/1 0/1 17/3 -1/2 23/4 -1/1 0/1 52/9 -2/1 -1/1 81/14 -12/11 -1/1 191/33 -1/1 110/19 -1/1 -16/17 29/5 -1/1 -2/3 6/1 -1/1 0/1 25/4 -1/1 -2/3 19/3 -1/3 0/1 13/2 0/1 1/1 7/1 1/0 15/2 -2/1 -1/1 8/1 -2/1 -1/1 9/1 -4/3 -1/1 19/2 -14/13 -1/1 29/3 -1/1 10/1 -1/1 -6/7 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,-2,-3) (-1/1,1/0) -> (-1/1,-1/2) Parabolic Matrix(423,200,184,87) (-1/2,-7/15) -> (39/17,23/10) Hyperbolic Matrix(539,250,774,359) (-7/15,-6/13) -> (16/23,23/33) Hyperbolic Matrix(593,272,944,433) (-6/13,-11/24) -> (5/8,22/35) Hyperbolic Matrix(57,26,-410,-187) (-11/24,-5/11) -> (-1/7,-3/22) Hyperbolic Matrix(1403,634,582,263) (-5/11,-14/31) -> (12/5,41/17) Hyperbolic Matrix(817,368,464,209) (-14/31,-9/20) -> (7/4,30/17) Hyperbolic Matrix(347,156,932,419) (-9/20,-13/29) -> (13/35,3/8) Hyperbolic Matrix(407,182,1098,491) (-13/29,-4/9) -> (10/27,13/35) Hyperbolic Matrix(743,328,632,279) (-4/9,-15/34) -> (7/6,20/17) Hyperbolic Matrix(1031,454,570,251) (-15/34,-11/25) -> (9/5,29/16) Hyperbolic Matrix(173,76,-972,-427) (-11/25,-7/16) -> (-5/28,-3/17) Hyperbolic Matrix(1877,820,396,173) (-7/16,-24/55) -> (52/11,19/4) Hyperbolic Matrix(2723,1188,4316,1883) (-24/55,-17/39) -> (41/65,12/19) Hyperbolic Matrix(395,172,852,371) (-17/39,-10/23) -> (6/13,7/15) Hyperbolic Matrix(167,72,-392,-169) (-10/23,-3/7) -> (-3/7,-14/33) Parabolic Matrix(1165,494,-3054,-1295) (-14/33,-11/26) -> (-29/76,-8/21) Hyperbolic Matrix(4321,1826,1886,797) (-11/26,-30/71) -> (16/7,55/24) Hyperbolic Matrix(999,422,1882,795) (-30/71,-19/45) -> (9/17,8/15) Hyperbolic Matrix(275,116,1164,491) (-19/45,-8/19) -> (4/17,5/21) Hyperbolic Matrix(661,278,554,233) (-8/19,-21/50) -> (19/16,6/5) Hyperbolic Matrix(1821,764,1156,485) (-21/50,-13/31) -> (11/7,41/26) Hyperbolic Matrix(277,116,-1268,-531) (-13/31,-5/12) -> (-7/32,-5/23) Hyperbolic Matrix(327,136,440,183) (-5/12,-17/41) -> (17/23,3/4) Hyperbolic Matrix(1531,634,326,135) (-17/41,-12/29) -> (14/3,33/7) Hyperbolic Matrix(653,270,1202,497) (-12/29,-19/46) -> (13/24,6/11) Hyperbolic Matrix(325,134,-1414,-583) (-19/46,-7/17) -> (-3/13,-11/48) Hyperbolic Matrix(487,200,56,23) (-7/17,-16/39) -> (8/1,9/1) Hyperbolic Matrix(1517,622,978,401) (-16/39,-9/22) -> (31/20,14/9) Hyperbolic Matrix(323,132,1084,443) (-9/22,-11/27) -> (11/37,3/10) Hyperbolic Matrix(271,110,914,371) (-11/27,-2/5) -> (8/27,11/37) Hyperbolic Matrix(583,230,474,187) (-2/5,-11/28) -> (27/22,16/13) Hyperbolic Matrix(1159,454,314,123) (-11/28,-9/23) -> (11/3,37/10) Hyperbolic Matrix(527,206,-1998,-781) (-9/23,-16/41) -> (-14/53,-5/19) Hyperbolic Matrix(945,368,208,81) (-16/41,-7/18) -> (9/2,32/7) Hyperbolic Matrix(259,100,-676,-261) (-7/18,-5/13) -> (-5/13,-13/34) Parabolic Matrix(1555,594,1966,751) (-13/34,-21/55) -> (15/19,19/24) Hyperbolic Matrix(1137,434,-6002,-2291) (-21/55,-29/76) -> (-11/58,-7/37) Hyperbolic Matrix(1757,668,1444,549) (-8/21,-19/50) -> (17/14,28/23) Hyperbolic Matrix(2013,764,772,293) (-19/50,-11/29) -> (13/5,47/18) Hyperbolic Matrix(723,274,-2578,-977) (-11/29,-14/37) -> (-16/57,-7/25) Hyperbolic Matrix(1645,622,722,273) (-14/37,-3/8) -> (41/18,16/7) Hyperbolic Matrix(457,170,-1578,-587) (-3/8,-13/35) -> (-9/31,-11/38) Hyperbolic Matrix(151,56,968,359) (-13/35,-10/27) -> (2/13,3/19) Hyperbolic Matrix(2487,920,1576,583) (-10/27,-17/46) -> (41/26,30/19) Hyperbolic Matrix(2437,900,5884,2173) (-17/46,-24/65) -> (12/29,29/70) Hyperbolic Matrix(1571,580,1980,731) (-24/65,-7/19) -> (23/29,4/5) Hyperbolic Matrix(1925,708,2428,893) (-7/19,-25/68) -> (19/24,23/29) Hyperbolic Matrix(49,18,558,205) (-25/68,-18/49) -> (0/1,1/10) Hyperbolic Matrix(2021,742,1114,409) (-18/49,-11/30) -> (29/16,20/11) Hyperbolic Matrix(1109,406,-3734,-1367) (-11/30,-15/41) -> (-11/37,-19/64) Hyperbolic Matrix(203,74,502,183) (-15/41,-4/11) -> (2/5,11/27) Hyperbolic Matrix(449,162,-1250,-451) (-4/11,-9/25) -> (-9/25,-14/39) Parabolic Matrix(1295,464,2096,751) (-14/39,-5/14) -> (21/34,34/55) Hyperbolic Matrix(647,230,346,123) (-5/14,-11/31) -> (13/7,15/8) Hyperbolic Matrix(1885,668,1188,421) (-11/31,-6/17) -> (46/29,27/17) Hyperbolic Matrix(935,328,248,87) (-6/17,-7/20) -> (15/4,34/9) Hyperbolic Matrix(1819,634,1030,359) (-7/20,-8/23) -> (30/17,53/30) Hyperbolic Matrix(47,16,-144,-49) (-8/23,-1/3) -> (-1/3,-8/25) Parabolic Matrix(801,256,704,225) (-8/25,-7/22) -> (25/22,8/7) Hyperbolic Matrix(1029,326,1594,505) (-7/22,-6/19) -> (20/31,31/48) Hyperbolic Matrix(281,88,744,233) (-6/19,-5/16) -> (3/8,14/37) Hyperbolic Matrix(1113,346,1766,549) (-5/16,-9/29) -> (17/27,29/46) Hyperbolic Matrix(323,100,604,187) (-9/29,-4/13) -> (8/15,7/13) Hyperbolic Matrix(321,98,-1058,-323) (-4/13,-7/23) -> (-7/23,-10/33) Parabolic Matrix(1745,528,1008,305) (-10/33,-3/10) -> (45/26,26/15) Hyperbolic Matrix(455,136,184,55) (-3/10,-11/37) -> (27/11,5/2) Hyperbolic Matrix(3369,1000,2456,729) (-19/64,-8/27) -> (48/35,11/8) Hyperbolic Matrix(1001,296,1816,537) (-8/27,-13/44) -> (11/20,16/29) Hyperbolic Matrix(501,148,44,13) (-13/44,-18/61) -> (10/1,1/0) Hyperbolic Matrix(3133,924,2404,709) (-18/61,-5/17) -> (43/33,30/23) Hyperbolic Matrix(2715,796,2084,611) (-5/17,-17/58) -> (13/10,43/33) Hyperbolic Matrix(5249,1538,2174,637) (-17/58,-12/41) -> (70/29,29/12) Hyperbolic Matrix(1403,410,2214,647) (-12/41,-7/24) -> (19/30,26/41) Hyperbolic Matrix(859,250,134,39) (-7/24,-9/31) -> (19/3,13/2) Hyperbolic Matrix(857,248,584,169) (-11/38,-2/7) -> (22/15,3/2) Hyperbolic Matrix(625,176,1424,401) (-2/7,-9/32) -> (7/16,18/41) Hyperbolic Matrix(3473,976,2224,625) (-9/32,-16/57) -> (64/41,25/16) Hyperbolic Matrix(1467,410,2086,583) (-7/25,-12/43) -> (26/37,19/27) Hyperbolic Matrix(977,272,176,49) (-12/43,-5/18) -> (11/2,28/5) Hyperbolic Matrix(131,36,-484,-133) (-5/18,-3/11) -> (-3/11,-7/26) Parabolic Matrix(305,82,-1618,-435) (-7/26,-11/41) -> (-7/37,-3/16) Hyperbolic Matrix(1485,398,1138,305) (-11/41,-4/15) -> (30/23,17/13) Hyperbolic Matrix(173,46,786,209) (-4/15,-9/34) -> (7/32,2/9) Hyperbolic Matrix(3569,944,2000,529) (-9/34,-14/53) -> (66/37,25/14) Hyperbolic Matrix(1129,296,1560,409) (-5/19,-6/23) -> (34/47,21/29) Hyperbolic Matrix(1037,270,434,113) (-6/23,-1/4) -> (43/18,12/5) Hyperbolic Matrix(715,172,212,51) (-1/4,-5/21) -> (37/11,27/8) Hyperbolic Matrix(839,198,250,59) (-5/21,-4/17) -> (10/3,37/11) Hyperbolic Matrix(753,176,1168,273) (-4/17,-7/30) -> (9/14,20/31) Hyperbolic Matrix(43,10,374,87) (-7/30,-3/13) -> (1/9,1/8) Hyperbolic Matrix(3737,856,1576,361) (-11/48,-8/35) -> (64/27,19/8) Hyperbolic Matrix(913,208,496,113) (-8/35,-5/22) -> (11/6,24/13) Hyperbolic Matrix(247,56,1160,263) (-5/22,-7/31) -> (7/33,3/14) Hyperbolic Matrix(331,74,246,55) (-7/31,-2/9) -> (4/3,23/17) Hyperbolic Matrix(945,208,368,81) (-2/9,-7/32) -> (41/16,18/7) Hyperbolic Matrix(857,186,1350,293) (-5/23,-8/37) -> (26/41,7/11) Hyperbolic Matrix(409,88,488,105) (-8/37,-3/14) -> (5/6,16/19) Hyperbolic Matrix(731,156,164,35) (-3/14,-7/33) -> (31/7,9/2) Hyperbolic Matrix(1379,292,732,155) (-7/33,-11/52) -> (15/8,17/9) Hyperbolic Matrix(1337,282,934,197) (-11/52,-4/19) -> (10/7,43/30) Hyperbolic Matrix(39,8,-200,-41) (-4/19,-1/5) -> (-1/5,-4/21) Parabolic Matrix(3873,736,1184,225) (-4/21,-11/58) -> (85/26,36/11) Hyperbolic Matrix(707,132,316,59) (-3/16,-5/27) -> (29/13,9/4) Hyperbolic Matrix(2983,550,1882,347) (-5/27,-7/38) -> (19/12,65/41) Hyperbolic Matrix(1805,332,1332,245) (-7/38,-2/11) -> (42/31,19/14) Hyperbolic Matrix(977,176,272,49) (-2/11,-5/28) -> (43/12,18/5) Hyperbolic Matrix(387,68,700,123) (-3/17,-4/23) -> (16/29,5/9) Hyperbolic Matrix(427,74,502,87) (-4/23,-1/6) -> (17/20,6/7) Hyperbolic Matrix(723,116,268,43) (-1/6,-3/19) -> (35/13,27/10) Hyperbolic Matrix(607,94,226,35) (-3/19,-2/13) -> (8/3,35/13) Hyperbolic Matrix(301,46,530,81) (-2/13,-3/20) -> (17/30,4/7) Hyperbolic Matrix(375,56,904,135) (-3/20,-1/7) -> (17/41,5/12) Hyperbolic Matrix(1001,136,184,25) (-3/22,-2/15) -> (38/7,11/2) Hyperbolic Matrix(589,78,370,49) (-2/15,-1/8) -> (35/22,8/5) Hyperbolic Matrix(471,56,328,39) (-1/8,-1/9) -> (33/23,23/16) Hyperbolic Matrix(107,10,246,23) (-1/9,0/1) -> (10/23,17/39) Hyperbolic Matrix(261,-28,28,-3) (1/10,1/9) -> (9/1,19/2) Hyperbolic Matrix(197,-26,538,-71) (1/8,1/7) -> (15/41,11/30) Hyperbolic Matrix(223,-34,610,-93) (1/7,2/13) -> (4/11,15/41) Hyperbolic Matrix(1105,-176,496,-79) (3/19,1/6) -> (49/22,29/13) Hyperbolic Matrix(435,-76,1036,-181) (1/6,3/17) -> (13/31,21/50) Hyperbolic Matrix(597,-106,490,-87) (3/17,2/11) -> (28/23,11/9) Hyperbolic Matrix(135,-26,26,-5) (2/11,1/5) -> (5/1,16/3) Hyperbolic Matrix(899,-188,636,-133) (1/5,4/19) -> (24/17,41/29) Hyperbolic Matrix(1823,-386,1346,-285) (4/19,7/33) -> (23/17,42/31) Hyperbolic Matrix(343,-74,394,-85) (3/14,5/23) -> (13/15,7/8) Hyperbolic Matrix(2417,-528,1680,-367) (5/23,7/32) -> (23/16,59/41) Hyperbolic Matrix(79,-18,338,-77) (2/9,3/13) -> (3/13,4/17) Parabolic Matrix(1137,-272,464,-111) (5/21,1/4) -> (49/20,27/11) Hyperbolic Matrix(405,-106,1066,-279) (1/4,5/19) -> (11/29,19/50) Hyperbolic Matrix(431,-114,1138,-301) (5/19,4/15) -> (14/37,11/29) Hyperbolic Matrix(403,-108,556,-149) (4/15,3/11) -> (21/29,8/11) Hyperbolic Matrix(275,-76,76,-21) (3/11,2/7) -> (18/5,11/3) Hyperbolic Matrix(421,-122,1018,-295) (2/7,7/24) -> (19/46,12/29) Hyperbolic Matrix(841,-246,694,-203) (7/24,5/17) -> (23/19,17/14) Hyperbolic Matrix(963,-284,668,-197) (5/17,8/27) -> (36/25,13/9) Hyperbolic Matrix(25,-8,72,-23) (3/10,1/3) -> (1/3,5/14) Parabolic Matrix(307,-110,494,-177) (5/14,4/11) -> (18/29,5/8) Hyperbolic Matrix(725,-266,586,-215) (11/30,7/19) -> (21/17,5/4) Hyperbolic Matrix(1051,-388,772,-285) (7/19,10/27) -> (34/25,15/11) Hyperbolic Matrix(2341,-890,1786,-679) (19/50,8/21) -> (38/29,21/16) Hyperbolic Matrix(555,-212,788,-301) (8/21,5/13) -> (19/27,12/17) Hyperbolic Matrix(299,-116,116,-45) (5/13,2/5) -> (18/7,13/5) Hyperbolic Matrix(2113,-862,478,-195) (11/27,9/22) -> (53/12,31/7) Hyperbolic Matrix(477,-196,1156,-475) (9/22,7/17) -> (7/17,19/46) Parabolic Matrix(7421,-3076,3076,-1275) (29/70,17/41) -> (41/17,111/46) Hyperbolic Matrix(969,-406,790,-331) (5/12,13/31) -> (11/9,27/22) Hyperbolic Matrix(4055,-1704,2344,-985) (21/50,8/19) -> (64/37,45/26) Hyperbolic Matrix(315,-134,134,-57) (8/19,3/7) -> (7/3,26/11) Hyperbolic Matrix(1115,-484,804,-349) (3/7,10/23) -> (18/13,43/31) Hyperbolic Matrix(2205,-962,1538,-671) (17/39,7/16) -> (43/30,33/23) Hyperbolic Matrix(3023,-1328,2224,-977) (18/41,11/25) -> (53/39,34/25) Hyperbolic Matrix(267,-118,310,-137) (11/25,4/9) -> (6/7,13/15) Hyperbolic Matrix(111,-50,242,-109) (4/9,5/11) -> (5/11,6/13) Parabolic Matrix(413,-194,66,-31) (7/15,1/2) -> (25/4,19/3) Hyperbolic Matrix(357,-188,188,-99) (1/2,9/17) -> (17/9,19/10) Hyperbolic Matrix(873,-472,664,-359) (7/13,13/24) -> (21/16,25/19) Hyperbolic Matrix(1945,-1064,744,-407) (6/11,17/31) -> (81/31,34/13) Hyperbolic Matrix(3077,-1690,1178,-647) (17/31,11/20) -> (47/18,81/31) Hyperbolic Matrix(369,-206,206,-115) (5/9,9/16) -> (25/14,9/5) Hyperbolic Matrix(2231,-1258,1002,-565) (9/16,22/39) -> (20/9,49/22) Hyperbolic Matrix(981,-554,1514,-855) (22/39,13/23) -> (11/17,24/37) Hyperbolic Matrix(1043,-590,1614,-913) (13/23,17/30) -> (31/48,11/17) Hyperbolic Matrix(61,-36,100,-59) (4/7,3/5) -> (3/5,8/13) Parabolic Matrix(911,-562,1266,-781) (8/13,21/34) -> (23/32,18/25) Hyperbolic Matrix(1721,-1064,296,-183) (34/55,13/21) -> (29/5,6/1) Hyperbolic Matrix(1423,-882,434,-269) (13/21,18/29) -> (36/11,23/7) Hyperbolic Matrix(983,-618,746,-469) (22/35,17/27) -> (25/19,4/3) Hyperbolic Matrix(10205,-6436,6436,-4059) (29/46,41/65) -> (65/41,111/70) Hyperbolic Matrix(2471,-1562,666,-421) (12/19,31/49) -> (63/17,26/7) Hyperbolic Matrix(3703,-2344,1000,-633) (31/49,19/30) -> (37/10,63/17) Hyperbolic Matrix(429,-274,274,-175) (7/11,9/14) -> (25/16,11/7) Hyperbolic Matrix(2795,-1814,2134,-1385) (24/37,13/20) -> (55/42,38/29) Hyperbolic Matrix(599,-392,136,-89) (13/20,2/3) -> (22/5,53/12) Hyperbolic Matrix(247,-170,170,-117) (2/3,9/13) -> (13/9,16/11) Hyperbolic Matrix(963,-668,284,-197) (9/13,16/23) -> (44/13,17/5) Hyperbolic Matrix(2205,-1538,962,-671) (23/33,7/10) -> (55/24,39/17) Hyperbolic Matrix(827,-580,452,-317) (7/10,26/37) -> (42/23,11/6) Hyperbolic Matrix(899,-636,188,-133) (12/17,17/24) -> (19/4,24/5) Hyperbolic Matrix(281,-200,392,-279) (17/24,5/7) -> (5/7,23/32) Parabolic Matrix(1115,-804,484,-349) (18/25,13/18) -> (23/10,30/13) Hyperbolic Matrix(2117,-1530,1338,-967) (13/18,34/47) -> (68/43,19/12) Hyperbolic Matrix(555,-406,406,-297) (8/11,11/15) -> (15/11,26/19) Hyperbolic Matrix(1051,-772,388,-285) (11/15,14/19) -> (46/17,19/7) Hyperbolic Matrix(1823,-1346,386,-285) (14/19,17/23) -> (33/7,52/11) Hyperbolic Matrix(127,-98,162,-125) (3/4,7/9) -> (7/9,11/14) Parabolic Matrix(1557,-1226,842,-663) (11/14,26/33) -> (24/13,37/20) Hyperbolic Matrix(967,-762,250,-197) (26/33,15/19) -> (27/7,4/1) Hyperbolic Matrix(725,-586,266,-215) (4/5,13/16) -> (49/18,30/11) Hyperbolic Matrix(969,-790,406,-331) (13/16,9/11) -> (31/13,43/18) Hyperbolic Matrix(597,-490,106,-87) (9/11,14/17) -> (28/5,17/3) Hyperbolic Matrix(841,-694,246,-203) (14/17,5/6) -> (41/12,24/7) Hyperbolic Matrix(573,-484,676,-571) (16/19,11/13) -> (11/13,28/33) Parabolic Matrix(1799,-1528,312,-265) (28/33,17/20) -> (23/4,52/9) Hyperbolic Matrix(17,-16,16,-15) (7/8,1/1) -> (1/1,9/8) Parabolic Matrix(511,-578,450,-509) (9/8,17/15) -> (17/15,25/22) Parabolic Matrix(343,-394,74,-85) (8/7,7/6) -> (37/8,14/3) Hyperbolic Matrix(573,-676,484,-571) (20/17,13/11) -> (13/11,32/27) Parabolic Matrix(3265,-3872,1888,-2239) (32/27,19/16) -> (83/48,64/37) Hyperbolic Matrix(1187,-1436,348,-421) (6/5,23/19) -> (17/5,58/17) Hyperbolic Matrix(1403,-1732,516,-637) (16/13,21/17) -> (19/7,68/25) Hyperbolic Matrix(127,-162,98,-125) (5/4,9/7) -> (9/7,13/10) Parabolic Matrix(2135,-2794,554,-725) (17/13,55/42) -> (77/20,27/7) Hyperbolic Matrix(4531,-6156,3148,-4277) (19/14,53/39) -> (59/41,95/66) Hyperbolic Matrix(1999,-2738,1458,-1997) (26/19,37/27) -> (37/27,48/35) Parabolic Matrix(403,-556,108,-149) (11/8,18/13) -> (26/7,15/4) Hyperbolic Matrix(1273,-1766,550,-763) (43/31,25/18) -> (37/16,7/3) Hyperbolic Matrix(629,-874,362,-503) (25/18,7/5) -> (33/19,7/4) Hyperbolic Matrix(691,-974,398,-561) (7/5,24/17) -> (26/15,33/19) Hyperbolic Matrix(901,-1274,186,-263) (41/29,17/12) -> (29/6,5/1) Hyperbolic Matrix(555,-788,212,-301) (17/12,10/7) -> (34/13,21/8) Hyperbolic Matrix(5457,-7856,944,-1359) (95/66,36/25) -> (52/9,81/14) Hyperbolic Matrix(495,-722,338,-493) (16/11,19/13) -> (19/13,22/15) Parabolic Matrix(681,-1046,278,-427) (3/2,20/13) -> (22/9,49/20) Hyperbolic Matrix(981,-1514,554,-855) (20/13,17/11) -> (23/13,62/35) Hyperbolic Matrix(1043,-1614,590,-913) (17/11,31/20) -> (53/30,23/13) Hyperbolic Matrix(1951,-3042,1250,-1949) (14/9,39/25) -> (39/25,64/41) Parabolic Matrix(3039,-4802,1922,-3037) (30/19,49/31) -> (49/31,68/43) Parabolic Matrix(10989,-17426,3218,-5103) (111/70,46/29) -> (140/41,41/12) Hyperbolic Matrix(915,-1454,494,-785) (27/17,35/22) -> (37/20,13/7) Hyperbolic Matrix(61,-100,36,-59) (8/5,5/3) -> (5/3,12/7) Parabolic Matrix(271,-466,82,-141) (12/7,19/11) -> (23/7,10/3) Hyperbolic Matrix(6989,-12084,1524,-2635) (19/11,83/48) -> (55/12,133/29) Hyperbolic Matrix(1905,-3376,496,-879) (62/35,39/22) -> (23/6,50/13) Hyperbolic Matrix(357,-634,58,-103) (39/22,16/9) -> (6/1,25/4) Hyperbolic Matrix(1887,-3362,1058,-1885) (16/9,41/23) -> (41/23,66/37) Parabolic Matrix(1055,-1922,578,-1053) (20/11,31/17) -> (31/17,42/23) Parabolic Matrix(1709,-3252,628,-1195) (19/10,2/1) -> (166/61,49/18) Hyperbolic Matrix(111,-242,50,-109) (2/1,11/5) -> (11/5,20/9) Parabolic Matrix(499,-1132,108,-245) (9/4,25/11) -> (23/5,37/8) Hyperbolic Matrix(1611,-3668,596,-1357) (25/11,41/18) -> (27/10,73/27) Hyperbolic Matrix(667,-1540,68,-157) (30/13,67/29) -> (29/3,10/1) Hyperbolic Matrix(1015,-2346,106,-245) (67/29,37/16) -> (19/2,29/3) Hyperbolic Matrix(1711,-4050,722,-1709) (26/11,45/19) -> (45/19,64/27) Parabolic Matrix(435,-1036,76,-181) (19/8,31/13) -> (17/3,23/4) Hyperbolic Matrix(4613,-11132,956,-2307) (111/46,70/29) -> (82/17,29/6) Hyperbolic Matrix(421,-1018,122,-295) (29/12,17/7) -> (31/9,7/2) Hyperbolic Matrix(447,-1090,130,-317) (17/7,22/9) -> (24/7,31/9) Hyperbolic Matrix(415,-1058,162,-413) (5/2,23/9) -> (23/9,41/16) Parabolic Matrix(405,-1066,106,-279) (21/8,29/11) -> (19/5,23/6) Hyperbolic Matrix(431,-1138,114,-301) (29/11,8/3) -> (34/9,19/5) Hyperbolic Matrix(2497,-6752,544,-1471) (73/27,46/17) -> (78/17,23/5) Hyperbolic Matrix(10063,-27378,3698,-10061) (68/25,117/43) -> (117/43,166/61) Parabolic Matrix(197,-538,26,-71) (30/11,11/4) -> (15/2,8/1) Hyperbolic Matrix(25,-72,8,-23) (11/4,3/1) -> (3/1,13/4) Parabolic Matrix(1471,-4802,450,-1469) (13/4,49/15) -> (49/15,85/26) Parabolic Matrix(971,-3284,212,-717) (27/8,44/13) -> (32/7,55/12) Hyperbolic Matrix(5743,-19602,1682,-5741) (58/17,99/29) -> (99/29,140/41) Parabolic Matrix(351,-1250,98,-349) (7/2,25/7) -> (25/7,43/12) Parabolic Matrix(6113,-23520,1056,-4063) (50/13,127/33) -> (191/33,110/19) Hyperbolic Matrix(6493,-24994,1122,-4319) (127/33,77/20) -> (81/14,191/33) Hyperbolic Matrix(79,-338,18,-77) (4/1,13/3) -> (13/3,22/5) Parabolic Matrix(3683,-16892,636,-2917) (133/29,78/17) -> (110/19,29/5) Hyperbolic Matrix(1167,-5618,242,-1165) (24/5,53/11) -> (53/11,82/17) Parabolic Matrix(271,-1458,50,-269) (16/3,27/5) -> (27/5,38/7) Parabolic Matrix(29,-196,4,-27) (13/2,7/1) -> (7/1,15/2) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,-2,-3) -> Matrix(1,0,0,1) Matrix(423,200,184,87) -> Matrix(5,4,-4,-3) Matrix(539,250,774,359) -> Matrix(1,0,4,1) Matrix(593,272,944,433) -> Matrix(1,2,-4,-7) Matrix(57,26,-410,-187) -> Matrix(5,4,-4,-3) Matrix(1403,634,582,263) -> Matrix(3,2,4,3) Matrix(817,368,464,209) -> Matrix(3,2,-8,-5) Matrix(347,156,932,419) -> Matrix(7,4,-16,-9) Matrix(407,182,1098,491) -> Matrix(5,2,-8,-3) Matrix(743,328,632,279) -> Matrix(1,0,4,1) Matrix(1031,454,570,251) -> Matrix(1,0,0,1) Matrix(173,76,-972,-427) -> Matrix(1,0,0,1) Matrix(1877,820,396,173) -> Matrix(5,4,-4,-3) Matrix(2723,1188,4316,1883) -> Matrix(3,2,-8,-5) Matrix(395,172,852,371) -> Matrix(7,4,-16,-9) Matrix(167,72,-392,-169) -> Matrix(3,2,-8,-5) Matrix(1165,494,-3054,-1295) -> Matrix(1,0,0,1) Matrix(4321,1826,1886,797) -> Matrix(7,2,-4,-1) Matrix(999,422,1882,795) -> Matrix(1,0,4,1) Matrix(275,116,1164,491) -> Matrix(3,2,-8,-5) Matrix(661,278,554,233) -> Matrix(1,0,4,1) Matrix(1821,764,1156,485) -> Matrix(1,0,4,1) Matrix(277,116,-1268,-531) -> Matrix(1,0,4,1) Matrix(327,136,440,183) -> Matrix(1,0,0,1) Matrix(1531,634,326,135) -> Matrix(7,2,-4,-1) Matrix(653,270,1202,497) -> Matrix(1,0,0,1) Matrix(325,134,-1414,-583) -> Matrix(1,0,0,1) Matrix(487,200,56,23) -> Matrix(5,4,-4,-3) Matrix(1517,622,978,401) -> Matrix(3,2,4,3) Matrix(323,132,1084,443) -> Matrix(3,2,-8,-5) Matrix(271,110,914,371) -> Matrix(9,4,-16,-7) Matrix(583,230,474,187) -> Matrix(1,0,0,1) Matrix(1159,454,314,123) -> Matrix(1,0,0,1) Matrix(527,206,-1998,-781) -> Matrix(1,0,0,1) Matrix(945,368,208,81) -> Matrix(1,-2,0,1) Matrix(259,100,-676,-261) -> Matrix(3,2,-8,-5) Matrix(1555,594,1966,751) -> Matrix(1,0,0,1) Matrix(1137,434,-6002,-2291) -> Matrix(7,2,-4,-1) Matrix(1757,668,1444,549) -> Matrix(1,0,4,1) Matrix(2013,764,772,293) -> Matrix(1,0,4,1) Matrix(723,274,-2578,-977) -> Matrix(1,0,4,1) Matrix(1645,622,722,273) -> Matrix(7,2,-4,-1) Matrix(457,170,-1578,-587) -> Matrix(1,0,-12,1) Matrix(151,56,968,359) -> Matrix(1,0,-4,1) Matrix(2487,920,1576,583) -> Matrix(1,0,0,1) Matrix(2437,900,5884,2173) -> Matrix(1,0,-4,1) Matrix(1571,580,1980,731) -> Matrix(1,0,-4,1) Matrix(1925,708,2428,893) -> Matrix(1,2,-4,-7) Matrix(49,18,558,205) -> Matrix(1,0,0,1) Matrix(2021,742,1114,409) -> Matrix(1,0,0,1) Matrix(1109,406,-3734,-1367) -> Matrix(1,0,0,1) Matrix(203,74,502,183) -> Matrix(1,0,0,1) Matrix(449,162,-1250,-451) -> Matrix(3,2,-8,-5) Matrix(1295,464,2096,751) -> Matrix(1,0,0,1) Matrix(647,230,346,123) -> Matrix(1,0,0,1) Matrix(1885,668,1188,421) -> Matrix(1,0,4,1) Matrix(935,328,248,87) -> Matrix(1,0,4,1) Matrix(1819,634,1030,359) -> Matrix(1,0,8,1) Matrix(47,16,-144,-49) -> Matrix(1,0,0,1) Matrix(801,256,704,225) -> Matrix(1,0,28,1) Matrix(1029,326,1594,505) -> Matrix(1,0,-8,1) Matrix(281,88,744,233) -> Matrix(1,0,-4,1) Matrix(1113,346,1766,549) -> Matrix(1,0,-4,1) Matrix(323,100,604,187) -> Matrix(1,0,0,1) Matrix(321,98,-1058,-323) -> Matrix(1,-2,0,1) Matrix(1745,528,1008,305) -> Matrix(1,0,0,1) Matrix(455,136,184,55) -> Matrix(1,0,0,1) Matrix(3369,1000,2456,729) -> Matrix(1,0,0,1) Matrix(1001,296,1816,537) -> Matrix(1,0,0,1) Matrix(501,148,44,13) -> Matrix(1,0,0,1) Matrix(3133,924,2404,709) -> Matrix(5,4,-4,-3) Matrix(2715,796,2084,611) -> Matrix(7,2,-4,-1) Matrix(5249,1538,2174,637) -> Matrix(1,0,4,1) Matrix(1403,410,2214,647) -> Matrix(1,0,0,1) Matrix(859,250,134,39) -> Matrix(1,0,4,1) Matrix(857,248,584,169) -> Matrix(1,0,20,1) Matrix(625,176,1424,401) -> Matrix(3,-2,-4,3) Matrix(3473,976,2224,625) -> Matrix(1,0,0,1) Matrix(1467,410,2086,583) -> Matrix(1,0,0,1) Matrix(977,272,176,49) -> Matrix(3,-2,-4,3) Matrix(131,36,-484,-133) -> Matrix(1,-2,0,1) Matrix(305,82,-1618,-435) -> Matrix(1,0,0,1) Matrix(1485,398,1138,305) -> Matrix(1,0,0,1) Matrix(173,46,786,209) -> Matrix(5,2,-8,-3) Matrix(3569,944,2000,529) -> Matrix(1,0,0,1) Matrix(1129,296,1560,409) -> Matrix(1,0,0,1) Matrix(1037,270,434,113) -> Matrix(1,0,0,1) Matrix(715,172,212,51) -> Matrix(1,-4,0,1) Matrix(839,198,250,59) -> Matrix(1,2,0,1) Matrix(753,176,1168,273) -> Matrix(1,2,-4,-7) Matrix(43,10,374,87) -> Matrix(3,4,-4,-5) Matrix(3737,856,1576,361) -> Matrix(1,0,0,1) Matrix(913,208,496,113) -> Matrix(1,0,0,1) Matrix(247,56,1160,263) -> Matrix(3,-2,-4,3) Matrix(331,74,246,55) -> Matrix(1,0,0,1) Matrix(945,208,368,81) -> Matrix(1,0,4,1) Matrix(857,186,1350,293) -> Matrix(1,0,-4,1) Matrix(409,88,488,105) -> Matrix(1,0,-4,1) Matrix(731,156,164,35) -> Matrix(1,-4,0,1) Matrix(1379,292,732,155) -> Matrix(1,0,-4,1) Matrix(1337,282,934,197) -> Matrix(1,0,-4,1) Matrix(39,8,-200,-41) -> Matrix(1,-2,0,1) Matrix(3873,736,1184,225) -> Matrix(1,0,0,1) Matrix(707,132,316,59) -> Matrix(1,-2,0,1) Matrix(2983,550,1882,347) -> Matrix(1,2,0,1) Matrix(1805,332,1332,245) -> Matrix(1,0,0,1) Matrix(977,176,272,49) -> Matrix(3,4,-4,-5) Matrix(387,68,700,123) -> Matrix(1,0,0,1) Matrix(427,74,502,87) -> Matrix(1,0,-4,1) Matrix(723,116,268,43) -> Matrix(1,-2,0,1) Matrix(607,94,226,35) -> Matrix(1,4,0,1) Matrix(301,46,530,81) -> Matrix(1,2,0,1) Matrix(375,56,904,135) -> Matrix(1,2,-4,-7) Matrix(1001,136,184,25) -> Matrix(11,12,-12,-13) Matrix(589,78,370,49) -> Matrix(3,2,4,3) Matrix(471,56,328,39) -> Matrix(1,0,-4,1) Matrix(107,10,246,23) -> Matrix(3,4,-4,-5) Matrix(261,-28,28,-3) -> Matrix(9,8,-8,-7) Matrix(197,-26,538,-71) -> Matrix(3,2,-8,-5) Matrix(223,-34,610,-93) -> Matrix(1,0,0,1) Matrix(1105,-176,496,-79) -> Matrix(1,-4,0,1) Matrix(435,-76,1036,-181) -> Matrix(1,0,0,1) Matrix(597,-106,490,-87) -> Matrix(1,2,0,1) Matrix(135,-26,26,-5) -> Matrix(5,4,-4,-3) Matrix(899,-188,636,-133) -> Matrix(3,2,-8,-5) Matrix(1823,-386,1346,-285) -> Matrix(5,4,-4,-3) Matrix(343,-74,394,-85) -> Matrix(3,2,-32,-21) Matrix(2417,-528,1680,-367) -> Matrix(3,2,-20,-13) Matrix(79,-18,338,-77) -> Matrix(11,6,-24,-13) Matrix(1137,-272,464,-111) -> Matrix(5,2,-8,-3) Matrix(405,-106,1066,-279) -> Matrix(3,2,-8,-5) Matrix(431,-114,1138,-301) -> Matrix(1,0,0,1) Matrix(403,-108,556,-149) -> Matrix(1,0,0,1) Matrix(275,-76,76,-21) -> Matrix(1,0,0,1) Matrix(421,-122,1018,-295) -> Matrix(3,2,-8,-5) Matrix(841,-246,694,-203) -> Matrix(3,2,4,3) Matrix(963,-284,668,-197) -> Matrix(3,2,-20,-13) Matrix(25,-8,72,-23) -> Matrix(3,2,-8,-5) Matrix(307,-110,494,-177) -> Matrix(1,0,0,1) Matrix(725,-266,586,-215) -> Matrix(1,0,4,1) Matrix(1051,-388,772,-285) -> Matrix(1,0,0,1) Matrix(2341,-890,1786,-679) -> Matrix(5,2,-8,-3) Matrix(555,-212,788,-301) -> Matrix(1,0,4,1) Matrix(299,-116,116,-45) -> Matrix(1,0,4,1) Matrix(2113,-862,478,-195) -> Matrix(1,-4,0,1) Matrix(477,-196,1156,-475) -> Matrix(3,2,-8,-5) Matrix(7421,-3076,3076,-1275) -> Matrix(1,0,4,1) Matrix(969,-406,790,-331) -> Matrix(1,0,0,1) Matrix(4055,-1704,2344,-985) -> Matrix(1,0,0,1) Matrix(315,-134,134,-57) -> Matrix(1,0,0,1) Matrix(1115,-484,804,-349) -> Matrix(5,4,-4,-3) Matrix(2205,-962,1538,-671) -> Matrix(3,2,-8,-5) Matrix(3023,-1328,2224,-977) -> Matrix(1,0,0,1) Matrix(267,-118,310,-137) -> Matrix(3,2,-20,-13) Matrix(111,-50,242,-109) -> Matrix(11,6,-24,-13) Matrix(413,-194,66,-31) -> Matrix(5,2,-8,-3) Matrix(357,-188,188,-99) -> Matrix(1,0,-8,1) Matrix(873,-472,664,-359) -> Matrix(1,0,0,1) Matrix(1945,-1064,744,-407) -> Matrix(1,0,0,1) Matrix(3077,-1690,1178,-647) -> Matrix(1,2,0,1) Matrix(369,-206,206,-115) -> Matrix(1,0,0,1) Matrix(2231,-1258,1002,-565) -> Matrix(1,-4,0,1) Matrix(981,-554,1514,-855) -> Matrix(3,2,-8,-5) Matrix(1043,-590,1614,-913) -> Matrix(1,0,0,1) Matrix(61,-36,100,-59) -> Matrix(3,2,-8,-5) Matrix(911,-562,1266,-781) -> Matrix(7,2,-4,-1) Matrix(1721,-1064,296,-183) -> Matrix(5,2,-8,-3) Matrix(1423,-882,434,-269) -> Matrix(7,2,-4,-1) Matrix(983,-618,746,-469) -> Matrix(7,2,-4,-1) Matrix(10205,-6436,6436,-4059) -> Matrix(1,0,4,1) Matrix(2471,-1562,666,-421) -> Matrix(7,2,-4,-1) Matrix(3703,-2344,1000,-633) -> Matrix(1,0,4,1) Matrix(429,-274,274,-175) -> Matrix(1,0,4,1) Matrix(2795,-1814,2134,-1385) -> Matrix(17,6,-20,-7) Matrix(599,-392,136,-89) -> Matrix(23,6,-4,-1) Matrix(247,-170,170,-117) -> Matrix(1,0,-12,1) Matrix(963,-668,284,-197) -> Matrix(9,-2,-4,1) Matrix(2205,-1538,962,-671) -> Matrix(1,-2,0,1) Matrix(827,-580,452,-317) -> Matrix(1,0,-4,1) Matrix(899,-636,188,-133) -> Matrix(1,-2,0,1) Matrix(281,-200,392,-279) -> Matrix(1,-2,0,1) Matrix(1115,-804,484,-349) -> Matrix(5,4,-4,-3) Matrix(2117,-1530,1338,-967) -> Matrix(3,2,4,3) Matrix(555,-406,406,-297) -> Matrix(1,0,0,1) Matrix(1051,-772,388,-285) -> Matrix(1,0,0,1) Matrix(1823,-1346,386,-285) -> Matrix(5,4,-4,-3) Matrix(127,-98,162,-125) -> Matrix(3,2,-8,-5) Matrix(1557,-1226,842,-663) -> Matrix(5,2,-8,-3) Matrix(967,-762,250,-197) -> Matrix(5,2,-8,-3) Matrix(725,-586,266,-215) -> Matrix(1,0,4,1) Matrix(969,-790,406,-331) -> Matrix(1,0,0,1) Matrix(597,-490,106,-87) -> Matrix(5,2,-8,-3) Matrix(841,-694,246,-203) -> Matrix(7,2,-4,-1) Matrix(573,-484,676,-571) -> Matrix(7,2,-32,-9) Matrix(1799,-1528,312,-265) -> Matrix(1,0,4,1) Matrix(17,-16,16,-15) -> Matrix(1,0,0,1) Matrix(511,-578,450,-509) -> Matrix(1,0,56,1) Matrix(343,-394,74,-85) -> Matrix(17,-2,-8,1) Matrix(573,-676,484,-571) -> Matrix(5,-2,8,-3) Matrix(3265,-3872,1888,-2239) -> Matrix(3,-2,-4,3) Matrix(1187,-1436,348,-421) -> Matrix(1,-2,0,1) Matrix(1403,-1732,516,-637) -> Matrix(1,0,-4,1) Matrix(127,-162,98,-125) -> Matrix(1,-2,0,1) Matrix(2135,-2794,554,-725) -> Matrix(3,4,-4,-5) Matrix(4531,-6156,3148,-4277) -> Matrix(5,4,-24,-19) Matrix(1999,-2738,1458,-1997) -> Matrix(1,0,0,1) Matrix(403,-556,108,-149) -> Matrix(1,0,0,1) Matrix(1273,-1766,550,-763) -> Matrix(3,4,-4,-5) Matrix(629,-874,362,-503) -> Matrix(5,4,-4,-3) Matrix(691,-974,398,-561) -> Matrix(7,2,-4,-1) Matrix(901,-1274,186,-263) -> Matrix(7,2,-4,-1) Matrix(555,-788,212,-301) -> Matrix(1,0,4,1) Matrix(5457,-7856,944,-1359) -> Matrix(21,4,-16,-3) Matrix(495,-722,338,-493) -> Matrix(1,0,40,1) Matrix(681,-1046,278,-427) -> Matrix(3,-2,-4,3) Matrix(981,-1514,554,-855) -> Matrix(1,-2,0,1) Matrix(1043,-1614,590,-913) -> Matrix(1,0,0,1) Matrix(1951,-3042,1250,-1949) -> Matrix(1,0,0,1) Matrix(3039,-4802,1922,-3037) -> Matrix(5,-2,8,-3) Matrix(10989,-17426,3218,-5103) -> Matrix(1,-2,0,1) Matrix(915,-1454,494,-785) -> Matrix(3,-2,-4,3) Matrix(61,-100,36,-59) -> Matrix(1,-2,0,1) Matrix(271,-466,82,-141) -> Matrix(1,0,0,1) Matrix(6989,-12084,1524,-2635) -> Matrix(13,10,-4,-3) Matrix(1905,-3376,496,-879) -> Matrix(5,4,-4,-3) Matrix(357,-634,58,-103) -> Matrix(1,0,0,1) Matrix(1887,-3362,1058,-1885) -> Matrix(1,0,0,1) Matrix(1055,-1922,578,-1053) -> Matrix(3,2,-8,-5) Matrix(1709,-3252,628,-1195) -> Matrix(1,0,16,1) Matrix(111,-242,50,-109) -> Matrix(1,-6,0,1) Matrix(499,-1132,108,-245) -> Matrix(9,16,-4,-7) Matrix(1611,-3668,596,-1357) -> Matrix(1,0,0,1) Matrix(667,-1540,68,-157) -> Matrix(15,16,-16,-17) Matrix(1015,-2346,106,-245) -> Matrix(25,24,-24,-23) Matrix(1711,-4050,722,-1709) -> Matrix(1,0,0,1) Matrix(435,-1036,76,-181) -> Matrix(1,0,0,1) Matrix(4613,-11132,956,-2307) -> Matrix(1,-2,0,1) Matrix(421,-1018,122,-295) -> Matrix(1,-2,0,1) Matrix(447,-1090,130,-317) -> Matrix(1,0,0,1) Matrix(415,-1058,162,-413) -> Matrix(1,0,8,1) Matrix(405,-1066,106,-279) -> Matrix(1,-2,0,1) Matrix(431,-1138,114,-301) -> Matrix(1,0,0,1) Matrix(2497,-6752,544,-1471) -> Matrix(11,14,-4,-5) Matrix(10063,-27378,3698,-10061) -> Matrix(1,0,24,1) Matrix(197,-538,26,-71) -> Matrix(1,-2,0,1) Matrix(25,-72,8,-23) -> Matrix(1,-2,0,1) Matrix(1471,-4802,450,-1469) -> Matrix(1,0,0,1) Matrix(971,-3284,212,-717) -> Matrix(1,0,0,1) Matrix(5743,-19602,1682,-5741) -> Matrix(1,0,0,1) Matrix(351,-1250,98,-349) -> Matrix(7,8,-8,-9) Matrix(6113,-23520,1056,-4063) -> Matrix(27,28,-28,-29) Matrix(6493,-24994,1122,-4319) -> Matrix(29,28,-28,-27) Matrix(79,-338,18,-77) -> Matrix(1,-6,0,1) Matrix(3683,-16892,636,-2917) -> Matrix(7,22,-8,-25) Matrix(1167,-5618,242,-1165) -> Matrix(1,0,0,1) Matrix(271,-1458,50,-269) -> Matrix(23,24,-24,-25) Matrix(29,-196,4,-27) -> Matrix(1,-2,0,1) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 12 Minimal number of generators: 3 Number of equivalence classes of cusps: 4 Genus: 0 Degree of H/liftables -> H/(image of liftables): 32 Degree of the the map X: 64 Degree of the the map Y: 256 ----------------------------------------------------------------------- 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): 384 Minimal number of generators: 65 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: 40 Genus: 13 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -1/1 1/7 3/13 1/3 7/17 5/11 3/5 31/49 5/7 7/9 1/1 17/15 13/11 11/9 9/7 37/27 7/5 19/13 5/3 23/13 41/23 31/17 2/1 11/5 7/3 45/19 17/7 3/1 25/7 11/3 19/5 4/1 13/3 23/5 5/1 27/5 17/3 6/1 7/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 -1/2 1/0 0/1 -1/1 0/1 1/7 -1/2 2/13 -1/3 0/1 1/6 -1/1 0/1 2/11 -4/3 -1/1 1/5 -1/1 -2/3 3/14 -9/13 -2/3 5/23 -5/8 2/9 -3/5 -4/7 3/13 -1/2 1/4 -1/1 0/1 1/3 -1/2 3/8 -1/3 0/1 11/29 -1/2 8/21 -1/3 0/1 5/13 -1/3 0/1 2/5 -1/1 0/1 7/17 -1/2 12/29 -1/3 0/1 5/12 0/1 1/1 8/19 -1/1 0/1 3/7 -1/1 0/1 7/16 -1/1 -2/3 11/25 -3/4 4/9 -2/3 -3/5 5/11 -1/2 1/2 -1/3 0/1 3/5 -1/2 5/8 -2/5 -1/3 17/27 -1/4 12/19 -1/3 -2/7 31/49 -1/4 19/30 -1/3 0/1 7/11 -1/3 0/1 9/14 -1/3 0/1 11/17 -1/2 2/3 -1/5 0/1 9/13 0/1 1/5 7/10 0/1 1/1 5/7 1/0 13/18 -1/1 0/1 21/29 -1/1 0/1 8/11 -1/1 0/1 11/15 -1/1 0/1 3/4 -1/1 0/1 7/9 -1/2 4/5 -1/3 0/1 9/11 -1/2 5/6 -1/3 0/1 11/13 -1/4 6/7 -1/5 0/1 13/15 -1/8 7/8 -1/15 0/1 1/1 -1/1 0/1 9/8 -1/15 0/1 17/15 0/1 8/7 0/1 1/13 7/6 0/1 1/3 13/11 1/2 6/5 0/1 1/1 17/14 1/1 2/1 11/9 1/0 16/13 -1/3 0/1 5/4 0/1 1/1 9/7 1/0 4/3 -1/1 0/1 19/14 -4/3 -1/1 15/11 -1/1 0/1 26/19 -1/1 0/1 37/27 -1/2 1/0 11/8 -1/1 0/1 7/5 -1/2 17/12 -1/3 0/1 10/7 -1/3 0/1 23/16 -1/5 0/1 13/9 -1/7 0/1 16/11 -1/17 0/1 19/13 0/1 3/2 0/1 1/3 5/3 1/0 7/4 -1/1 -2/3 23/13 1/0 16/9 -1/1 0/1 41/23 -1/2 1/0 25/14 -1/1 0/1 9/5 -1/1 0/1 20/11 -1/1 0/1 31/17 -1/2 11/6 -1/3 0/1 13/7 -1/2 2/1 0/1 1/1 11/5 1/0 9/4 -3/1 -2/1 25/11 -3/2 16/7 -2/1 -1/1 23/10 -4/3 -1/1 7/3 -1/1 0/1 26/11 -1/1 0/1 45/19 -1/2 1/0 19/8 -1/1 0/1 31/13 -1/2 12/5 -1/3 0/1 17/7 1/0 22/9 -4/3 -1/1 5/2 -1/1 0/1 3/1 1/0 7/2 -2/1 -1/1 25/7 -1/1 18/5 -1/1 -2/3 11/3 -1/1 0/1 26/7 -1/1 0/1 15/4 -1/1 0/1 19/5 1/0 4/1 -1/1 0/1 13/3 1/0 9/2 -4/1 -3/1 23/5 -5/2 37/8 -11/5 -2/1 14/3 -2/1 -9/5 19/4 -2/1 -1/1 5/1 -2/1 -1/1 16/3 -8/7 -1/1 27/5 -1/1 11/2 -1/1 -4/5 17/3 -1/2 6/1 -1/1 0/1 7/1 1/0 8/1 -2/1 -1/1 1/0 -1/1 0/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(0,-1,1,2) (-1/1,1/0) -> (-1/1,0/1) Parabolic Matrix(15,-2,98,-13) (0/1,1/7) -> (1/7,2/13) Parabolic Matrix(346,-55,151,-24) (2/13,1/6) -> (16/7,23/10) Hyperbolic Matrix(151,-26,122,-21) (1/6,2/11) -> (16/13,5/4) Hyperbolic Matrix(135,-26,26,-5) (2/11,1/5) -> (5/1,16/3) Hyperbolic Matrix(305,-64,224,-47) (1/5,3/14) -> (19/14,15/11) Hyperbolic Matrix(343,-74,394,-85) (3/14,5/23) -> (13/15,7/8) Hyperbolic Matrix(368,-81,209,-46) (5/23,2/9) -> (7/4,23/13) Hyperbolic Matrix(40,-9,169,-38) (2/9,3/13) -> (3/13,1/4) Parabolic Matrix(13,-4,36,-11) (1/4,1/3) -> (1/3,3/8) Parabolic Matrix(278,-105,233,-88) (3/8,11/29) -> (13/11,6/5) Hyperbolic Matrix(476,-181,405,-154) (11/29,8/21) -> (7/6,13/11) Hyperbolic Matrix(545,-208,752,-287) (8/21,5/13) -> (21/29,8/11) Hyperbolic Matrix(289,-112,80,-31) (5/13,2/5) -> (18/5,11/3) Hyperbolic Matrix(239,-98,578,-237) (2/5,7/17) -> (7/17,12/29) Parabolic Matrix(634,-263,135,-56) (12/29,5/12) -> (14/3,19/4) Hyperbolic Matrix(395,-166,326,-137) (5/12,8/19) -> (6/5,17/14) Hyperbolic Matrix(315,-134,134,-57) (8/19,3/7) -> (7/3,26/11) Hyperbolic Matrix(369,-160,256,-111) (3/7,7/16) -> (23/16,13/9) Hyperbolic Matrix(768,-337,433,-190) (7/16,11/25) -> (23/13,16/9) Hyperbolic Matrix(267,-118,310,-137) (11/25,4/9) -> (6/7,13/15) Hyperbolic Matrix(56,-25,121,-54) (4/9,5/11) -> (5/11,1/2) Parabolic Matrix(31,-18,50,-29) (1/2,3/5) -> (3/5,5/8) Parabolic Matrix(520,-327,423,-266) (5/8,17/27) -> (11/9,16/13) Hyperbolic Matrix(668,-421,549,-346) (17/27,12/19) -> (17/14,11/9) Hyperbolic Matrix(1520,-961,2401,-1518) (12/19,31/49) -> (31/49,19/30) Parabolic Matrix(616,-391,167,-106) (19/30,7/11) -> (11/3,26/7) Hyperbolic Matrix(401,-256,224,-143) (7/11,9/14) -> (25/14,9/5) Hyperbolic Matrix(622,-401,273,-176) (9/14,11/17) -> (25/11,16/7) Hyperbolic Matrix(222,-145,49,-32) (11/17,2/3) -> (9/2,23/5) Hyperbolic Matrix(247,-170,170,-117) (2/3,9/13) -> (13/9,16/11) Hyperbolic Matrix(369,-256,160,-111) (9/13,7/10) -> (23/10,7/3) Hyperbolic Matrix(141,-100,196,-139) (7/10,5/7) -> (5/7,13/18) Parabolic Matrix(742,-537,409,-296) (13/18,21/29) -> (9/5,20/11) Hyperbolic Matrix(555,-406,406,-297) (8/11,11/15) -> (15/11,26/19) Hyperbolic Matrix(305,-224,64,-47) (11/15,3/4) -> (19/4,5/1) Hyperbolic Matrix(64,-49,81,-62) (3/4,7/9) -> (7/9,4/5) Parabolic Matrix(151,-122,26,-21) (4/5,9/11) -> (17/3,6/1) Hyperbolic Matrix(395,-326,166,-137) (9/11,5/6) -> (19/8,31/13) Hyperbolic Matrix(166,-139,43,-36) (5/6,11/13) -> (19/5,4/1) Hyperbolic Matrix(328,-279,87,-74) (11/13,6/7) -> (15/4,19/5) Hyperbolic Matrix(17,-16,16,-15) (7/8,1/1) -> (1/1,9/8) Parabolic Matrix(256,-289,225,-254) (9/8,17/15) -> (17/15,8/7) Parabolic Matrix(343,-394,74,-85) (8/7,7/6) -> (37/8,14/3) Hyperbolic Matrix(64,-81,49,-62) (5/4,9/7) -> (9/7,4/3) Parabolic Matrix(136,-183,55,-74) (4/3,19/14) -> (22/9,5/2) Hyperbolic Matrix(1000,-1369,729,-998) (26/19,37/27) -> (37/27,11/8) Parabolic Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(417,-592,112,-159) (17/12,10/7) -> (26/7,15/4) Hyperbolic Matrix(72,-103,7,-10) (10/7,23/16) -> (8/1,1/0) Hyperbolic Matrix(248,-361,169,-246) (16/11,19/13) -> (19/13,3/2) Parabolic Matrix(31,-50,18,-29) (3/2,5/3) -> (5/3,7/4) Parabolic Matrix(944,-1681,529,-942) (16/9,41/23) -> (41/23,25/14) Parabolic Matrix(528,-961,289,-526) (20/11,31/17) -> (31/17,11/6) Parabolic Matrix(270,-497,113,-208) (11/6,13/7) -> (31/13,12/5) Hyperbolic Matrix(94,-177,17,-32) (13/7,2/1) -> (11/2,17/3) Hyperbolic Matrix(56,-121,25,-54) (2/1,11/5) -> (11/5,9/4) Parabolic Matrix(499,-1132,108,-245) (9/4,25/11) -> (23/5,37/8) Hyperbolic Matrix(856,-2025,361,-854) (26/11,45/19) -> (45/19,19/8) Parabolic Matrix(239,-578,98,-237) (12/5,17/7) -> (17/7,22/9) Parabolic Matrix(13,-36,4,-11) (5/2,3/1) -> (3/1,7/2) Parabolic Matrix(176,-625,49,-174) (7/2,25/7) -> (25/7,18/5) Parabolic Matrix(40,-169,9,-38) (4/1,13/3) -> (13/3,9/2) Parabolic Matrix(136,-729,25,-134) (16/3,27/5) -> (27/5,11/2) Parabolic Matrix(15,-98,2,-13) (6/1,7/1) -> (7/1,8/1) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(0,-1,1,2) -> Matrix(1,0,0,1) Matrix(15,-2,98,-13) -> Matrix(1,1,-4,-3) Matrix(346,-55,151,-24) -> Matrix(1,-1,0,1) Matrix(151,-26,122,-21) -> Matrix(1,1,0,1) Matrix(135,-26,26,-5) -> Matrix(5,4,-4,-3) Matrix(305,-64,224,-47) -> Matrix(1,1,-4,-3) Matrix(343,-74,394,-85) -> Matrix(3,2,-32,-21) Matrix(368,-81,209,-46) -> Matrix(3,2,-8,-5) Matrix(40,-9,169,-38) -> Matrix(5,3,-12,-7) Matrix(13,-4,36,-11) -> Matrix(1,1,-4,-3) Matrix(278,-105,233,-88) -> Matrix(1,0,4,1) Matrix(476,-181,405,-154) -> Matrix(3,1,8,3) Matrix(545,-208,752,-287) -> Matrix(3,1,-4,-1) Matrix(289,-112,80,-31) -> Matrix(3,1,-4,-1) Matrix(239,-98,578,-237) -> Matrix(1,1,-4,-3) Matrix(634,-263,135,-56) -> Matrix(7,2,-4,-1) Matrix(395,-166,326,-137) -> Matrix(1,1,0,1) Matrix(315,-134,134,-57) -> Matrix(1,0,0,1) Matrix(369,-160,256,-111) -> Matrix(1,1,-8,-7) Matrix(768,-337,433,-190) -> Matrix(1,1,-4,-3) Matrix(267,-118,310,-137) -> Matrix(3,2,-20,-13) Matrix(56,-25,121,-54) -> Matrix(5,3,-12,-7) Matrix(31,-18,50,-29) -> Matrix(1,1,-4,-3) Matrix(520,-327,423,-266) -> Matrix(3,1,-4,-1) Matrix(668,-421,549,-346) -> Matrix(1,0,4,1) Matrix(1520,-961,2401,-1518) -> Matrix(3,1,-16,-5) Matrix(616,-391,167,-106) -> Matrix(3,1,-4,-1) Matrix(401,-256,224,-143) -> Matrix(3,1,-4,-1) Matrix(622,-401,273,-176) -> Matrix(7,2,-4,-1) Matrix(222,-145,49,-32) -> Matrix(11,3,-4,-1) Matrix(247,-170,170,-117) -> Matrix(1,0,-12,1) Matrix(369,-256,160,-111) -> Matrix(5,-1,-4,1) Matrix(141,-100,196,-139) -> Matrix(1,-1,0,1) Matrix(742,-537,409,-296) -> Matrix(1,0,0,1) Matrix(555,-406,406,-297) -> Matrix(1,0,0,1) Matrix(305,-224,64,-47) -> Matrix(1,-1,0,1) Matrix(64,-49,81,-62) -> Matrix(1,1,-4,-3) Matrix(151,-122,26,-21) -> Matrix(3,1,-4,-1) Matrix(395,-326,166,-137) -> Matrix(3,1,-4,-1) Matrix(166,-139,43,-36) -> Matrix(3,1,-4,-1) Matrix(328,-279,87,-74) -> Matrix(1,0,4,1) Matrix(17,-16,16,-15) -> Matrix(1,0,0,1) Matrix(256,-289,225,-254) -> Matrix(1,0,28,1) Matrix(343,-394,74,-85) -> Matrix(17,-2,-8,1) Matrix(64,-81,49,-62) -> Matrix(1,-1,0,1) Matrix(136,-183,55,-74) -> Matrix(1,0,0,1) Matrix(1000,-1369,729,-998) -> Matrix(1,0,0,1) Matrix(141,-196,100,-139) -> Matrix(1,1,-4,-3) Matrix(417,-592,112,-159) -> Matrix(3,1,-4,-1) Matrix(72,-103,7,-10) -> Matrix(3,1,-4,-1) Matrix(248,-361,169,-246) -> Matrix(1,0,20,1) Matrix(31,-50,18,-29) -> Matrix(1,-1,0,1) Matrix(944,-1681,529,-942) -> Matrix(1,0,0,1) Matrix(528,-961,289,-526) -> Matrix(1,1,-4,-3) Matrix(270,-497,113,-208) -> Matrix(1,0,0,1) Matrix(94,-177,17,-32) -> Matrix(3,1,-4,-1) Matrix(56,-121,25,-54) -> Matrix(1,-3,0,1) Matrix(499,-1132,108,-245) -> Matrix(9,16,-4,-7) Matrix(856,-2025,361,-854) -> Matrix(1,0,0,1) Matrix(239,-578,98,-237) -> Matrix(1,-1,0,1) Matrix(13,-36,4,-11) -> Matrix(1,-1,0,1) Matrix(176,-625,49,-174) -> Matrix(3,4,-4,-5) Matrix(40,-169,9,-38) -> Matrix(1,-3,0,1) Matrix(136,-729,25,-134) -> Matrix(11,12,-12,-13) Matrix(15,-98,2,-13) -> Matrix(1,-1,0,1) 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 elliptic points of order 2: 0 Number of equivalence classes of elliptic points of order 3: 0 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 16 ----------------------------------------------------------------------- INFORMATION ON THE IMAGE IN PGL(2,Z) OF THE GROUP OF EXTENDED MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE c d -1/1 (-1/1,0/1) 0 1 1/1 (-1/1,0/1) 0 16 17/15 0/1 28 1 8/7 (0/1,1/13) 0 32 7/6 (0/1,1/3) 0 32 13/11 1/2 2 4 6/5 (0/1,1/1) 0 32 11/9 1/0 2 8 5/4 (0/1,1/1) 0 32 9/7 1/0 2 2 4/3 (-1/1,0/1) 0 32 15/11 (-1/1,0/1) 0 16 37/27 (-1/1,0/1) 0 1 11/8 (-1/1,0/1) 0 32 7/5 -1/2 2 8 17/12 (-1/3,0/1) 0 32 10/7 (-1/3,0/1) 0 32 13/9 (-1/7,0/1) 0 16 19/13 0/1 20 1 3/2 (0/1,1/3) 0 32 5/3 1/0 2 4 7/4 (-1/1,-2/3) 0 32 23/13 1/0 2 8 16/9 (-1/1,0/1) 0 32 41/23 (-1/1,0/1) 0 1 9/5 (-1/1,0/1) 0 16 20/11 (-1/1,0/1) 0 32 31/17 -1/2 2 2 11/6 (-1/3,0/1) 0 32 13/7 -1/2 2 8 2/1 (0/1,1/1) 0 32 11/5 1/0 6 2 9/4 (-3/1,-2/1) 0 32 25/11 -3/2 2 8 16/7 (-2/1,-1/1) 0 32 23/10 (-4/3,-1/1) 0 32 7/3 (-1/1,0/1) 0 16 45/19 (-1/1,0/1) 0 1 19/8 (-1/1,0/1) 0 32 31/13 -1/2 2 8 12/5 (-1/3,0/1) 0 32 17/7 1/0 2 4 22/9 (-4/3,-1/1) 0 32 5/2 (-1/1,0/1) 0 32 3/1 1/0 2 8 7/2 (-2/1,-1/1) 0 32 25/7 -1/1 4 1 11/3 (-1/1,0/1) 0 16 26/7 (-1/1,0/1) 0 32 15/4 (-1/1,0/1) 0 32 19/5 1/0 2 4 4/1 (-1/1,0/1) 0 32 13/3 1/0 6 2 9/2 (-4/1,-3/1) 0 32 23/5 -5/2 2 8 37/8 (-11/5,-2/1) 0 32 14/3 (-2/1,-9/5) 0 32 19/4 (-2/1,-1/1) 0 32 5/1 (-2/1,-1/1) 0 16 27/5 -1/1 12 1 11/2 (-1/1,-4/5) 0 32 17/3 -1/2 2 8 6/1 (-1/1,0/1) 0 32 7/1 1/0 2 4 8/1 (-2/1,-1/1) 0 32 1/0 (-1/1,0/1) 0 32 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,-1) (-1/1,1/0) -> (-1/1,1/0) Reflection Matrix(0,1,1,0) (-1/1,1/1) -> (-1/1,1/1) Reflection Matrix(16,-17,15,-16) (1/1,17/15) -> (1/1,17/15) Reflection Matrix(239,-272,210,-239) (17/15,8/7) -> (17/15,8/7) Reflection Matrix(343,-394,74,-85) (8/7,7/6) -> (37/8,14/3) Hyperbolic Matrix(279,-328,74,-87) (7/6,13/11) -> (15/4,19/5) Glide Reflection Matrix(139,-166,36,-43) (13/11,6/5) -> (19/5,4/1) Glide Reflection Matrix(326,-395,137,-166) (6/5,11/9) -> (19/8,31/13) Glide Reflection Matrix(122,-151,21,-26) (11/9,5/4) -> (17/3,6/1) Glide Reflection Matrix(64,-81,49,-62) (5/4,9/7) -> (9/7,4/3) Parabolic Matrix(224,-305,47,-64) (4/3,15/11) -> (19/4,5/1) Glide Reflection Matrix(406,-555,297,-406) (15/11,37/27) -> (15/11,37/27) Reflection Matrix(593,-814,432,-593) (37/27,11/8) -> (37/27,11/8) Reflection Matrix(141,-196,100,-139) (11/8,7/5) -> (7/5,17/12) Parabolic Matrix(417,-592,112,-159) (17/12,10/7) -> (26/7,15/4) Hyperbolic Matrix(256,-369,111,-160) (10/7,13/9) -> (23/10,7/3) Glide Reflection Matrix(170,-247,117,-170) (13/9,19/13) -> (13/9,19/13) Reflection Matrix(77,-114,52,-77) (19/13,3/2) -> (19/13,3/2) Reflection Matrix(31,-50,18,-29) (3/2,5/3) -> (5/3,7/4) Parabolic Matrix(209,-368,46,-81) (7/4,23/13) -> (9/2,23/5) Glide Reflection Matrix(433,-768,190,-337) (23/13,16/9) -> (25/11,16/7) Glide Reflection Matrix(737,-1312,414,-737) (16/9,41/23) -> (16/9,41/23) Reflection Matrix(206,-369,115,-206) (41/23,9/5) -> (41/23,9/5) Reflection Matrix(251,-454,68,-123) (9/5,20/11) -> (11/3,26/7) Glide Reflection Matrix(528,-961,289,-526) (20/11,31/17) -> (31/17,11/6) Parabolic Matrix(270,-497,113,-208) (11/6,13/7) -> (31/13,12/5) Hyperbolic Matrix(94,-177,17,-32) (13/7,2/1) -> (11/2,17/3) Hyperbolic Matrix(56,-121,25,-54) (2/1,11/5) -> (11/5,9/4) Parabolic Matrix(499,-1132,108,-245) (9/4,25/11) -> (23/5,37/8) Hyperbolic Matrix(87,-200,10,-23) (16/7,23/10) -> (8/1,1/0) Glide Reflection Matrix(134,-315,57,-134) (7/3,45/19) -> (7/3,45/19) Reflection Matrix(721,-1710,304,-721) (45/19,19/8) -> (45/19,19/8) Reflection Matrix(239,-578,98,-237) (12/5,17/7) -> (17/7,22/9) Parabolic Matrix(199,-488,42,-103) (22/9,5/2) -> (14/3,19/4) Glide Reflection Matrix(13,-36,4,-11) (5/2,3/1) -> (3/1,7/2) Parabolic Matrix(99,-350,28,-99) (7/2,25/7) -> (7/2,25/7) Reflection Matrix(76,-275,21,-76) (25/7,11/3) -> (25/7,11/3) Reflection Matrix(40,-169,9,-38) (4/1,13/3) -> (13/3,9/2) Parabolic Matrix(26,-135,5,-26) (5/1,27/5) -> (5/1,27/5) Reflection Matrix(109,-594,20,-109) (27/5,11/2) -> (27/5,11/2) Reflection Matrix(15,-98,2,-13) (6/1,7/1) -> (7/1,8/1) Parabolic IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,2,0,-1) -> Matrix(-1,0,2,1) (-1/1,1/0) -> (-1/1,0/1) Matrix(0,1,1,0) -> Matrix(-1,0,2,1) (-1/1,1/1) -> (-1/1,0/1) Matrix(16,-17,15,-16) -> Matrix(-1,0,2,1) (1/1,17/15) -> (-1/1,0/1) Matrix(239,-272,210,-239) -> Matrix(1,0,26,-1) (17/15,8/7) -> (0/1,1/13) Matrix(343,-394,74,-85) -> Matrix(17,-2,-8,1) Matrix(279,-328,74,-87) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(139,-166,36,-43) -> Matrix(1,-1,-2,1) Matrix(326,-395,137,-166) -> Matrix(1,-1,-2,1) Matrix(122,-151,21,-26) -> Matrix(1,-1,-2,1) Matrix(64,-81,49,-62) -> Matrix(1,-1,0,1) 1/0 Matrix(224,-305,47,-64) -> Matrix(3,1,-2,-1) Matrix(406,-555,297,-406) -> Matrix(-1,0,2,1) (15/11,37/27) -> (-1/1,0/1) Matrix(593,-814,432,-593) -> Matrix(-1,0,2,1) (37/27,11/8) -> (-1/1,0/1) Matrix(141,-196,100,-139) -> Matrix(1,1,-4,-3) -1/2 Matrix(417,-592,112,-159) -> Matrix(3,1,-4,-1) -1/2 Matrix(256,-369,111,-160) -> Matrix(7,1,-6,-1) Matrix(170,-247,117,-170) -> Matrix(-1,0,14,1) (13/9,19/13) -> (-1/7,0/1) Matrix(77,-114,52,-77) -> Matrix(1,0,6,-1) (19/13,3/2) -> (0/1,1/3) Matrix(31,-50,18,-29) -> Matrix(1,-1,0,1) 1/0 Matrix(209,-368,46,-81) -> Matrix(5,2,-2,-1) Matrix(433,-768,190,-337) -> Matrix(3,1,-2,-1) Matrix(737,-1312,414,-737) -> Matrix(-1,0,2,1) (16/9,41/23) -> (-1/1,0/1) Matrix(206,-369,115,-206) -> Matrix(-1,0,2,1) (41/23,9/5) -> (-1/1,0/1) Matrix(251,-454,68,-123) -> Matrix(-1,0,2,1) *** -> (-1/1,0/1) Matrix(528,-961,289,-526) -> Matrix(1,1,-4,-3) -1/2 Matrix(270,-497,113,-208) -> Matrix(1,0,0,1) Matrix(94,-177,17,-32) -> Matrix(3,1,-4,-1) -1/2 Matrix(56,-121,25,-54) -> Matrix(1,-3,0,1) 1/0 Matrix(499,-1132,108,-245) -> Matrix(9,16,-4,-7) -2/1 Matrix(87,-200,10,-23) -> Matrix(3,4,-2,-3) *** -> (-2/1,-1/1) Matrix(134,-315,57,-134) -> Matrix(-1,0,2,1) (7/3,45/19) -> (-1/1,0/1) Matrix(721,-1710,304,-721) -> Matrix(-1,0,2,1) (45/19,19/8) -> (-1/1,0/1) Matrix(239,-578,98,-237) -> Matrix(1,-1,0,1) 1/0 Matrix(199,-488,42,-103) -> Matrix(3,1,-2,-1) Matrix(13,-36,4,-11) -> Matrix(1,-1,0,1) 1/0 Matrix(99,-350,28,-99) -> Matrix(3,4,-2,-3) (7/2,25/7) -> (-2/1,-1/1) Matrix(76,-275,21,-76) -> Matrix(-1,0,2,1) (25/7,11/3) -> (-1/1,0/1) Matrix(40,-169,9,-38) -> Matrix(1,-3,0,1) 1/0 Matrix(26,-135,5,-26) -> Matrix(3,4,-2,-3) (5/1,27/5) -> (-2/1,-1/1) Matrix(109,-594,20,-109) -> Matrix(9,8,-10,-9) (27/5,11/2) -> (-1/1,-4/5) Matrix(15,-98,2,-13) -> Matrix(1,-1,0,1) 1/0 ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.