INFORMATION ON THE IMAGE IN PSL(2,Z) OF THE GROUP OF PURE MODULAR GROUP LIFTABLES UNDER ITS PULLBACK ACTION ON THE UPPER HALF-PLANE Index in PSL(2,Z): 1152 Minimal number of generators: 193 Number of equivalence classes of cusps: 72 Genus: 61 REPRESENTATIVES OF THE CUSP EQUIVALENCE CLASSSES -6/7 -5/7 -2/3 -4/7 -7/15 -13/28 -19/42 -37/84 -3/7 -5/12 -23/63 -5/14 -1/3 -13/42 -25/84 -2/7 -5/18 -4/15 -11/42 -2/9 -3/14 -11/63 -1/6 -3/19 -3/20 -1/7 -2/15 -1/9 -1/10 0/1 1/9 1/8 1/7 2/13 1/6 3/17 2/11 3/16 4/21 1/5 4/19 3/14 2/9 3/13 4/17 5/21 1/4 3/11 5/18 2/7 1/3 5/14 8/21 41/105 2/5 5/12 3/7 13/28 7/15 1/2 4/7 64/105 13/21 40/63 2/3 5/7 16/21 17/21 52/63 6/7 1/1 1/0 CUSPS AT THE FUNDAMENTAL DOMAIN AND THEIR IMAGES UNDER THE PULLBACK MAP CUSP IMAGE PSEUDOIMAGES -1/1 1/1 1/0 -8/9 1/0 -7/8 2/1 -6/7 1/0 -11/13 2/1 1/0 -5/6 1/1 -19/23 7/4 2/1 -14/17 2/1 3/1 -9/11 1/1 2/1 -13/16 4/1 -17/21 1/0 -4/5 0/1 1/0 -15/19 0/1 1/0 -11/14 1/1 -18/23 3/2 2/1 -7/9 3/2 1/0 -17/22 2/1 -10/13 2/1 1/0 -13/17 5/1 1/0 -16/21 1/0 -3/4 0/1 -14/19 0/1 1/0 -11/15 1/2 1/0 -41/56 1/1 -30/41 0/1 1/1 -19/26 2/3 -8/11 3/2 2/1 -13/18 3/1 -5/7 1/0 -17/24 -1/1 -29/41 -1/1 1/0 -12/17 -1/1 0/1 -43/61 -1/6 0/1 -74/105 0/1 -31/44 0/1 -19/27 1/2 1/0 -26/37 0/1 1/0 -7/10 0/1 -23/33 3/2 1/0 -16/23 3/2 2/1 -25/36 3/1 -9/13 4/1 1/0 -11/16 0/1 -2/3 1/0 -11/17 -1/1 1/0 -9/14 1/0 -16/25 -3/1 -2/1 -7/11 -2/1 -1/1 -12/19 0/1 1/0 -17/27 -1/2 1/0 -22/35 1/0 -5/8 0/1 -13/21 1/0 -8/13 -2/1 1/0 -11/18 -1/1 -25/41 -1/1 1/0 -64/105 1/0 -39/64 -2/1 -14/23 -2/1 1/0 -3/5 -1/1 0/1 -16/27 1/0 -13/22 0/1 -10/17 -2/1 -1/1 -17/29 -1/2 0/1 -41/70 -1/1 -24/41 -1/1 0/1 -7/12 -1/1 -11/19 -1/2 0/1 -4/7 0/1 -13/23 0/1 1/0 -22/39 1/0 -9/16 0/1 -23/41 -1/1 1/0 -14/25 -2/1 -1/1 -19/34 0/1 -5/9 -1/2 1/0 -11/20 0/1 -6/11 0/1 1/2 -7/13 0/1 1/0 -15/28 -1/1 -8/15 -1/2 -1/2 0/1 -7/15 1/4 1/2 -13/28 1/3 -6/13 0/1 1/2 -5/11 -1/1 0/1 -19/42 0/1 -14/31 0/1 1/10 -9/20 0/1 -4/9 1/2 -15/34 2/3 -26/59 4/5 1/1 -37/84 1/1 -11/25 1/1 1/0 -18/41 0/1 1/1 -7/16 2/1 -3/7 0/1 -11/26 2/9 -8/19 0/1 1/4 -13/31 2/7 1/3 -44/105 1/3 -31/74 2/5 -18/43 0/1 1/3 -5/12 1/3 -17/41 1/3 1/2 -29/70 1/3 -12/29 2/5 1/2 -7/17 1/2 1/1 -16/39 1/2 -25/61 1/2 2/3 -9/22 0/1 -11/27 1/2 1/0 -2/5 0/1 1/2 -9/23 0/1 1/2 -25/64 2/3 -41/105 1/1 -16/41 0/1 1/1 -7/18 1/1 -12/31 -1/2 0/1 -5/13 0/1 1/0 -8/21 0/1 -3/8 0/1 -10/27 1/2 -7/19 0/1 1/2 -11/30 1/3 -15/41 1/3 1/2 -19/52 2/5 -23/63 1/2 -4/11 0/1 1/2 -9/25 3/7 1/2 -5/14 1/2 -6/17 2/3 1/1 -7/20 0/1 -1/3 1/2 1/0 -7/22 0/1 -6/19 0/1 1/2 -5/16 2/5 -9/29 6/13 1/2 -13/42 1/2 -4/13 1/2 4/7 -7/23 2/3 3/4 -3/10 2/3 -14/47 1/2 2/3 -25/84 2/3 -11/37 2/3 1/1 -8/27 1/2 -13/44 2/3 -5/17 3/4 1/1 -2/7 1/1 -7/25 1/2 1/1 -12/43 0/1 1/1 -5/18 1/1 -8/29 0/1 1/0 -3/11 0/1 1/3 -7/26 2/3 -11/41 1/2 1/1 -15/56 1/1 -4/15 1/2 -5/19 0/1 1/2 -11/42 1/2 -6/23 1/2 2/3 -1/4 2/3 -5/21 1/1 -4/17 1/1 4/3 -3/13 2/1 1/0 -8/35 1/0 -13/57 -1/2 1/0 -5/22 0/1 -2/9 1/2 -9/41 1/2 1/1 -7/32 2/3 -5/23 2/3 3/4 -3/14 1/1 -4/19 0/1 1/2 -1/5 2/3 1/1 -4/21 1/1 -3/16 6/5 -2/11 2/1 1/0 -3/17 -1/1 1/0 -7/40 0/1 -11/63 0/1 -4/23 0/1 1/4 -1/6 1/1 -3/19 0/1 1/4 -2/13 1/2 2/3 -3/20 2/3 -1/7 1/1 -3/22 2/1 -2/15 1/0 -1/8 0/1 -1/9 1/2 1/0 -1/10 2/3 0/1 0/1 1/1 1/9 1/2 1/0 1/8 0/1 1/7 1/1 2/13 2/1 1/0 1/6 1/1 4/23 -1/2 0/1 3/17 1/3 1/2 2/11 1/2 2/3 3/16 6/7 4/21 1/1 1/5 1/1 2/1 4/19 0/1 1/0 3/14 1/1 5/23 3/2 2/1 2/9 1/0 5/22 0/1 3/13 1/2 2/3 4/17 4/5 1/1 5/21 1/1 1/4 2/1 5/19 0/1 1/0 4/15 1/0 15/56 1/1 11/41 1/1 1/0 7/26 2/1 3/11 -1/1 0/1 5/18 1/1 2/7 1/1 7/24 1/1 12/41 1/1 2/1 5/17 1/1 3/2 18/61 11/6 2/1 31/105 2/1 13/44 2/1 8/27 1/0 11/37 1/1 2/1 3/10 2/1 10/33 1/0 7/23 3/2 2/1 11/36 3/1 4/13 4/1 1/0 5/16 -2/1 1/3 1/2 1/0 6/17 1/1 2/1 5/14 1/0 9/25 -3/1 1/0 4/11 0/1 1/0 7/19 0/1 1/0 10/27 1/0 13/35 -1/1 3/8 0/1 8/21 0/1 5/13 0/1 1/2 7/18 1/1 16/41 0/1 1/1 41/105 1/1 25/64 2/1 9/23 0/1 1/0 2/5 0/1 1/0 11/27 1/2 1/0 9/22 0/1 7/17 1/1 1/0 12/29 -2/1 1/0 29/70 -1/1 17/41 -1/1 1/0 5/12 -1/1 8/19 -1/2 0/1 3/7 0/1 10/23 0/1 1/2 17/39 1/4 1/2 7/16 2/3 18/41 0/1 1/1 11/25 1/2 1/1 15/34 2/1 4/9 1/0 9/20 0/1 5/11 0/1 1/3 6/13 0/1 1/0 13/28 -1/1 7/15 -1/2 1/0 1/2 0/1 8/15 1/4 15/28 1/3 7/13 0/1 1/2 6/11 0/1 1/0 23/42 0/1 17/31 0/1 1/11 11/20 0/1 5/9 1/4 1/2 19/34 0/1 33/59 3/10 1/3 47/84 1/3 14/25 1/3 2/5 23/41 1/3 1/2 9/16 0/1 4/7 0/1 15/26 0/1 11/19 0/1 1/4 18/31 0/1 1/4 61/105 1/4 43/74 2/7 25/43 1/4 1/3 7/12 1/3 24/41 0/1 1/3 41/70 1/3 17/29 0/1 1/4 10/17 1/3 2/5 23/39 1/4 1/2 36/61 0/1 1/2 13/22 0/1 16/27 1/2 3/5 0/1 1/3 14/23 2/5 1/2 39/64 2/5 64/105 1/2 25/41 1/3 1/2 11/18 1/3 19/31 5/13 2/5 8/13 2/5 1/2 13/21 1/2 5/8 0/1 17/27 1/4 1/2 12/19 0/1 1/2 19/30 1/3 26/41 0/1 1/3 33/52 2/7 40/63 1/3 7/11 1/3 2/5 16/25 2/5 3/7 9/14 1/2 11/17 1/3 1/2 13/20 0/1 2/3 1/2 15/22 2/3 13/19 0/1 1/2 11/16 0/1 20/29 6/13 1/2 29/42 1/2 9/13 1/2 4/7 16/23 2/3 3/4 7/10 0/1 33/47 0/1 1/1 59/84 0/1 26/37 0/1 1/2 19/27 1/2 1/0 31/44 0/1 12/17 0/1 1/3 5/7 1/2 18/25 4/7 3/5 31/43 1/2 3/5 13/18 3/5 21/29 1/2 2/3 8/11 2/3 3/4 19/26 2/1 30/41 0/1 1/1 41/56 1/1 11/15 1/2 1/0 14/19 0/1 1/2 31/42 1/2 17/23 1/2 2/3 3/4 0/1 16/21 1/2 13/17 1/2 5/9 10/13 1/2 2/3 27/35 3/5 44/57 5/8 17/22 2/3 7/9 1/2 3/4 32/41 2/3 1/1 25/32 0/1 18/23 2/3 3/4 11/14 1/1 15/19 0/1 1/2 4/5 0/1 1/2 17/21 1/2 13/16 4/7 9/11 2/3 1/1 14/17 3/5 2/3 33/40 2/3 52/63 2/3 19/23 2/3 7/10 5/6 1/1 16/19 0/1 1/4 11/13 1/2 2/3 17/20 0/1 6/7 1/2 19/22 2/3 13/15 1/2 3/4 7/8 2/3 8/9 1/2 9/10 0/1 1/1 1/2 1/1 1/0 1/1 GENERATING SET ASSOCIATED TO THE FUNDAMENTAL DOMAIN GENERATOR EDGE PAIRING TYPE Matrix(1,2,0,1) (-1/1,1/0) -> (1/1,1/0) Parabolic Matrix(83,74,-378,-337) (-1/1,-8/9) -> (-2/9,-9/41) Hyperbolic Matrix(167,148,378,335) (-8/9,-7/8) -> (15/34,4/9) Hyperbolic Matrix(211,184,-336,-293) (-7/8,-6/7) -> (-22/35,-5/8) Hyperbolic Matrix(125,106,-546,-463) (-6/7,-11/13) -> (-3/13,-8/35) Hyperbolic Matrix(379,320,-546,-461) (-11/13,-5/6) -> (-25/36,-9/13) Hyperbolic Matrix(295,244,966,799) (-5/6,-19/23) -> (7/23,11/36) Hyperbolic Matrix(1007,830,-1428,-1177) (-19/23,-14/17) -> (-12/17,-43/61) Hyperbolic Matrix(295,242,462,379) (-14/17,-9/11) -> (7/11,16/25) Hyperbolic Matrix(125,102,462,377) (-9/11,-13/16) -> (7/26,3/11) Hyperbolic Matrix(545,442,672,545) (-13/16,-17/21) -> (17/21,13/16) Hyperbolic Matrix(169,136,210,169) (-17/21,-4/5) -> (4/5,17/21) Hyperbolic Matrix(83,66,210,167) (-4/5,-15/19) -> (9/23,2/5) Hyperbolic Matrix(127,100,588,463) (-15/19,-11/14) -> (3/14,5/23) Hyperbolic Matrix(125,98,588,461) (-11/14,-18/23) -> (4/19,3/14) Hyperbolic Matrix(673,526,-966,-755) (-18/23,-7/9) -> (-23/33,-16/23) Hyperbolic Matrix(209,162,378,293) (-7/9,-17/22) -> (11/20,5/9) Hyperbolic Matrix(83,64,-546,-421) (-17/22,-10/13) -> (-2/13,-3/20) Hyperbolic Matrix(295,226,714,547) (-10/13,-13/17) -> (7/17,12/29) Hyperbolic Matrix(545,416,714,545) (-13/17,-16/21) -> (16/21,13/17) Hyperbolic Matrix(127,96,168,127) (-16/21,-3/4) -> (3/4,16/21) Hyperbolic Matrix(43,32,-168,-125) (-3/4,-14/19) -> (-6/23,-1/4) Hyperbolic Matrix(503,370,798,587) (-14/19,-11/15) -> (17/27,12/19) Hyperbolic Matrix(587,430,1260,923) (-11/15,-41/56) -> (13/28,7/15) Hyperbolic Matrix(3025,2214,5166,3781) (-41/56,-30/41) -> (24/41,41/70) Hyperbolic Matrix(755,552,1722,1259) (-30/41,-19/26) -> (7/16,18/41) Hyperbolic Matrix(85,62,462,337) (-19/26,-8/11) -> (2/11,3/16) Hyperbolic Matrix(293,212,-756,-547) (-8/11,-13/18) -> (-7/18,-12/31) Hyperbolic Matrix(209,150,-294,-211) (-13/18,-5/7) -> (-5/7,-17/24) Parabolic Matrix(1051,744,1722,1219) (-17/24,-29/41) -> (25/41,11/18) Hyperbolic Matrix(965,682,1722,1217) (-29/41,-12/17) -> (14/25,23/41) Hyperbolic Matrix(5167,3642,6258,4411) (-43/61,-74/105) -> (52/63,19/23) Hyperbolic Matrix(5753,4054,6972,4913) (-74/105,-31/44) -> (33/40,52/63) Hyperbolic Matrix(335,236,714,503) (-31/44,-19/27) -> (7/15,1/2) Hyperbolic Matrix(461,324,1134,797) (-19/27,-26/37) -> (2/5,11/27) Hyperbolic Matrix(251,176,-840,-589) (-26/37,-7/10) -> (-3/10,-14/47) Hyperbolic Matrix(43,30,-420,-293) (-7/10,-23/33) -> (-1/9,-1/10) Hyperbolic Matrix(167,116,966,671) (-16/23,-25/36) -> (1/6,4/23) Hyperbolic Matrix(209,144,-672,-463) (-9/13,-11/16) -> (-5/16,-9/29) Hyperbolic Matrix(379,260,-672,-461) (-11/16,-2/3) -> (-22/39,-9/16) Hyperbolic Matrix(293,190,-714,-463) (-2/3,-11/17) -> (-7/17,-16/39) Hyperbolic Matrix(211,136,588,379) (-11/17,-9/14) -> (5/14,9/25) Hyperbolic Matrix(209,134,588,377) (-9/14,-16/25) -> (6/17,5/14) Hyperbolic Matrix(379,242,462,295) (-16/25,-7/11) -> (9/11,14/17) Hyperbolic Matrix(335,212,-798,-505) (-7/11,-12/19) -> (-8/19,-13/31) Hyperbolic Matrix(587,370,798,503) (-12/19,-17/27) -> (11/15,14/19) Hyperbolic Matrix(671,422,-2940,-1849) (-17/27,-22/35) -> (-8/35,-13/57) Hyperbolic Matrix(209,130,336,209) (-5/8,-13/21) -> (13/21,5/8) Hyperbolic Matrix(337,208,546,337) (-13/21,-8/13) -> (8/13,13/21) Hyperbolic Matrix(209,128,-756,-463) (-8/13,-11/18) -> (-5/18,-8/29) Hyperbolic Matrix(1091,666,1512,923) (-11/18,-25/41) -> (31/43,13/18) Hyperbolic Matrix(5249,3200,8610,5249) (-25/41,-64/105) -> (64/105,25/41) Hyperbolic Matrix(8191,4992,13440,8191) (-64/105,-39/64) -> (39/64,64/105) Hyperbolic Matrix(2603,1586,4410,2687) (-39/64,-14/23) -> (36/61,13/22) Hyperbolic Matrix(43,26,210,127) (-14/23,-3/5) -> (1/5,4/19) Hyperbolic Matrix(337,200,1134,673) (-3/5,-16/27) -> (8/27,11/37) Hyperbolic Matrix(125,74,-924,-547) (-16/27,-13/22) -> (-3/22,-2/15) Hyperbolic Matrix(251,148,-714,-421) (-13/22,-10/17) -> (-6/17,-7/20) Hyperbolic Matrix(167,98,714,419) (-10/17,-17/29) -> (3/13,4/17) Hyperbolic Matrix(925,542,1722,1009) (-17/29,-41/70) -> (15/28,7/13) Hyperbolic Matrix(3781,2214,5166,3025) (-41/70,-24/41) -> (30/41,41/56) Hyperbolic Matrix(1091,638,1722,1007) (-24/41,-7/12) -> (19/30,26/41) Hyperbolic Matrix(293,170,-798,-463) (-7/12,-11/19) -> (-7/19,-11/30) Hyperbolic Matrix(167,96,-294,-169) (-11/19,-4/7) -> (-4/7,-13/23) Parabolic Matrix(1343,758,-3276,-1849) (-13/23,-22/39) -> (-16/39,-25/61) Hyperbolic Matrix(463,260,1722,967) (-9/16,-23/41) -> (11/41,7/26) Hyperbolic Matrix(1513,848,2100,1177) (-23/41,-14/25) -> (18/25,31/43) Hyperbolic Matrix(1259,704,-2856,-1597) (-14/25,-19/34) -> (-15/34,-26/59) Hyperbolic Matrix(43,24,378,211) (-19/34,-5/9) -> (1/9,1/8) Hyperbolic Matrix(293,162,378,209) (-5/9,-11/20) -> (17/22,7/9) Hyperbolic Matrix(379,208,-840,-461) (-11/20,-6/11) -> (-14/31,-9/20) Hyperbolic Matrix(335,182,462,251) (-6/11,-7/13) -> (21/29,8/11) Hyperbolic Matrix(1009,542,1722,925) (-7/13,-15/28) -> (41/70,17/29) Hyperbolic Matrix(337,180,1260,673) (-15/28,-8/15) -> (4/15,15/56) Hyperbolic Matrix(211,112,714,379) (-8/15,-1/2) -> (13/44,8/27) Hyperbolic Matrix(503,236,714,335) (-1/2,-7/15) -> (19/27,31/44) Hyperbolic Matrix(923,430,1260,587) (-7/15,-13/28) -> (41/56,11/15) Hyperbolic Matrix(713,330,1722,797) (-13/28,-6/13) -> (12/29,29/70) Hyperbolic Matrix(335,154,546,251) (-6/13,-5/11) -> (19/31,8/13) Hyperbolic Matrix(967,438,1764,799) (-5/11,-19/42) -> (23/42,17/31) Hyperbolic Matrix(965,436,1764,797) (-19/42,-14/31) -> (6/11,23/42) Hyperbolic Matrix(85,38,378,169) (-9/20,-4/9) -> (2/9,5/22) Hyperbolic Matrix(335,148,378,167) (-4/9,-15/34) -> (7/8,8/9) Hyperbolic Matrix(3949,1740,7056,3109) (-26/59,-37/84) -> (47/84,14/25) Hyperbolic Matrix(3947,1738,7056,3107) (-37/84,-11/25) -> (33/59,47/84) Hyperbolic Matrix(505,222,1722,757) (-11/25,-18/41) -> (12/41,5/17) Hyperbolic Matrix(1259,552,1722,755) (-18/41,-7/16) -> (19/26,30/41) Hyperbolic Matrix(125,54,-294,-127) (-7/16,-3/7) -> (-3/7,-11/26) Parabolic Matrix(251,106,-798,-337) (-11/26,-8/19) -> (-6/19,-5/16) Hyperbolic Matrix(1975,828,3108,1303) (-13/31,-44/105) -> (40/63,7/11) Hyperbolic Matrix(6425,2692,10122,4241) (-44/105,-31/74) -> (33/52,40/63) Hyperbolic Matrix(3443,1442,4410,1847) (-31/74,-18/43) -> (32/41,25/32) Hyperbolic Matrix(589,246,1008,421) (-18/43,-5/12) -> (7/12,24/41) Hyperbolic Matrix(587,244,1008,419) (-5/12,-17/41) -> (25/43,7/12) Hyperbolic Matrix(1385,574,5166,2141) (-17/41,-29/70) -> (15/56,11/41) Hyperbolic Matrix(797,330,1722,713) (-29/70,-12/29) -> (6/13,13/28) Hyperbolic Matrix(547,226,714,295) (-12/29,-7/17) -> (13/17,10/13) Hyperbolic Matrix(1723,706,4410,1807) (-25/61,-9/22) -> (25/64,9/23) Hyperbolic Matrix(421,172,-1848,-755) (-9/22,-11/27) -> (-13/57,-5/22) Hyperbolic Matrix(797,324,1134,461) (-11/27,-2/5) -> (26/37,19/27) Hyperbolic Matrix(167,66,210,83) (-2/5,-9/23) -> (15/19,4/5) Hyperbolic Matrix(1177,460,1722,673) (-9/23,-25/64) -> (15/22,13/19) Hyperbolic Matrix(5249,2050,13440,5249) (-25/64,-41/105) -> (41/105,25/64) Hyperbolic Matrix(3361,1312,8610,3361) (-41/105,-16/41) -> (16/41,41/105) Hyperbolic Matrix(503,196,1722,671) (-16/41,-7/18) -> (7/24,12/41) Hyperbolic Matrix(295,114,546,211) (-12/31,-5/13) -> (7/13,6/11) Hyperbolic Matrix(209,80,546,209) (-5/13,-8/21) -> (8/21,5/13) Hyperbolic Matrix(127,48,336,127) (-8/21,-3/8) -> (3/8,8/21) Hyperbolic Matrix(43,16,-336,-125) (-3/8,-10/27) -> (-2/15,-1/8) Hyperbolic Matrix(211,78,798,295) (-10/27,-7/19) -> (5/19,4/15) Hyperbolic Matrix(715,262,1722,631) (-11/30,-15/41) -> (17/41,5/12) Hyperbolic Matrix(421,154,462,169) (-15/41,-19/52) -> (9/10,1/1) Hyperbolic Matrix(5881,2148,10122,3697) (-19/52,-23/63) -> (61/105,43/74) Hyperbolic Matrix(1805,658,3108,1133) (-23/63,-4/11) -> (18/31,61/105) Hyperbolic Matrix(83,30,462,167) (-4/11,-9/25) -> (3/17,2/11) Hyperbolic Matrix(379,136,588,211) (-9/25,-5/14) -> (9/14,11/17) Hyperbolic Matrix(377,134,588,209) (-5/14,-6/17) -> (16/25,9/14) Hyperbolic Matrix(41,14,-126,-43) (-7/20,-1/3) -> (-1/3,-7/22) Parabolic Matrix(1049,332,1722,545) (-7/22,-6/19) -> (14/23,39/64) Hyperbolic Matrix(1219,378,1764,547) (-9/29,-13/42) -> (29/42,9/13) Hyperbolic Matrix(1217,376,1764,545) (-13/42,-4/13) -> (20/29,29/42) Hyperbolic Matrix(85,26,-546,-167) (-4/13,-7/23) -> (-3/19,-2/13) Hyperbolic Matrix(211,64,-966,-293) (-7/23,-3/10) -> (-7/32,-5/23) Hyperbolic Matrix(4957,1476,7056,2101) (-14/47,-25/84) -> (59/84,26/37) Hyperbolic Matrix(4955,1474,7056,2099) (-25/84,-11/37) -> (33/47,59/84) Hyperbolic Matrix(673,200,1134,337) (-11/37,-8/27) -> (16/27,3/5) Hyperbolic Matrix(379,112,714,211) (-8/27,-13/44) -> (1/2,8/15) Hyperbolic Matrix(251,74,-1428,-421) (-13/44,-5/17) -> (-3/17,-7/40) Hyperbolic Matrix(83,24,-294,-85) (-5/17,-2/7) -> (-2/7,-7/25) Parabolic Matrix(923,258,2100,587) (-7/25,-12/43) -> (18/41,11/25) Hyperbolic Matrix(589,164,1512,421) (-12/43,-5/18) -> (7/18,16/41) Hyperbolic Matrix(211,58,462,127) (-8/29,-3/11) -> (5/11,6/13) Hyperbolic Matrix(377,102,462,125) (-3/11,-7/26) -> (13/16,9/11) Hyperbolic Matrix(967,260,1722,463) (-7/26,-11/41) -> (23/41,9/16) Hyperbolic Matrix(2141,574,5166,1385) (-11/41,-15/56) -> (29/70,17/41) Hyperbolic Matrix(673,180,1260,337) (-15/56,-4/15) -> (8/15,15/28) Hyperbolic Matrix(295,78,798,211) (-4/15,-5/19) -> (7/19,10/27) Hyperbolic Matrix(1303,342,1764,463) (-5/19,-11/42) -> (31/42,17/23) Hyperbolic Matrix(1301,340,1764,461) (-11/42,-6/23) -> (14/19,31/42) Hyperbolic Matrix(41,10,168,41) (-1/4,-5/21) -> (5/21,1/4) Hyperbolic Matrix(169,40,714,169) (-5/21,-4/17) -> (4/17,5/21) Hyperbolic Matrix(419,98,714,167) (-4/17,-3/13) -> (17/29,10/17) Hyperbolic Matrix(169,38,378,85) (-5/22,-2/9) -> (4/9,9/20) Hyperbolic Matrix(2563,562,4410,967) (-9/41,-7/32) -> (43/74,25/43) Hyperbolic Matrix(463,100,588,127) (-5/23,-3/14) -> (11/14,15/19) Hyperbolic Matrix(461,98,588,125) (-3/14,-4/19) -> (18/23,11/14) Hyperbolic Matrix(127,26,210,43) (-4/19,-1/5) -> (3/5,14/23) Hyperbolic Matrix(41,8,210,41) (-1/5,-4/21) -> (4/21,1/5) Hyperbolic Matrix(127,24,672,127) (-4/21,-3/16) -> (3/16,4/21) Hyperbolic Matrix(337,62,462,85) (-3/16,-2/11) -> (8/11,19/26) Hyperbolic Matrix(167,30,462,83) (-2/11,-3/17) -> (9/25,4/11) Hyperbolic Matrix(2059,360,6972,1219) (-7/40,-11/63) -> (31/105,13/44) Hyperbolic Matrix(1847,322,6258,1091) (-11/63,-4/23) -> (18/61,31/105) Hyperbolic Matrix(211,36,252,43) (-4/23,-1/6) -> (5/6,16/19) Hyperbolic Matrix(209,34,252,41) (-1/6,-3/19) -> (19/23,5/6) Hyperbolic Matrix(41,6,-294,-43) (-3/20,-1/7) -> (-1/7,-3/22) Parabolic Matrix(211,24,378,43) (-1/8,-1/9) -> (5/9,19/34) Hyperbolic Matrix(293,26,462,41) (-1/10,0/1) -> (26/41,33/52) Hyperbolic Matrix(295,-32,378,-41) (0/1,1/9) -> (7/9,32/41) Hyperbolic Matrix(125,-16,336,-43) (1/8,1/7) -> (13/35,3/8) Hyperbolic Matrix(421,-64,546,-83) (1/7,2/13) -> (10/13,27/35) Hyperbolic Matrix(167,-26,546,-85) (2/13,1/6) -> (11/36,4/13) Hyperbolic Matrix(421,-74,1428,-251) (4/23,3/17) -> (5/17,18/61) Hyperbolic Matrix(293,-64,966,-211) (5/23,2/9) -> (10/33,7/23) Hyperbolic Matrix(463,-106,546,-125) (5/22,3/13) -> (11/13,17/20) Hyperbolic Matrix(125,-32,168,-43) (1/4,5/19) -> (17/23,3/4) Hyperbolic Matrix(463,-128,756,-209) (3/11,5/18) -> (11/18,19/31) Hyperbolic Matrix(85,-24,294,-83) (5/18,2/7) -> (2/7,7/24) Parabolic Matrix(589,-176,840,-251) (11/37,3/10) -> (7/10,33/47) Hyperbolic Matrix(377,-114,420,-127) (3/10,10/33) -> (8/9,9/10) Hyperbolic Matrix(463,-144,672,-209) (4/13,5/16) -> (11/16,20/29) Hyperbolic Matrix(293,-92,672,-211) (5/16,1/3) -> (17/39,7/16) Hyperbolic Matrix(421,-148,714,-251) (1/3,6/17) -> (10/17,23/39) Hyperbolic Matrix(463,-170,798,-293) (4/11,7/19) -> (11/19,18/31) Hyperbolic Matrix(2269,-842,2940,-1091) (10/27,13/35) -> (27/35,44/57) Hyperbolic Matrix(547,-212,756,-293) (5/13,7/18) -> (13/18,21/29) Hyperbolic Matrix(799,-326,924,-377) (11/27,9/22) -> (19/22,13/15) Hyperbolic Matrix(463,-190,714,-293) (9/22,7/17) -> (11/17,13/20) Hyperbolic Matrix(505,-212,798,-335) (5/12,8/19) -> (12/19,19/30) Hyperbolic Matrix(127,-54,294,-125) (8/19,3/7) -> (3/7,10/23) Parabolic Matrix(1933,-842,3276,-1427) (10/23,17/39) -> (23/39,36/61) Hyperbolic Matrix(1597,-704,2856,-1259) (11/25,15/34) -> (19/34,33/59) Hyperbolic Matrix(461,-208,840,-379) (9/20,5/11) -> (17/31,11/20) Hyperbolic Matrix(169,-96,294,-167) (9/16,4/7) -> (4/7,15/26) Parabolic Matrix(547,-316,798,-461) (15/26,11/19) -> (13/19,11/16) Hyperbolic Matrix(1427,-844,1848,-1093) (13/22,16/27) -> (44/57,17/22) Hyperbolic Matrix(293,-184,336,-211) (5/8,17/27) -> (13/15,7/8) Hyperbolic Matrix(85,-56,126,-83) (13/20,2/3) -> (2/3,15/22) Parabolic Matrix(461,-320,546,-379) (9/13,16/23) -> (16/19,11/13) Hyperbolic Matrix(755,-526,966,-673) (16/23,7/10) -> (25/32,18/23) Hyperbolic Matrix(1177,-830,1428,-1007) (31/44,12/17) -> (14/17,33/40) Hyperbolic Matrix(211,-150,294,-209) (12/17,5/7) -> (5/7,18/25) Parabolic Matrix(253,-216,294,-251) (17/20,6/7) -> (6/7,19/22) Parabolic IMAGES OF THE GENERATORS UNDER THE VIRTUAL ENDOMORPHISM Matrix(1,2,0,1) -> Matrix(1,-2,2,-3) Matrix(83,74,-378,-337) -> Matrix(1,-2,2,-3) Matrix(167,148,378,335) -> Matrix(1,0,0,1) Matrix(211,184,-336,-293) -> Matrix(1,-2,0,1) Matrix(125,106,-546,-463) -> Matrix(1,0,0,1) Matrix(379,320,-546,-461) -> Matrix(1,2,0,1) Matrix(295,244,966,799) -> Matrix(5,-8,2,-3) Matrix(1007,830,-1428,-1177) -> Matrix(1,-2,-2,5) Matrix(295,242,462,379) -> Matrix(1,0,2,1) Matrix(125,102,462,377) -> Matrix(1,-2,0,1) Matrix(545,442,672,545) -> Matrix(1,-8,2,-15) Matrix(169,136,210,169) -> Matrix(1,0,2,1) Matrix(83,66,210,167) -> Matrix(1,0,0,1) Matrix(127,100,588,463) -> Matrix(3,-2,2,-1) Matrix(125,98,588,461) -> Matrix(1,-2,2,-3) Matrix(673,526,-966,-755) -> Matrix(1,0,0,1) Matrix(209,162,378,293) -> Matrix(1,-2,4,-7) Matrix(83,64,-546,-421) -> Matrix(1,-4,2,-7) Matrix(295,226,714,547) -> Matrix(1,-4,0,1) Matrix(545,416,714,545) -> Matrix(1,-10,2,-19) Matrix(127,96,168,127) -> Matrix(1,0,2,1) Matrix(43,32,-168,-125) -> Matrix(1,-2,2,-3) Matrix(503,370,798,587) -> Matrix(1,0,2,1) Matrix(587,430,1260,923) -> Matrix(1,0,-2,1) Matrix(3025,2214,5166,3781) -> Matrix(1,0,2,1) Matrix(755,552,1722,1259) -> Matrix(1,0,0,1) Matrix(85,62,462,337) -> Matrix(3,-4,4,-5) Matrix(293,212,-756,-547) -> Matrix(1,-2,0,1) Matrix(209,150,-294,-211) -> Matrix(1,-4,0,1) Matrix(1051,744,1722,1219) -> Matrix(1,2,2,5) Matrix(965,682,1722,1217) -> Matrix(1,2,2,5) Matrix(5167,3642,6258,4411) -> Matrix(19,2,28,3) Matrix(5753,4054,6972,4913) -> Matrix(17,-2,26,-3) Matrix(335,236,714,503) -> Matrix(1,0,-2,1) Matrix(461,324,1134,797) -> Matrix(1,0,0,1) Matrix(251,176,-840,-589) -> Matrix(1,-2,2,-3) Matrix(43,30,-420,-293) -> Matrix(1,-2,2,-3) Matrix(167,116,966,671) -> Matrix(1,-2,0,1) Matrix(209,144,-672,-463) -> Matrix(1,2,2,5) Matrix(379,260,-672,-461) -> Matrix(1,0,0,1) Matrix(293,190,-714,-463) -> Matrix(1,0,2,1) Matrix(211,136,588,379) -> Matrix(1,-2,0,1) Matrix(209,134,588,377) -> Matrix(1,4,0,1) Matrix(379,242,462,295) -> Matrix(1,0,2,1) Matrix(335,212,-798,-505) -> Matrix(1,0,4,1) Matrix(587,370,798,503) -> Matrix(1,0,2,1) Matrix(671,422,-2940,-1849) -> Matrix(1,0,0,1) Matrix(209,130,336,209) -> Matrix(1,0,2,1) Matrix(337,208,546,337) -> Matrix(1,4,2,9) Matrix(209,128,-756,-463) -> Matrix(1,2,0,1) Matrix(1091,666,1512,923) -> Matrix(1,-2,2,-3) Matrix(5249,3200,8610,5249) -> Matrix(1,2,2,5) Matrix(8191,4992,13440,8191) -> Matrix(1,4,2,9) Matrix(2603,1586,4410,2687) -> Matrix(1,2,2,5) Matrix(43,26,210,127) -> Matrix(1,2,0,1) Matrix(337,200,1134,673) -> Matrix(1,2,0,1) Matrix(125,74,-924,-547) -> Matrix(1,2,0,1) Matrix(251,148,-714,-421) -> Matrix(1,0,2,1) Matrix(167,98,714,419) -> Matrix(3,2,4,3) Matrix(925,542,1722,1009) -> Matrix(1,0,4,1) Matrix(3781,2214,5166,3025) -> Matrix(1,0,2,1) Matrix(1091,638,1722,1007) -> Matrix(1,0,4,1) Matrix(293,170,-798,-463) -> Matrix(1,0,4,1) Matrix(167,96,-294,-169) -> Matrix(1,0,2,1) Matrix(1343,758,-3276,-1849) -> Matrix(1,-2,2,-3) Matrix(463,260,1722,967) -> Matrix(1,2,0,1) Matrix(1513,848,2100,1177) -> Matrix(1,-2,2,-3) Matrix(1259,704,-2856,-1597) -> Matrix(3,2,4,3) Matrix(43,24,378,211) -> Matrix(1,0,2,1) Matrix(293,162,378,209) -> Matrix(3,2,4,3) Matrix(379,208,-840,-461) -> Matrix(1,0,8,1) Matrix(335,182,462,251) -> Matrix(1,-2,2,-3) Matrix(1009,542,1722,925) -> Matrix(1,0,4,1) Matrix(337,180,1260,673) -> Matrix(1,0,2,1) Matrix(211,112,714,379) -> Matrix(5,2,2,1) Matrix(503,236,714,335) -> Matrix(1,0,-2,1) Matrix(923,430,1260,587) -> Matrix(1,0,-2,1) Matrix(713,330,1722,797) -> Matrix(5,-2,-2,1) Matrix(335,154,546,251) -> Matrix(3,-2,8,-5) Matrix(967,438,1764,799) -> Matrix(1,0,12,1) Matrix(965,436,1764,797) -> Matrix(1,0,-10,1) Matrix(85,38,378,169) -> Matrix(1,0,-2,1) Matrix(335,148,378,167) -> Matrix(1,0,0,1) Matrix(3949,1740,7056,3109) -> Matrix(7,-6,20,-17) Matrix(3947,1738,7056,3107) -> Matrix(3,-4,10,-13) Matrix(505,222,1722,757) -> Matrix(3,-2,2,-1) Matrix(1259,552,1722,755) -> Matrix(1,0,0,1) Matrix(125,54,-294,-127) -> Matrix(1,0,4,1) Matrix(251,106,-798,-337) -> Matrix(1,0,-2,1) Matrix(1975,828,3108,1303) -> Matrix(13,-4,36,-11) Matrix(6425,2692,10122,4241) -> Matrix(11,-4,36,-13) Matrix(3443,1442,4410,1847) -> Matrix(5,-2,8,-3) Matrix(589,246,1008,421) -> Matrix(1,0,0,1) Matrix(587,244,1008,419) -> Matrix(5,-2,18,-7) Matrix(1385,574,5166,2141) -> Matrix(1,0,-2,1) Matrix(797,330,1722,713) -> Matrix(5,-2,-2,1) Matrix(547,226,714,295) -> Matrix(9,-4,16,-7) Matrix(1723,706,4410,1807) -> Matrix(3,-2,2,-1) Matrix(421,172,-1848,-755) -> Matrix(1,0,-2,1) Matrix(797,324,1134,461) -> Matrix(1,0,0,1) Matrix(167,66,210,83) -> Matrix(1,0,0,1) Matrix(1177,460,1722,673) -> Matrix(1,0,0,1) Matrix(5249,2050,13440,5249) -> Matrix(5,-4,4,-3) Matrix(3361,1312,8610,3361) -> Matrix(1,0,0,1) Matrix(503,196,1722,671) -> Matrix(3,-2,2,-1) Matrix(295,114,546,211) -> Matrix(1,0,2,1) Matrix(209,80,546,209) -> Matrix(1,0,2,1) Matrix(127,48,336,127) -> Matrix(1,0,-4,1) Matrix(43,16,-336,-125) -> Matrix(1,0,-2,1) Matrix(211,78,798,295) -> Matrix(1,0,-2,1) Matrix(715,262,1722,631) -> Matrix(5,-2,-2,1) Matrix(421,154,462,169) -> Matrix(5,-2,8,-3) Matrix(5881,2148,10122,3697) -> Matrix(9,-4,34,-15) Matrix(1805,658,3108,1133) -> Matrix(1,0,2,1) Matrix(83,30,462,167) -> Matrix(5,-2,8,-3) Matrix(379,136,588,211) -> Matrix(5,-2,8,-3) Matrix(377,134,588,209) -> Matrix(7,-4,16,-9) Matrix(41,14,-126,-43) -> Matrix(1,0,0,1) Matrix(1049,332,1722,545) -> Matrix(3,-2,8,-5) Matrix(1219,378,1764,547) -> Matrix(21,-10,40,-19) Matrix(1217,376,1764,545) -> Matrix(19,-10,40,-21) Matrix(85,26,-546,-167) -> Matrix(3,-2,8,-5) Matrix(211,64,-966,-293) -> Matrix(1,0,0,1) Matrix(4957,1476,7056,2101) -> Matrix(3,-2,8,-5) Matrix(4955,1474,7056,2099) -> Matrix(3,-2,2,-1) Matrix(673,200,1134,337) -> Matrix(3,-2,8,-5) Matrix(379,112,714,211) -> Matrix(3,-2,14,-9) Matrix(251,74,-1428,-421) -> Matrix(3,-2,-4,3) Matrix(83,24,-294,-85) -> Matrix(3,-2,2,-1) Matrix(923,258,2100,587) -> Matrix(1,0,0,1) Matrix(589,164,1512,421) -> Matrix(1,0,0,1) Matrix(211,58,462,127) -> Matrix(1,0,0,1) Matrix(377,102,462,125) -> Matrix(5,-2,8,-3) Matrix(967,260,1722,463) -> Matrix(3,-2,8,-5) Matrix(2141,574,5166,1385) -> Matrix(1,0,-2,1) Matrix(673,180,1260,337) -> Matrix(1,0,2,1) Matrix(295,78,798,211) -> Matrix(1,0,-2,1) Matrix(1303,342,1764,463) -> Matrix(5,-2,8,-3) Matrix(1301,340,1764,461) -> Matrix(3,-2,8,-5) Matrix(41,10,168,41) -> Matrix(5,-4,4,-3) Matrix(169,40,714,169) -> Matrix(7,-8,8,-9) Matrix(419,98,714,167) -> Matrix(1,-2,4,-7) Matrix(169,38,378,85) -> Matrix(1,0,-2,1) Matrix(2563,562,4410,967) -> Matrix(1,0,2,1) Matrix(463,100,588,127) -> Matrix(3,-2,2,-1) Matrix(461,98,588,125) -> Matrix(1,-2,2,-3) Matrix(127,26,210,43) -> Matrix(3,-2,8,-5) Matrix(41,8,210,41) -> Matrix(5,-4,4,-3) Matrix(127,24,672,127) -> Matrix(11,-12,12,-13) Matrix(337,62,462,85) -> Matrix(3,-4,4,-5) Matrix(167,30,462,83) -> Matrix(1,-2,0,1) Matrix(2059,360,6972,1219) -> Matrix(13,2,6,1) Matrix(1847,322,6258,1091) -> Matrix(19,-2,10,-1) Matrix(211,36,252,43) -> Matrix(1,0,0,1) Matrix(209,34,252,41) -> Matrix(1,-2,2,-3) Matrix(41,6,-294,-43) -> Matrix(5,-4,4,-3) Matrix(211,24,378,43) -> Matrix(1,0,2,1) Matrix(293,26,462,41) -> Matrix(1,0,2,1) Matrix(295,-32,378,-41) -> Matrix(1,-2,2,-3) Matrix(125,-16,336,-43) -> Matrix(1,0,-2,1) Matrix(421,-64,546,-83) -> Matrix(1,-4,2,-7) Matrix(167,-26,546,-85) -> Matrix(1,2,0,1) Matrix(421,-74,1428,-251) -> Matrix(7,-2,4,-1) Matrix(293,-64,966,-211) -> Matrix(1,0,0,1) Matrix(463,-106,546,-125) -> Matrix(1,0,0,1) Matrix(125,-32,168,-43) -> Matrix(1,-2,2,-3) Matrix(463,-128,756,-209) -> Matrix(3,-2,8,-5) Matrix(85,-24,294,-83) -> Matrix(3,-2,2,-1) Matrix(589,-176,840,-251) -> Matrix(1,-2,2,-3) Matrix(377,-114,420,-127) -> Matrix(1,-2,2,-3) Matrix(463,-144,672,-209) -> Matrix(1,2,2,5) Matrix(293,-92,672,-211) -> Matrix(1,0,2,1) Matrix(421,-148,714,-251) -> Matrix(1,0,2,1) Matrix(463,-170,798,-293) -> Matrix(1,0,4,1) Matrix(2269,-842,2940,-1091) -> Matrix(5,8,8,13) Matrix(547,-212,756,-293) -> Matrix(5,-2,8,-3) Matrix(799,-326,924,-377) -> Matrix(1,-2,2,-3) Matrix(463,-190,714,-293) -> Matrix(1,0,2,1) Matrix(505,-212,798,-335) -> Matrix(1,0,4,1) Matrix(127,-54,294,-125) -> Matrix(1,0,4,1) Matrix(1933,-842,3276,-1427) -> Matrix(1,0,0,1) Matrix(1597,-704,2856,-1259) -> Matrix(1,-2,4,-7) Matrix(461,-208,840,-379) -> Matrix(1,0,8,1) Matrix(169,-96,294,-167) -> Matrix(1,0,2,1) Matrix(547,-316,798,-461) -> Matrix(1,0,-2,1) Matrix(1427,-844,1848,-1093) -> Matrix(9,-2,14,-3) Matrix(293,-184,336,-211) -> Matrix(5,-2,8,-3) Matrix(85,-56,126,-83) -> Matrix(5,-2,8,-3) Matrix(461,-320,546,-379) -> Matrix(3,-2,8,-5) Matrix(755,-526,966,-673) -> Matrix(1,0,0,1) Matrix(1177,-830,1428,-1007) -> Matrix(9,-2,14,-3) Matrix(211,-150,294,-209) -> Matrix(9,-4,16,-7) Matrix(253,-216,294,-251) -> Matrix(5,-2,8,-3) INFORMATION ON THE IMAGE OF THIS GROUP UNDER THE VIRTUAL ENDOMORPHISM Index in PSL(2,Z): 6 Minimal number of generators: 2 Number of equivalence classes of cusps: 3 Genus: 0 Degree of H/liftables -> H/(image of liftables): 44 Degree of the the map X: 44 Degree of the the map Y: 192 ----------------------------------------------------------------------- Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift elements of DeckMod(f) via pi_1: 0 DeckMod(f) is trivial. Elements among 0, lambda1, lambda2 and lambda1+lambda2 which lift modular group liftables via pi_1: 0 The subgroup of modular group liftables which arise from translations is trivial. ----------------------------------------------------------------------- The image of the modular group liftables in PSL(2,Z) equals the image of the pure modular group liftables. ----------------------------------------------------------------------- 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) 0 21 1/9 0 7 1/8 0/1 1 21 1/7 1/1 2 3 2/13 (2/1,1/0) 0 21 1/6 1/1 1 7 4/23 (-1/2,0/1) 0 21 3/17 (1/3,1/2) 0 21 2/11 (1/2,2/3) 0 21 3/16 6/7 1 21 4/21 1/1 8 1 1/5 (1/1,2/1) 0 21 4/19 (0/1,1/0) 0 21 3/14 1/1 2 3 5/23 (3/2,2/1) 0 21 2/9 1/0 1 7 5/22 0/1 1 21 3/13 (1/2,2/3) 0 21 4/17 (4/5,1/1) 0 21 5/21 1/1 6 1 1/4 2/1 1 21 5/19 (0/1,1/0) 0 21 4/15 1/0 1 7 15/56 1/1 1 3 11/41 (1/1,1/0) 0 21 7/26 2/1 1 21 3/11 (-1/1,0/1) 0 21 5/18 1/1 1 7 2/7 1/1 1 3 7/24 1/1 1 7 12/41 (1/1,2/1) 0 21 5/17 (1/1,3/2) 0 21 18/61 (11/6,2/1) 0 21 31/105 2/1 8 1 13/44 2/1 1 21 8/27 1/0 1 7 11/37 (1/1,2/1) 0 21 3/10 2/1 1 21 10/33 1/0 1 7 7/23 (3/2,2/1) 0 21 11/36 3/1 1 7 4/13 (4/1,1/0) 0 21 5/16 -2/1 1 21 1/3 0 7 6/17 (1/1,2/1) 0 21 5/14 1/0 3 3 9/25 (-3/1,1/0) 0 21 4/11 (0/1,1/0) 0 21 7/19 (0/1,1/0) 0 21 10/27 1/0 1 7 13/35 -1/1 2 3 3/8 0/1 1 21 8/21 0/1 3 1 5/13 (0/1,1/2) 0 21 7/18 1/1 1 7 16/41 (0/1,1/1) 0 21 41/105 1/1 2 1 25/64 2/1 1 21 9/23 (0/1,1/0) 0 21 2/5 (0/1,1/0) 0 21 11/27 0 7 9/22 0/1 1 21 7/17 (1/1,1/0) 0 21 12/29 (-2/1,1/0) 0 21 29/70 -1/1 1 3 17/41 (-1/1,1/0) 0 21 5/12 -1/1 1 7 8/19 (-1/2,0/1) 0 21 3/7 0/1 2 3 10/23 (0/1,1/2) 0 21 17/39 0 7 7/16 2/3 1 21 18/41 (0/1,1/1) 0 21 11/25 (1/2,1/1) 0 21 15/34 2/1 1 21 4/9 1/0 1 7 9/20 0/1 1 21 5/11 (0/1,1/3) 0 21 6/13 (0/1,1/0) 0 21 13/28 -1/1 1 3 7/15 0 7 1/2 0/1 1 21 8/15 1/4 1 7 15/28 1/3 1 3 7/13 (0/1,1/2) 0 21 6/11 (0/1,1/0) 0 21 23/42 0/1 11 1 17/31 (0/1,1/11) 0 21 11/20 0/1 1 21 5/9 0 7 19/34 0/1 1 21 33/59 (3/10,1/3) 0 21 47/84 1/3 5 1 14/25 (1/3,2/5) 0 21 23/41 (1/3,1/2) 0 21 9/16 0/1 1 21 4/7 0/1 1 3 15/26 0/1 1 21 11/19 (0/1,1/4) 0 21 18/31 (0/1,1/4) 0 21 61/105 1/4 2 1 43/74 2/7 1 21 25/43 (1/4,1/3) 0 21 7/12 1/3 1 7 24/41 (0/1,1/3) 0 21 41/70 1/3 1 3 17/29 (0/1,1/4) 0 21 10/17 (1/3,2/5) 0 21 23/39 0 7 36/61 (0/1,1/2) 0 21 13/22 0/1 1 21 16/27 1/2 1 7 3/5 (0/1,1/3) 0 21 14/23 (2/5,1/2) 0 21 39/64 2/5 1 21 64/105 1/2 1 1 25/41 (1/3,1/2) 0 21 11/18 1/3 1 7 19/31 (5/13,2/5) 0 21 8/13 (2/5,1/2) 0 21 13/21 1/2 2 1 5/8 0/1 1 21 17/27 0 7 12/19 (0/1,1/2) 0 21 19/30 1/3 1 7 26/41 (0/1,1/3) 0 21 33/52 2/7 1 21 40/63 1/3 4 1 7/11 (1/3,2/5) 0 21 16/25 (2/5,3/7) 0 21 9/14 1/2 3 3 11/17 (1/3,1/2) 0 21 13/20 0/1 1 21 2/3 1/2 1 7 15/22 2/3 1 21 13/19 (0/1,1/2) 0 21 11/16 0/1 1 21 20/29 (6/13,1/2) 0 21 29/42 1/2 10 1 9/13 (1/2,4/7) 0 21 16/23 (2/3,3/4) 0 21 7/10 0/1 1 21 33/47 (0/1,1/1) 0 21 59/84 0/1 1 1 26/37 (0/1,1/2) 0 21 19/27 0 7 31/44 0/1 1 21 12/17 (0/1,1/3) 0 21 5/7 1/2 2 3 18/25 (4/7,3/5) 0 21 31/43 (1/2,3/5) 0 21 13/18 3/5 1 7 21/29 (1/2,2/3) 0 21 8/11 (2/3,3/4) 0 21 19/26 2/1 1 21 30/41 (0/1,1/1) 0 21 41/56 1/1 1 3 11/15 0 7 14/19 (0/1,1/2) 0 21 31/42 1/2 2 1 17/23 (1/2,2/3) 0 21 3/4 0/1 1 21 16/21 1/2 5 1 13/17 (1/2,5/9) 0 21 10/13 (1/2,2/3) 0 21 27/35 3/5 2 3 44/57 5/8 1 7 17/22 2/3 1 21 7/9 0 7 32/41 (2/3,1/1) 0 21 25/32 0/1 1 21 18/23 (2/3,3/4) 0 21 11/14 1/1 2 3 15/19 (0/1,1/2) 0 21 4/5 (0/1,1/2) 0 21 17/21 1/2 4 1 13/16 4/7 1 21 9/11 (2/3,1/1) 0 21 14/17 (3/5,2/3) 0 21 33/40 2/3 1 21 52/63 2/3 9 1 19/23 (2/3,7/10) 0 21 5/6 1/1 1 7 16/19 (0/1,1/4) 0 21 11/13 (1/2,2/3) 0 21 17/20 0/1 1 21 6/7 1/2 1 3 19/22 2/3 1 21 13/15 0 7 7/8 2/3 1 21 8/9 1/2 1 7 9/10 0/1 1 21 1/1 (1/2,1/1) 0 21 1/0 1/1 1 1 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(295,-32,378,-41) (0/1,1/9) -> (7/9,32/41) Hyperbolic Matrix(211,-24,378,-43) (1/9,1/8) -> (5/9,19/34) Glide Reflection Matrix(125,-16,336,-43) (1/8,1/7) -> (13/35,3/8) Hyperbolic Matrix(421,-64,546,-83) (1/7,2/13) -> (10/13,27/35) Hyperbolic Matrix(167,-26,546,-85) (2/13,1/6) -> (11/36,4/13) Hyperbolic Matrix(211,-36,252,-43) (1/6,4/23) -> (5/6,16/19) Glide Reflection Matrix(421,-74,1428,-251) (4/23,3/17) -> (5/17,18/61) Hyperbolic Matrix(167,-30,462,-83) (3/17,2/11) -> (9/25,4/11) Glide Reflection Matrix(337,-62,462,-85) (2/11,3/16) -> (8/11,19/26) Glide Reflection Matrix(127,-24,672,-127) (3/16,4/21) -> (3/16,4/21) Reflection Matrix(41,-8,210,-41) (4/21,1/5) -> (4/21,1/5) Reflection Matrix(127,-26,210,-43) (1/5,4/19) -> (3/5,14/23) Glide Reflection Matrix(461,-98,588,-125) (4/19,3/14) -> (18/23,11/14) Glide Reflection Matrix(463,-100,588,-127) (3/14,5/23) -> (11/14,15/19) Glide Reflection Matrix(293,-64,966,-211) (5/23,2/9) -> (10/33,7/23) Hyperbolic Matrix(169,-38,378,-85) (2/9,5/22) -> (4/9,9/20) Glide Reflection Matrix(463,-106,546,-125) (5/22,3/13) -> (11/13,17/20) Hyperbolic Matrix(419,-98,714,-167) (3/13,4/17) -> (17/29,10/17) Glide Reflection Matrix(169,-40,714,-169) (4/17,5/21) -> (4/17,5/21) Reflection Matrix(41,-10,168,-41) (5/21,1/4) -> (5/21,1/4) Reflection Matrix(125,-32,168,-43) (1/4,5/19) -> (17/23,3/4) Hyperbolic Matrix(295,-78,798,-211) (5/19,4/15) -> (7/19,10/27) Glide Reflection Matrix(673,-180,1260,-337) (4/15,15/56) -> (8/15,15/28) Glide Reflection Matrix(2141,-574,5166,-1385) (15/56,11/41) -> (29/70,17/41) Glide Reflection Matrix(967,-260,1722,-463) (11/41,7/26) -> (23/41,9/16) Glide Reflection Matrix(377,-102,462,-125) (7/26,3/11) -> (13/16,9/11) Glide Reflection Matrix(463,-128,756,-209) (3/11,5/18) -> (11/18,19/31) Hyperbolic Matrix(85,-24,294,-83) (5/18,2/7) -> (2/7,7/24) Parabolic Matrix(671,-196,1722,-503) (7/24,12/41) -> (7/18,16/41) Glide Reflection Matrix(757,-222,1722,-505) (12/41,5/17) -> (18/41,11/25) Glide Reflection Matrix(3781,-1116,12810,-3781) (18/61,31/105) -> (18/61,31/105) Reflection Matrix(2729,-806,9240,-2729) (31/105,13/44) -> (31/105,13/44) Reflection Matrix(379,-112,714,-211) (13/44,8/27) -> (1/2,8/15) Glide Reflection Matrix(673,-200,1134,-337) (8/27,11/37) -> (16/27,3/5) Glide Reflection Matrix(589,-176,840,-251) (11/37,3/10) -> (7/10,33/47) Hyperbolic Matrix(377,-114,420,-127) (3/10,10/33) -> (8/9,9/10) Hyperbolic Matrix(799,-244,966,-295) (7/23,11/36) -> (19/23,5/6) Glide Reflection Matrix(463,-144,672,-209) (4/13,5/16) -> (11/16,20/29) Hyperbolic Matrix(293,-92,672,-211) (5/16,1/3) -> (17/39,7/16) Hyperbolic Matrix(421,-148,714,-251) (1/3,6/17) -> (10/17,23/39) Hyperbolic Matrix(377,-134,588,-209) (6/17,5/14) -> (16/25,9/14) Glide Reflection Matrix(379,-136,588,-211) (5/14,9/25) -> (9/14,11/17) Glide Reflection Matrix(463,-170,798,-293) (4/11,7/19) -> (11/19,18/31) Hyperbolic Matrix(2269,-842,2940,-1091) (10/27,13/35) -> (27/35,44/57) Hyperbolic Matrix(127,-48,336,-127) (3/8,8/21) -> (3/8,8/21) Reflection Matrix(209,-80,546,-209) (8/21,5/13) -> (8/21,5/13) Reflection Matrix(547,-212,756,-293) (5/13,7/18) -> (13/18,21/29) Hyperbolic Matrix(3361,-1312,8610,-3361) (16/41,41/105) -> (16/41,41/105) Reflection Matrix(5249,-2050,13440,-5249) (41/105,25/64) -> (41/105,25/64) Reflection Matrix(1177,-460,1722,-673) (25/64,9/23) -> (15/22,13/19) Glide Reflection Matrix(167,-66,210,-83) (9/23,2/5) -> (15/19,4/5) Glide Reflection Matrix(797,-324,1134,-461) (2/5,11/27) -> (26/37,19/27) Glide Reflection Matrix(799,-326,924,-377) (11/27,9/22) -> (19/22,13/15) Hyperbolic Matrix(463,-190,714,-293) (9/22,7/17) -> (11/17,13/20) Hyperbolic Matrix(547,-226,714,-295) (7/17,12/29) -> (13/17,10/13) Glide Reflection Matrix(797,-330,1722,-713) (12/29,29/70) -> (6/13,13/28) Glide Reflection Matrix(587,-244,1008,-419) (17/41,5/12) -> (25/43,7/12) Glide Reflection Matrix(505,-212,798,-335) (5/12,8/19) -> (12/19,19/30) Hyperbolic Matrix(127,-54,294,-125) (8/19,3/7) -> (3/7,10/23) Parabolic Matrix(1933,-842,3276,-1427) (10/23,17/39) -> (23/39,36/61) Hyperbolic Matrix(1259,-552,1722,-755) (7/16,18/41) -> (19/26,30/41) Glide Reflection Matrix(1597,-704,2856,-1259) (11/25,15/34) -> (19/34,33/59) Hyperbolic Matrix(335,-148,378,-167) (15/34,4/9) -> (7/8,8/9) Glide Reflection Matrix(461,-208,840,-379) (9/20,5/11) -> (17/31,11/20) Hyperbolic Matrix(335,-154,546,-251) (5/11,6/13) -> (19/31,8/13) Glide Reflection Matrix(923,-430,1260,-587) (13/28,7/15) -> (41/56,11/15) Glide Reflection Matrix(503,-236,714,-335) (7/15,1/2) -> (19/27,31/44) Glide Reflection Matrix(1009,-542,1722,-925) (15/28,7/13) -> (41/70,17/29) Glide Reflection Matrix(335,-182,462,-251) (7/13,6/11) -> (21/29,8/11) Glide Reflection Matrix(505,-276,924,-505) (6/11,23/42) -> (6/11,23/42) Reflection Matrix(1427,-782,2604,-1427) (23/42,17/31) -> (23/42,17/31) Reflection Matrix(293,-162,378,-209) (11/20,5/9) -> (17/22,7/9) Glide Reflection Matrix(5545,-3102,9912,-5545) (33/59,47/84) -> (33/59,47/84) Reflection Matrix(2351,-1316,4200,-2351) (47/84,14/25) -> (47/84,14/25) Reflection Matrix(1513,-848,2100,-1177) (14/25,23/41) -> (18/25,31/43) Glide Reflection Matrix(169,-96,294,-167) (9/16,4/7) -> (4/7,15/26) Parabolic Matrix(547,-316,798,-461) (15/26,11/19) -> (13/19,11/16) Hyperbolic Matrix(3781,-2196,6510,-3781) (18/31,61/105) -> (18/31,61/105) Reflection Matrix(9029,-5246,15540,-9029) (61/105,43/74) -> (61/105,43/74) Reflection Matrix(461,-268,504,-293) (43/74,25/43) -> (9/10,1/1) Glide Reflection Matrix(1091,-638,1722,-1007) (7/12,24/41) -> (19/30,26/41) Glide Reflection Matrix(3781,-2214,5166,-3025) (24/41,41/70) -> (30/41,41/56) Glide Reflection Matrix(2687,-1586,4410,-2603) (36/61,13/22) -> (14/23,39/64) Glide Reflection Matrix(1427,-844,1848,-1093) (13/22,16/27) -> (44/57,17/22) Hyperbolic Matrix(8191,-4992,13440,-8191) (39/64,64/105) -> (39/64,64/105) Reflection Matrix(5249,-3200,8610,-5249) (64/105,25/41) -> (64/105,25/41) Reflection Matrix(1091,-666,1512,-923) (25/41,11/18) -> (31/43,13/18) Glide Reflection Matrix(337,-208,546,-337) (8/13,13/21) -> (8/13,13/21) Reflection Matrix(209,-130,336,-209) (13/21,5/8) -> (13/21,5/8) Reflection Matrix(293,-184,336,-211) (5/8,17/27) -> (13/15,7/8) Hyperbolic Matrix(587,-370,798,-503) (17/27,12/19) -> (11/15,14/19) Glide Reflection Matrix(2689,-1706,3444,-2185) (26/41,33/52) -> (32/41,25/32) Glide Reflection Matrix(4159,-2640,6552,-4159) (33/52,40/63) -> (33/52,40/63) Reflection Matrix(881,-560,1386,-881) (40/63,7/11) -> (40/63,7/11) Reflection Matrix(379,-242,462,-295) (7/11,16/25) -> (9/11,14/17) Glide Reflection Matrix(85,-56,126,-83) (13/20,2/3) -> (2/3,15/22) Parabolic Matrix(1681,-1160,2436,-1681) (20/29,29/42) -> (20/29,29/42) Reflection Matrix(755,-522,1092,-755) (29/42,9/13) -> (29/42,9/13) Reflection Matrix(461,-320,546,-379) (9/13,16/23) -> (16/19,11/13) Hyperbolic Matrix(755,-526,966,-673) (16/23,7/10) -> (25/32,18/23) Hyperbolic Matrix(5545,-3894,7896,-5545) (33/47,59/84) -> (33/47,59/84) Reflection Matrix(4367,-3068,6216,-4367) (59/84,26/37) -> (59/84,26/37) Reflection Matrix(1177,-830,1428,-1007) (31/44,12/17) -> (14/17,33/40) Hyperbolic Matrix(211,-150,294,-209) (12/17,5/7) -> (5/7,18/25) Parabolic Matrix(1177,-868,1596,-1177) (14/19,31/42) -> (14/19,31/42) Reflection Matrix(1427,-1054,1932,-1427) (31/42,17/23) -> (31/42,17/23) Reflection Matrix(127,-96,168,-127) (3/4,16/21) -> (3/4,16/21) Reflection Matrix(545,-416,714,-545) (16/21,13/17) -> (16/21,13/17) Reflection Matrix(169,-136,210,-169) (4/5,17/21) -> (4/5,17/21) Reflection Matrix(545,-442,672,-545) (17/21,13/16) -> (17/21,13/16) Reflection Matrix(4159,-3432,5040,-4159) (33/40,52/63) -> (33/40,52/63) Reflection Matrix(2393,-1976,2898,-2393) (52/63,19/23) -> (52/63,19/23) Reflection Matrix(253,-216,294,-251) (17/20,6/7) -> (6/7,19/22) Parabolic Matrix(-1,2,0,1) (1/1,1/0) -> (1/1,1/0) Reflection IMAGES OF THE GENERATORS MAP ON REFLECTION AXES OR UNDER THE VIRTUAL ENDOMORPHISM FIXED POINT OF IMAGE Matrix(1,0,0,-1) -> Matrix(1,0,2,-1) (0/1,1/0) -> (0/1,1/1) Matrix(295,-32,378,-41) -> Matrix(1,-2,2,-3) 1/1 Matrix(211,-24,378,-43) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(125,-16,336,-43) -> Matrix(1,0,-2,1) 0/1 Matrix(421,-64,546,-83) -> Matrix(1,-4,2,-7) Matrix(167,-26,546,-85) -> Matrix(1,2,0,1) 1/0 Matrix(211,-36,252,-43) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(421,-74,1428,-251) -> Matrix(7,-2,4,-1) Matrix(167,-30,462,-83) -> Matrix(3,-2,-2,1) Matrix(337,-62,462,-85) -> Matrix(5,-4,6,-5) *** -> (2/3,1/1) Matrix(127,-24,672,-127) -> Matrix(13,-12,14,-13) (3/16,4/21) -> (6/7,1/1) Matrix(41,-8,210,-41) -> Matrix(3,-4,2,-3) (4/21,1/5) -> (1/1,2/1) Matrix(127,-26,210,-43) -> Matrix(1,-2,2,-5) Matrix(461,-98,588,-125) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(463,-100,588,-127) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(293,-64,966,-211) -> Matrix(1,0,0,1) Matrix(169,-38,378,-85) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(463,-106,546,-125) -> Matrix(1,0,0,1) Matrix(419,-98,714,-167) -> Matrix(3,-2,10,-7) Matrix(169,-40,714,-169) -> Matrix(9,-8,10,-9) (4/17,5/21) -> (4/5,1/1) Matrix(41,-10,168,-41) -> Matrix(3,-4,2,-3) (5/21,1/4) -> (1/1,2/1) Matrix(125,-32,168,-43) -> Matrix(1,-2,2,-3) 1/1 Matrix(295,-78,798,-211) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(673,-180,1260,-337) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(2141,-574,5166,-1385) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(967,-260,1722,-463) -> Matrix(1,-2,2,-5) Matrix(377,-102,462,-125) -> Matrix(1,2,2,3) Matrix(463,-128,756,-209) -> Matrix(3,-2,8,-5) 1/2 Matrix(85,-24,294,-83) -> Matrix(3,-2,2,-1) 1/1 Matrix(671,-196,1722,-503) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(757,-222,1722,-505) -> Matrix(-1,2,0,1) *** -> (1/1,1/0) Matrix(3781,-1116,12810,-3781) -> Matrix(23,-44,12,-23) (18/61,31/105) -> (11/6,2/1) Matrix(2729,-806,9240,-2729) -> Matrix(9,-20,4,-9) (31/105,13/44) -> (2/1,5/2) Matrix(379,-112,714,-211) -> Matrix(1,-2,4,-9) Matrix(673,-200,1134,-337) -> Matrix(1,-2,2,-5) Matrix(589,-176,840,-251) -> Matrix(1,-2,2,-3) 1/1 Matrix(377,-114,420,-127) -> Matrix(1,-2,2,-3) 1/1 Matrix(799,-244,966,-295) -> Matrix(3,-8,4,-11) Matrix(463,-144,672,-209) -> Matrix(1,2,2,5) Matrix(293,-92,672,-211) -> Matrix(1,0,2,1) 0/1 Matrix(421,-148,714,-251) -> Matrix(1,0,2,1) 0/1 Matrix(377,-134,588,-209) -> Matrix(1,-4,2,-9) Matrix(379,-136,588,-211) -> Matrix(1,2,2,3) Matrix(463,-170,798,-293) -> Matrix(1,0,4,1) 0/1 Matrix(2269,-842,2940,-1091) -> Matrix(5,8,8,13) Matrix(127,-48,336,-127) -> Matrix(-1,0,2,1) (3/8,8/21) -> (-1/1,0/1) Matrix(209,-80,546,-209) -> Matrix(1,0,4,-1) (8/21,5/13) -> (0/1,1/2) Matrix(547,-212,756,-293) -> Matrix(5,-2,8,-3) 1/2 Matrix(3361,-1312,8610,-3361) -> Matrix(1,0,2,-1) (16/41,41/105) -> (0/1,1/1) Matrix(5249,-2050,13440,-5249) -> Matrix(3,-4,2,-3) (41/105,25/64) -> (1/1,2/1) Matrix(1177,-460,1722,-673) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(167,-66,210,-83) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(797,-324,1134,-461) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(799,-326,924,-377) -> Matrix(1,-2,2,-3) 1/1 Matrix(463,-190,714,-293) -> Matrix(1,0,2,1) 0/1 Matrix(547,-226,714,-295) -> Matrix(1,4,2,7) Matrix(797,-330,1722,-713) -> Matrix(1,2,0,-1) *** -> (-1/1,1/0) Matrix(587,-244,1008,-419) -> Matrix(1,2,4,7) Matrix(505,-212,798,-335) -> Matrix(1,0,4,1) 0/1 Matrix(127,-54,294,-125) -> Matrix(1,0,4,1) 0/1 Matrix(1933,-842,3276,-1427) -> Matrix(1,0,0,1) Matrix(1259,-552,1722,-755) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(1597,-704,2856,-1259) -> Matrix(1,-2,4,-7) Matrix(335,-148,378,-167) -> Matrix(1,0,2,-1) *** -> (0/1,1/1) Matrix(461,-208,840,-379) -> Matrix(1,0,8,1) 0/1 Matrix(335,-154,546,-251) -> Matrix(1,-2,2,-5) Matrix(923,-430,1260,-587) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(503,-236,714,-335) -> Matrix(1,0,0,-1) *** -> (0/1,1/0) Matrix(1009,-542,1722,-925) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(335,-182,462,-251) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(505,-276,924,-505) -> Matrix(1,0,0,-1) (6/11,23/42) -> (0/1,1/0) Matrix(1427,-782,2604,-1427) -> Matrix(1,0,22,-1) (23/42,17/31) -> (0/1,1/11) Matrix(293,-162,378,-209) -> Matrix(7,-2,10,-3) Matrix(5545,-3102,9912,-5545) -> Matrix(19,-6,60,-19) (33/59,47/84) -> (3/10,1/3) Matrix(2351,-1316,4200,-2351) -> Matrix(11,-4,30,-11) (47/84,14/25) -> (1/3,2/5) Matrix(1513,-848,2100,-1177) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(169,-96,294,-167) -> Matrix(1,0,2,1) 0/1 Matrix(547,-316,798,-461) -> Matrix(1,0,-2,1) 0/1 Matrix(3781,-2196,6510,-3781) -> Matrix(1,0,8,-1) (18/31,61/105) -> (0/1,1/4) Matrix(9029,-5246,15540,-9029) -> Matrix(15,-4,56,-15) (61/105,43/74) -> (1/4,2/7) Matrix(461,-268,504,-293) -> Matrix(7,-2,10,-3) Matrix(1091,-638,1722,-1007) -> Matrix(1,0,6,-1) *** -> (0/1,1/3) Matrix(3781,-2214,5166,-3025) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(2687,-1586,4410,-2603) -> Matrix(5,-2,12,-5) *** -> (1/3,1/2) Matrix(1427,-844,1848,-1093) -> Matrix(9,-2,14,-3) Matrix(8191,-4992,13440,-8191) -> Matrix(9,-4,20,-9) (39/64,64/105) -> (2/5,1/2) Matrix(5249,-3200,8610,-5249) -> Matrix(5,-2,12,-5) (64/105,25/41) -> (1/3,1/2) Matrix(1091,-666,1512,-923) -> Matrix(3,-2,4,-3) *** -> (1/2,1/1) Matrix(337,-208,546,-337) -> Matrix(9,-4,20,-9) (8/13,13/21) -> (2/5,1/2) Matrix(209,-130,336,-209) -> Matrix(1,0,4,-1) (13/21,5/8) -> (0/1,1/2) Matrix(293,-184,336,-211) -> Matrix(5,-2,8,-3) 1/2 Matrix(587,-370,798,-503) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(2689,-1706,3444,-2185) -> Matrix(7,-2,10,-3) Matrix(4159,-2640,6552,-4159) -> Matrix(13,-4,42,-13) (33/52,40/63) -> (2/7,1/3) Matrix(881,-560,1386,-881) -> Matrix(11,-4,30,-11) (40/63,7/11) -> (1/3,2/5) Matrix(379,-242,462,-295) -> Matrix(1,0,4,-1) *** -> (0/1,1/2) Matrix(85,-56,126,-83) -> Matrix(5,-2,8,-3) 1/2 Matrix(1681,-1160,2436,-1681) -> Matrix(25,-12,52,-25) (20/29,29/42) -> (6/13,1/2) Matrix(755,-522,1092,-755) -> Matrix(15,-8,28,-15) (29/42,9/13) -> (1/2,4/7) Matrix(461,-320,546,-379) -> Matrix(3,-2,8,-5) 1/2 Matrix(755,-526,966,-673) -> Matrix(1,0,0,1) Matrix(5545,-3894,7896,-5545) -> Matrix(1,0,2,-1) (33/47,59/84) -> (0/1,1/1) Matrix(4367,-3068,6216,-4367) -> Matrix(1,0,4,-1) (59/84,26/37) -> (0/1,1/2) Matrix(1177,-830,1428,-1007) -> Matrix(9,-2,14,-3) Matrix(211,-150,294,-209) -> Matrix(9,-4,16,-7) 1/2 Matrix(1177,-868,1596,-1177) -> Matrix(1,0,4,-1) (14/19,31/42) -> (0/1,1/2) Matrix(1427,-1054,1932,-1427) -> Matrix(7,-4,12,-7) (31/42,17/23) -> (1/2,2/3) Matrix(127,-96,168,-127) -> Matrix(1,0,4,-1) (3/4,16/21) -> (0/1,1/2) Matrix(545,-416,714,-545) -> Matrix(19,-10,36,-19) (16/21,13/17) -> (1/2,5/9) Matrix(169,-136,210,-169) -> Matrix(1,0,4,-1) (4/5,17/21) -> (0/1,1/2) Matrix(545,-442,672,-545) -> Matrix(15,-8,28,-15) (17/21,13/16) -> (1/2,4/7) Matrix(4159,-3432,5040,-4159) -> Matrix(67,-44,102,-67) (33/40,52/63) -> (11/17,2/3) Matrix(2393,-1976,2898,-2393) -> Matrix(41,-28,60,-41) (52/63,19/23) -> (2/3,7/10) Matrix(253,-216,294,-251) -> Matrix(5,-2,8,-3) 1/2 Matrix(-1,2,0,1) -> Matrix(3,-2,4,-3) (1/1,1/0) -> (1/2,1/1) ----------------------------------------------------------------------- The pullback map was not drawn because it is too complicated.