Discriminant of quadratic order and factorisation : 19240 [2, 3; 5, 1; 13, 1; 37, 1] Class group : structure, generators, unit : [16, [4, 2, 2], [Qfb(17, 110, -105), Qfb(51, 94, -51), Qfb(7, 138, -7)], 8.80357439557636] unit = 3329 + 48*w norm unit = 1 List and structure of elments in class group : [((0, 0, 0), Qfb(1, 138, -49)), ((0, 0, 1), Qfb(7, 138, -7)), ((0, 1, 0), Qfb(-51, 110, 35)), ((0, 1, 1), Qfb(5, 130, -117)), ((1, 0, 0), Qfb(-55, 100, 42)), ((1, 0, 1), Qfb(39, 104, -54)), ((1, 1, 0), Qfb(-62, 112, 27)), ((1, 1, 1), Qfb(-46, 60, 85)), ((2, 0, 0), Qfb(-9, 122, 121)), ((2, 0, 1), Qfb(73, 48, -58)), ((2, 1, 0), Qfb(61, 66, -61)), ((2, 1, 1), Qfb(-2, 136, 93)), ((3, 0, 0), Qfb(-42, 124, 23)), ((3, 0, 1), Qfb(-39, 130, 15)), ((3, 1, 0), Qfb(-3, 134, 107)), ((3, 1, 1), Qfb(-11, 120, 110))] Group element : Euclid CF expansion a0+1/(a1+1/(...)): (0, 0, 0) [0, 2, 1, 4, 1, 2, 138, 2, 1, 4, 1, 2, 138, 2, 1, 4, 1, 2, 138, 2, 1, 4, 1, 2] (0, 0, 1) [0, 1, 2, 10, 2, 1, 68, 1, 2, 10, 2, 1, 68, 1, 2, 10, 2, 1, 68, 1, 2, 10, 2, 1] (0, 1, 0) [0, 3, 1, 19, 19, 1, 3, 3, 1, 19, 19, 1, 3, 3, 1, 19, 19, 1, 3, 3, 1, 19, 19, 1] (0, 1, 1) [-1, 2, 1, 1, 2, 9, 1, 1, 9, 2, 1, 1, 1, 1, 2, 9, 1, 1, 9, 2, 1, 1, 1, 1] (1, 0, 0) [0, 1, 4, 2, 45, 1, 3, 1, 1, 1, 4, 2, 45, 1, 3, 1, 1, 1, 4, 2, 45, 1, 3, 1] (1, 0, 1) [-1, 1, 1, 4, 22, 1, 8, 3, 2, 4, 22, 1, 8, 3, 2, 4, 22, 1, 8, 3, 2, 4, 22, 1] (1, 1, 0) [-1, 12, 1, 5, 1, 2, 6, 3, 1, 11, 1, 5, 1, 2, 6, 3, 1, 11, 1, 5, 1, 2, 6, 3] (1, 1, 1) [-1, 6, 2, 2, 1, 5, 3, 7, 1, 5, 2, 2, 1, 5, 3, 7, 1, 5, 2, 2, 1, 5, 3, 7] (2, 0, 0) [-1, 1, 13, 1, 12, 1, 14, 2, 14, 1, 12, 1, 14, 2, 14, 1, 12, 1, 14, 2, 14, 1, 12, 1] (2, 0, 1) [0, 1, 6, 1, 26, 1, 6, 1, 2, 1, 6, 1, 26, 1, 6, 1, 2, 1, 6, 1, 26, 1, 6, 1] (2, 1, 0) [-1, 2, 1, 1, 3, 1, 1, 2, 2, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 2, 1] (2, 1, 1) [-1, 1, 3, 1, 1, 3, 2, 2, 3, 1, 1, 4, 4, 1, 1, 3, 2, 2, 3, 1, 1, 4, 4, 1] (3, 0, 0) [0, 1, 1, 1, 3, 1, 45, 2, 4, 1, 1, 1, 3, 1, 45, 2, 4, 1, 1, 1, 3, 1, 45, 2] (3, 0, 1) [0, 3, 8, 1, 22, 4, 2, 3, 8, 1, 22, 4, 2, 3, 8, 1, 22, 4, 2, 3, 8, 1, 22, 4] (3, 1, 0) [0, 6, 2, 1, 5, 1, 11, 1, 3, 6, 2, 1, 5, 1, 11, 1, 3, 6, 2, 1, 5, 1, 11, 1] (3, 1, 1) [0, 3, 5, 1, 2, 2, 5, 1, 7, 3, 5, 1, 2, 2, 5, 1, 7, 3, 5, 1, 2, 2, 5, 1] Discriminant of quadratic order and factorisation : 51976 [2, 3; 73, 1; 89, 1] Class group : structure, generators, unit : [24, [12, 2], [Qfb(3, 224, -150), Qfb(15, 226, -15)], 10.1654671261551] unit = 12995 + 114*w norm unit = 1 List and structure of elments in class group : [((0, 0), Qfb(1, 226, -225)), ((0, 1), Qfb(30, 224, -15)), ((1, 0), Qfb(74, 204, -35)), ((1, 1), Qfb(-11, 210, 179)), ((2, 0), Qfb(18, 208, -121)), ((2, 1), Qfb(62, 112, -159)), ((3, 0), Qfb(61, 124, -150)), ((3, 1), Qfb(-42, 160, 157)), ((4, 0), Qfb(105, 106, -97)), ((4, 1), Qfb(14, 204, -185)), ((5, 0), Qfb(-75, 226, 3)), ((5, 1), Qfb(45, 224, -10)), ((6, 0), Qfb(114, 164, -55)), ((6, 1), Qfb(33, 208, -66)), ((7, 0), Qfb(3, 226, -75)), ((7, 1), Qfb(93, 50, -133)), ((8, 0), Qfb(55, 144, -142)), ((8, 1), Qfb(-7, 216, 190)), ((9, 0), Qfb(70, 176, -75)), ((9, 1), Qfb(21, 218, -53)), ((10, 0), Qfb(-25, 226, 9)), ((10, 1), Qfb(-31, 198, 103)), ((11, 0), Qfb(-70, 204, 37)), ((11, 1), Qfb(22, 208, -99))] Group element : Euclid CF expansion a0+1/(a1+1/(...)): (0, 0) [0, 1, 112, 1, 226, 1, 112, 1, 226, 1, 112, 1, 226, 1, 112, 1, 226, 1, 112, 1, 226, 1, 112, 1] (0, 1) [0, 15, 7, 1, 1, 7, 15, 15, 7, 1, 1, 7, 15, 15, 7, 1, 1, 7, 15, 15, 7, 1, 1, 7] (1, 0) [0, 1, 37, 3, 75, 1, 1, 1, 37, 3, 75, 1, 1, 1, 37, 3, 75, 1, 1, 1, 37, 3, 75, 1] (1, 1) [0, 5, 22, 1, 1, 2, 45, 5, 22, 1, 1, 2, 45, 5, 22, 1, 1, 2, 45, 5, 22, 1, 1, 2] (2, 0) [-1, 2, 12, 9, 25, 4, 1, 1, 12, 9, 25, 4, 1, 1, 12, 9, 25, 4, 1, 1, 12, 9, 25, 4] (2, 1) [0, 1, 2, 1, 6, 1, 6, 2, 14, 1, 2, 1, 2, 1, 6, 1, 6, 2, 14, 1, 2, 1, 2, 1] (3, 0) [0, 1, 3, 2, 1, 2, 2, 1, 7, 1, 2, 1, 5, 1, 3, 2, 1, 2, 2, 1, 7, 1, 2, 1] (3, 1) [-1, 1, 9, 1, 1, 1, 1, 1, 1, 1, 4, 1, 4, 4, 10, 1, 1, 1, 1, 1, 1, 1, 4, 1] (4, 0) [-1, 2, 1, 1, 1, 2, 3, 1, 3, 4, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 3, 4] (4, 1) [0, 1, 5, 1, 15, 2, 2, 1, 31, 1, 5, 1, 15, 2, 2, 1, 31, 1, 5, 1, 15, 2, 2, 1] (5, 0) [0, 1, 5, 3, 11, 1, 2, 6, 5, 1, 5, 3, 11, 1, 2, 6, 5, 1, 5, 3, 11, 1, 2, 6] (5, 1) [0, 1, 9, 1, 19, 1, 4, 2, 9, 1, 9, 1, 19, 1, 4, 2, 9, 1, 9, 1, 19, 1, 4, 2] (6, 0) [0, 3, 1, 1, 3, 2, 3, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 1, 3, 2, 3, 1, 1, 3] (6, 1) [-1, 1, 2, 3, 6, 1, 1, 1, 1, 6, 3, 3, 3, 3, 6, 1, 1, 1, 1, 6, 3, 3, 3, 3] (7, 0) [0, 1, 11, 3, 5, 1, 5, 6, 2, 1, 11, 3, 5, 1, 5, 6, 2, 1, 11, 3, 5, 1, 5, 6] (7, 1) [-1, 1, 1, 4, 1, 19, 1, 9, 1, 9, 2, 4, 1, 19, 1, 9, 1, 9, 2, 4, 1, 19, 1, 9] (8, 0) [-1, 1, 2, 1, 3, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 3, 1, 3, 2, 1, 1, 1, 1] (8, 1) [-1, 3, 2, 15, 1, 5, 1, 31, 1, 2, 2, 15, 1, 5, 1, 31, 1, 2, 2, 15, 1, 5, 1, 31] (9, 0) [0, 2, 1, 2, 3, 1, 5, 1, 2, 1, 7, 1, 2, 2, 1, 2, 3, 1, 5, 1, 2, 1, 7, 1] (9, 1) [-1, 1, 3, 4, 1, 4, 1, 1, 1, 1, 1, 1, 1, 10, 4, 4, 1, 4, 1, 1, 1, 1, 1, 1] (10, 0) [0, 9, 12, 1, 1, 4, 25, 9, 12, 1, 1, 4, 25, 9, 12, 1, 1, 4, 25, 9, 12, 1, 1, 4] (10, 1) [-1, 15, 2, 6, 1, 6, 1, 2, 1, 2, 1, 14, 2, 6, 1, 6, 1, 2, 1, 2, 1, 14, 2, 6] (11, 0) [0, 1, 1, 1, 75, 3, 37, 1, 1, 1, 75, 3, 37, 1, 1, 1, 75, 3, 37, 1, 1, 1, 75, 3] (11, 1) [0, 1, 1, 22, 5, 45, 2, 1, 1, 22, 5, 45, 2, 1, 1, 22, 5, 45, 2, 1, 1, 22, 5, 45] Discriminant of quadratic order and factorisation : 94636 [2, 2; 59, 1; 401, 1] Class group : structure, generators, unit : [18, [6, 3], [Qfb(19, 270, -286), Qfb(5, 304, -111)], 17.3563197258012] unit = 17247410 + 112131*w norm unit = 1 List and structure of elments in class group : [((0, 0), Qfb(1, 306, -250)), ((0, 1), Qfb(29, 258, -242)), ((0, 2), Qfb(29, 264, -215)), ((1, 0), Qfb(-123, 212, 101)), ((1, 1), Qfb(-66, 226, 165)), ((1, 2), Qfb(-19, 270, 286)), ((2, 0), Qfb(-39, 250, 206)), ((2, 1), Qfb(-18, 298, 81)), ((2, 2), Qfb(-10, 294, 205)), ((3, 0), Qfb(-130, 166, 129)), ((3, 1), Qfb(37, 288, -79)), ((3, 2), Qfb(37, 304, -15)), ((4, 0), Qfb(94, 230, -111)), ((4, 1), Qfb(-10, 306, 25)), ((4, 2), Qfb(-18, 278, 241)), ((5, 0), Qfb(30, 286, -107)), ((5, 1), Qfb(-19, 300, 61)), ((5, 2), Qfb(13, 296, -135))] Group element : Euclid CF expansion a0+1/(a1+1/(...)): (0, 0) [0, 1, 4, 2, 2, 153, 2, 2, 4, 1, 306, 1, 4, 2, 2, 153, 2, 2, 4, 1, 306, 1, 4, 2] (0, 1) [0, 1, 5, 1, 13, 7, 1, 4, 2, 2, 1, 27, 3, 1, 9, 1, 5, 1, 13, 7, 1, 4, 2, 2] (0, 2) [0, 1, 3, 27, 1, 2, 2, 4, 1, 7, 13, 1, 5, 1, 9, 1, 3, 27, 1, 2, 2, 4, 1, 7] (1, 0) [-1, 1, 1, 1, 1, 2, 1, 19, 1, 3, 1, 2, 2, 3, 1, 2, 9, 1, 8, 2, 2, 1, 1, 2] (1, 1) [-1, 2, 1, 1, 1, 1, 1, 2, 1, 11, 9, 4, 4, 2, 23, 4, 1, 1, 1, 1, 1, 1, 1, 2] (1, 2) [-1, 102, 1, 1, 1, 1, 7, 2, 50, 1, 4, 15, 1, 101, 1, 1, 1, 1, 7, 2, 50, 1, 4, 15] (2, 0) [-1, 3, 1, 4, 1, 5, 1, 2, 1, 1, 3, 2, 1, 2, 2, 2, 2, 1, 6, 7, 1, 2, 1, 4] (2, 1) [-1, 1, 2, 1, 2, 1, 4, 1, 1, 1, 33, 1, 1, 6, 1, 1, 1, 4, 1, 16, 3, 1, 2, 1] (2, 2) [-1, 3, 7, 6, 61, 2, 1, 3, 12, 30, 1, 2, 7, 6, 61, 2, 1, 3, 12, 30, 1, 2, 7, 6] (3, 0) [-1, 2, 5, 11, 4, 1, 1, 1, 4, 11, 5, 1, 1, 1, 1, 4, 1, 1, 1, 1, 5, 11, 4, 1] (3, 1) [0, 3, 1, 3, 2, 1, 9, 1, 1, 3, 1, 1, 1, 2, 1, 1, 2, 20, 8, 3, 1, 3, 2, 1] (3, 2) [0, 20, 2, 1, 1, 2, 1, 1, 1, 3, 1, 1, 9, 1, 2, 3, 1, 3, 8, 20, 2, 1, 1, 2] (4, 0) [0, 2, 2, 2, 1, 2, 3, 1, 1, 2, 1, 5, 1, 4, 1, 2, 1, 7, 6, 1, 2, 2, 2, 2] (4, 1) [-1, 1, 11, 3, 1, 2, 61, 6, 7, 2, 1, 30, 12, 3, 1, 2, 61, 6, 7, 2, 1, 30, 12, 3] (4, 2) [-1, 5, 1, 1, 1, 6, 1, 1, 33, 1, 1, 1, 4, 1, 2, 1, 3, 16, 1, 4, 1, 1, 1, 6] (5, 0) [0, 2, 1, 3, 2, 2, 1, 3, 1, 19, 1, 2, 1, 1, 2, 2, 8, 1, 9, 2, 1, 3, 2, 2] (5, 1) [-1, 1, 3, 1, 50, 2, 7, 1, 1, 1, 1, 101, 1, 15, 4, 1, 50, 2, 7, 1, 1, 1, 1, 101] (5, 2) [0, 2, 4, 4, 9, 11, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 23, 2, 4, 4, 9, 11, 1, 2] Discriminant of quadratic order and factorisation : 32009 Mat([32009, 1]) Class group : structure, generators, unit : [9, [3, 3], [Qfb(2, 177, -85), Qfb(5, 173, -104)], 17.4543643349769] unit = 18917767 + 212666*w norm unit = -1 List and structure of elments in class group : [((0, 0), Qfb(1, 177, -170)), ((0, 1), Qfb(5, 173, -104)), ((0, 2), Qfb(92, 165, -13)), ((1, 0), Qfb(2, 177, -85)), ((1, 1), Qfb(10, 173, -52)), ((1, 2), Qfb(122, 139, -26)), ((2, 0), Qfb(32, 125, -128)), ((2, 1), Qfb(122, 105, -43)), ((2, 2), Qfb(10, 167, -103))] Group element : Euclid CF expansion a0+1/(a1+1/(...)): (0, 0) [0, 1, 21, 2, 1, 2, 2, 2, 2, 1, 2, 21, 1, 177, 1, 21, 2, 1, 2, 2, 2, 2, 1, 2] (0, 1) [0, 1, 1, 2, 4, 13, 1, 1, 6, 1, 1, 1, 3, 4, 5, 35, 1, 1, 2, 4, 13, 1, 1, 6] (0, 2) [0, 13, 4, 2, 1, 1, 35, 5, 4, 3, 1, 1, 1, 6, 1, 1, 13, 4, 2, 1, 1, 35, 5, 4] (1, 0) [0, 2, 10, 1, 2, 5, 1, 4, 1, 2, 1, 43, 1, 88, 2, 10, 1, 2, 5, 1, 4, 1, 2, 1] (1, 1) [0, 3, 2, 1, 1, 1, 1, 6, 3, 1, 2, 1, 4, 1, 1, 8, 2, 1, 1, 17, 3, 2, 1, 1] (1, 2) [0, 6, 8, 1, 3, 1, 17, 10, 2, 7, 3, 3, 3, 1, 6, 8, 1, 3, 1, 17, 10, 2, 7, 3] (2, 0) [0, 1, 5, 2, 1, 10, 2, 88, 1, 43, 1, 2, 1, 4, 1, 5, 2, 1, 10, 2, 88, 1, 43, 1] (2, 1) [0, 3, 3, 3, 7, 2, 10, 17, 1, 3, 1, 8, 6, 1, 3, 3, 3, 7, 2, 10, 17, 1, 3, 1] (2, 2) [0, 1, 1, 2, 8, 1, 1, 4, 1, 2, 1, 3, 6, 1, 1, 1, 1, 2, 3, 17, 1, 1, 2, 8] Discriminant of quadratic order and factorisation : 42817 [47, 1; 911, 1] Class group : structure, generators, unit : [9, [3, 3], [Qfb(2, 205, -99), Qfb(3, 205, -66)], 22.0083317729958] unit = 1798718231 + 17469840*w norm unit = 1 List and structure of elments in class group : [((0, 0), Qfb(1, 205, -198)), ((0, 1), Qfb(3, 205, -66)), ((0, 2), Qfb(9, 205, -22)), ((1, 0), Qfb(2, 205, -99)), ((1, 1), Qfb(6, 205, -33)), ((1, 2), Qfb(18, 205, -11)), ((2, 0), Qfb(32, 161, -132)), ((2, 1), Qfb(103, 81, -88)), ((2, 2), Qfb(-22, 169, 162))] Group element : Euclid CF expansion a0+1/(a1+1/(...)): (0, 0) [0, 1, 24, 1, 6, 1, 2, 2, 1, 3, 1, 2, 2, 1, 6, 1, 24, 1, 205, 1, 24, 1, 6, 1] (0, 1) [0, 3, 8, 3, 2, 4, 3, 1, 2, 9, 22, 1, 7, 1, 1, 1, 68, 3, 8, 3, 2, 4, 3, 1] (0, 2) [0, 9, 2, 1, 3, 4, 2, 3, 8, 3, 68, 1, 1, 1, 7, 1, 22, 9, 2, 1, 3, 4, 2, 3] (1, 0) [0, 2, 12, 2, 3, 2, 1, 5, 1, 1, 2, 1, 5, 1, 2, 1, 50, 1, 102, 2, 12, 2, 3, 2] (1, 1) [0, 6, 4, 6, 1, 8, 1, 1, 5, 4, 1, 1, 10, 1, 16, 3, 34, 6, 4, 6, 1, 8, 1, 1] (1, 2) [0, 18, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 16, 1, 1, 1, 33, 1, 4, 1, 3, 2, 11, 18] (2, 0) [0, 1, 2, 1, 1, 5, 1, 2, 3, 2, 12, 2, 102, 1, 50, 1, 2, 1, 5, 1, 2, 1, 1, 5] (2, 1) [0, 1, 1, 1, 1, 2, 1, 18, 11, 2, 3, 1, 4, 1, 33, 1, 1, 1, 16, 1, 1, 2, 1, 1] (2, 2) [-1, 7, 4, 6, 34, 3, 16, 1, 10, 1, 1, 4, 5, 1, 1, 8, 1, 6, 4, 6, 34, 3, 16, 1] Discriminant of quadratic order and factorisation : 374344 [2, 3; 73, 1; 641, 1] Class group : structure, generators, unit : [32, [8, 4], [Qfb(31, 580, -306), Qfb(93, 518, -285)], 19.6406231624860] unit = 169349635 + 553578*w norm unit = 1 List and structure of elments in class group : [((0, 0), Qfb(1, 610, -561)), ((0, 1), Qfb(5, 602, -597)), ((0, 2), Qfb(2, 608, -585)), ((0, 3), Qfb(5, 608, -234)), ((1, 0), Qfb(221, 270, -341)), ((1, 1), Qfb(15, 602, -199)), ((1, 2), Qfb(6, 608, -195)), ((1, 3), Qfb(15, 608, -78)), ((2, 0), Qfb(-130, 432, 361)), ((2, 1), Qfb(-262, 476, 141)), ((2, 2), Qfb(18, 608, -65)), ((2, 3), Qfb(45, 608, -26)), ((3, 0), Qfb(235, 558, -67)), ((3, 1), Qfb(47, 558, -335)), ((3, 2), Qfb(-195, 302, 363)), ((3, 3), Qfb(-78, 536, 279)), ((4, 0), Qfb(242, 424, -201)), ((4, 1), Qfb(141, 464, -282)), ((4, 2), Qfb(121, 424, -402)), ((4, 3), Qfb(-234, 536, 93)), ((5, 0), Qfb(155, 332, -426)), ((5, 1), Qfb(-94, 476, 393)), ((5, 2), Qfb(-235, 288, 310)), ((5, 3), Qfb(31, 580, -306)), ((6, 0), Qfb(-142, 520, 183)), ((6, 1), Qfb(-282, 476, 131)), ((6, 2), Qfb(-71, 520, 366)), ((6, 3), Qfb(93, 518, -285)), ((7, 0), Qfb(-3, 610, 187)), ((7, 1), Qfb(-209, 214, 393)), ((7, 2), Qfb(-213, 236, 374)), ((7, 3), Qfb(279, 518, -95))] Group element : Euclid CF expansion a0+1/(a1+1/(...)): (0, 0) [0, 1, 11, 4, 5, 8, 5, 4, 11, 1, 610, 1, 11, 4, 5, 8, 5, 4, 11, 1, 610, 1, 11, 4] (0, 1) [0, 1, 60, 5, 4, 1, 2, 3, 1, 1, 5, 1, 1, 1, 1, 2, 121, 1, 60, 5, 4, 1, 2, 3] (0, 2) [0, 1, 23, 2, 10, 4, 10, 2, 23, 1, 304, 1, 23, 2, 10, 4, 10, 2, 23, 1, 304, 1, 23, 2] (0, 3) [0, 2, 1, 1, 1, 1, 5, 1, 1, 3, 2, 1, 4, 5, 60, 1, 121, 2, 1, 1, 1, 1, 5, 1] (1, 0) [0, 1, 3, 2, 2, 2, 1, 2, 1, 2, 15, 1, 2, 1, 3, 3, 203, 1, 1, 1, 3, 2, 2, 2] (1, 1) [0, 3, 20, 15, 1, 1, 1, 3, 2, 1, 17, 1, 5, 2, 40, 3, 20, 15, 1, 1, 1, 3, 2, 1] (1, 2) [0, 3, 7, 1, 4, 1, 2, 1, 2, 1, 31, 2, 7, 1, 1, 1, 101, 3, 7, 1, 4, 1, 2, 1] (1, 3) [0, 7, 1, 4, 1, 1, 5, 1, 8, 2, 2, 1, 2, 1, 19, 1, 1, 1, 40, 7, 1, 4, 1, 1] (2, 0) [-1, 3, 4, 9, 5, 2, 4, 1, 10, 3, 3, 1, 67, 4, 1, 2, 4, 9, 5, 2, 4, 1, 10, 3] (2, 1) [-1, 1, 2, 1, 6, 46, 1, 11, 55, 1, 1, 6, 13, 2, 3, 1, 6, 46, 1, 11, 55, 1, 1, 6] (2, 2) [0, 9, 2, 1, 1, 1, 1, 4, 10, 1, 9, 1, 4, 1, 1, 1, 7, 1, 33, 9, 2, 1, 1, 1] (2, 3) [0, 23, 2, 5, 1, 1, 27, 3, 1, 2, 1, 1, 6, 4, 1, 1, 13, 23, 2, 5, 1, 1, 27, 3] (3, 0) [0, 8, 1, 2, 1, 2, 2, 1, 1, 6, 1, 1, 1, 1, 3, 9, 1, 3, 22, 2, 2, 8, 1, 2] (3, 1) [0, 1, 1, 2, 1, 14, 1, 35, 18, 1, 1, 19, 4, 2, 12, 1, 1, 2, 1, 14, 1, 35, 18, 1] (3, 2) [-1, 4, 1, 6, 2, 2, 3, 3, 3, 3, 1, 1, 1, 4, 2, 1, 1, 1, 10, 1, 2, 2, 1, 3] (3, 3) [-1, 1, 1, 17, 1, 1, 8, 1, 3, 9, 1, 1, 1, 1, 2, 1, 5, 1, 3, 1, 2, 7, 2, 17] (4, 0) [0, 2, 1, 1, 2, 1, 3, 6, 1, 1, 1, 1, 6, 3, 1, 2, 1, 1, 2, 2, 7, 7, 2, 2] (4, 1) [0, 1, 1, 9, 1, 4, 3, 11, 1, 2, 5, 1, 5, 6, 2, 2, 4, 1, 3, 1, 1, 9, 1, 4] (4, 2) [0, 1, 3, 2, 7, 3, 3, 3, 3, 7, 2, 3, 1, 4, 3, 1, 1, 3, 4, 1, 3, 2, 7, 3] (4, 3) [-1, 1, 5, 5, 1, 5, 2, 1, 11, 3, 4, 1, 9, 1, 1, 3, 1, 4, 2, 2, 6, 5, 1, 5] (5, 0) [0, 1, 9, 3, 1, 1, 1, 1, 6, 1, 1, 2, 2, 1, 2, 1, 8, 2, 2, 22, 3, 1, 9, 3] (5, 1) [-1, 3, 1, 1, 1, 1, 9, 3, 1, 8, 1, 1, 17, 2, 7, 2, 1, 3, 1, 5, 1, 2, 1, 1] (5, 2) [-1, 3, 4, 1, 1, 1, 3, 3, 3, 3, 2, 2, 6, 1, 3, 1, 2, 2, 1, 10, 1, 1, 1, 2] (5, 3) [0, 1, 1, 18, 35, 1, 14, 1, 2, 1, 1, 12, 2, 4, 19, 1, 1, 18, 35, 1, 14, 1, 2, 1] (6, 0) [-1, 1, 2, 10, 1, 4, 2, 5, 9, 4, 2, 1, 4, 67, 1, 3, 3, 10, 1, 4, 2, 5, 9, 4] (6, 1) [-1, 1, 3, 6, 1, 1, 2, 1, 3, 27, 1, 1, 5, 2, 23, 13, 1, 1, 4, 6, 1, 1, 2, 1] (6, 2) [-1, 2, 1, 4, 1, 9, 1, 10, 4, 1, 1, 1, 1, 2, 9, 33, 1, 7, 1, 1, 1, 4, 1, 9] (6, 3) [0, 1, 1, 55, 11, 1, 46, 6, 1, 3, 2, 13, 6, 1, 1, 55, 11, 1, 46, 6, 1, 3, 2, 13] (7, 0) [-1, 1, 2, 3, 1, 2, 1, 15, 2, 1, 2, 1, 2, 2, 2, 3, 1, 1, 1, 203, 3, 3, 1, 2] (7, 1) [-1, 20, 1, 2, 1, 2, 2, 8, 1, 5, 1, 1, 4, 1, 7, 40, 1, 1, 1, 19, 1, 2, 1, 2] (7, 2) [-1, 8, 2, 31, 1, 2, 1, 2, 1, 4, 1, 7, 3, 101, 1, 1, 1, 7, 2, 31, 1, 2, 1, 2] (7, 3) [0, 5, 1, 17, 1, 2, 3, 1, 1, 1, 15, 20, 3, 40, 2, 5, 1, 17, 1, 2, 3, 1, 1, 1] Discriminant of quadratic order and factorisation : 378184 [2, 3; 41, 1; 1153, 1] Class group : structure, generators, unit : [80, [20, 4], [Qfb(13, 610, -117), Qfb(483, 514, -59)], 10.5159126272832] unit = 18449 + 60*w norm unit = 1 List and structure of elments in class group : [((0, 0), Qfb(1, 614, -297)), ((0, 1), Qfb(45, 542, -469)), ((0, 2), Qfb(159, 338, -415)), ((0, 3), Qfb(277, 442, -165)), ((1, 0), Qfb(3, 614, -99)), ((1, 1), Qfb(265, 338, -249)), ((1, 2), Qfb(299, 222, -275)), ((1, 3), Qfb(-110, 552, 167)), ((2, 0), Qfb(9, 614, -33)), ((2, 1), Qfb(374, 504, -83)), ((2, 2), Qfb(-66, 508, 455)), ((2, 3), Qfb(203, 480, -182)), ((3, 0), Qfb(27, 614, -11)), ((3, 1), Qfb(-71, 528, 350)), ((3, 2), Qfb(-22, 596, 261)), ((3, 3), Qfb(-153, 538, 145)), ((4, 0), Qfb(-33, 596, 174)), ((4, 1), Qfb(91, 584, -102)), ((4, 2), Qfb(87, 448, -510)), ((4, 3), Qfb(435, 332, -154)), ((5, 0), Qfb(-99, 596, 58)), ((5, 1), Qfb(-110, 508, 273)), ((5, 2), Qfb(29, 564, -518)), ((5, 3), Qfb(-17, 606, 161)), ((6, 0), Qfb(-297, 398, 185)), ((6, 1), Qfb(-102, 572, 125)), ((6, 2), Qfb(87, 506, -351)), ((6, 3), Qfb(-195, 352, 326)), ((7, 0), Qfb(-170, 368, 357)), ((7, 1), Qfb(145, 448, -306)), ((7, 2), Qfb(-117, 430, 413)), ((7, 3), Qfb(-65, 612, 14)), ((8, 0), Qfb(119, 584, -78)), ((8, 1), Qfb(74, 564, -203)), ((8, 2), Qfb(-39, 586, 223)), ((8, 3), Qfb(-195, 482, 187)), ((9, 0), Qfb(234, 376, -253)), ((9, 1), Qfb(-231, 508, 130)), ((9, 2), Qfb(-13, 612, 70)), ((9, 3), Qfb(158, 540, -137)), ((10, 0), Qfb(78, 532, -305)), ((10, 1), Qfb(-77, 508, 390)), ((10, 2), Qfb(-39, 560, 414)), ((10, 3), Qfb(77, 570, -173)), ((11, 0), Qfb(253, 376, -234)), ((11, 1), Qfb(-65, 508, 462)), ((11, 2), Qfb(138, 544, -149)), ((11, 3), Qfb(-63, 556, 274)), ((12, 0), Qfb(-119, 606, 23)), ((12, 1), Qfb(-195, 248, 406)), ((12, 2), Qfb(46, 544, -447)), ((12, 3), Qfb(-21, 598, 245)), ((13, 0), Qfb(181, 346, -357)), ((13, 1), Qfb(-290, 132, 311)), ((13, 2), Qfb(138, 452, -315)), ((13, 3), Qfb(-7, 612, 130)), ((14, 0), Qfb(-185, 398, 297)), ((14, 1), Qfb(-371, 192, 230)), ((14, 2), Qfb(-105, 598, 49)), ((14, 3), Qfb(-21, 584, 442)), ((15, 0), Qfb(99, 592, -70)), ((15, 1), Qfb(17, 584, -546)), ((15, 2), Qfb(-35, 598, 147)), ((15, 3), Qfb(-63, 542, 335)), ((16, 0), Qfb(33, 592, -210)), ((16, 1), Qfb(51, 584, -182)), ((16, 2), Qfb(-105, 458, 401)), ((16, 3), Qfb(-189, 290, 389)), ((17, 0), Qfb(11, 614, -27)), ((17, 1), Qfb(151, 522, -175)), ((17, 2), Qfb(-315, 38, 299)), ((17, 3), Qfb(71, 608, -30)), ((18, 0), Qfb(33, 614, -9)), ((18, 1), Qfb(166, 504, -187)), ((18, 2), Qfb(-18, 592, 385)), ((18, 3), Qfb(-10, 612, 91)), ((19, 0), Qfb(99, 614, -3)), ((19, 1), Qfb(-177, 514, 161)), ((19, 2), Qfb(-6, 604, 557)), ((19, 3), Qfb(-30, 572, 425))] Group element : Euclid CF expansion a0+1/(a1+1/(...)): (0, 0) [0, 2, 14, 2, 614, 2, 14, 2, 614, 2, 14, 2, 614, 2, 14, 2, 614, 2, 14, 2, 614, 2, 14, 2] (0, 1) [0, 4, 17, 3, 20, 1, 7, 4, 17, 3, 20, 1, 7, 4, 17, 3, 20, 1, 7, 4, 17, 3, 20, 1] (0, 2) [-1, 1, 1, 1, 5, 5, 1, 2, 7, 1, 1, 7, 2, 1, 5, 5, 1, 2, 7, 1, 1, 7, 2, 1] (0, 3) [-1, 1, 2, 17, 4, 7, 1, 20, 3, 17, 4, 7, 1, 20, 3, 17, 4, 7, 1, 20, 3, 17, 4, 7] (1, 0) [0, 3, 2, 1, 2, 3, 122, 1, 2, 3, 2, 1, 2, 3, 122, 1, 2, 3, 2, 1, 2, 3, 122, 1] (1, 1) [-1, 1, 86, 1, 1, 1, 3, 1, 1, 2, 1, 4, 87, 1, 1, 1, 3, 1, 1, 2, 1, 4, 87, 1] (1, 2) [-1, 1, 1, 7, 1, 28, 2, 2, 9, 1, 2, 7, 1, 28, 2, 2, 9, 1, 2, 7, 1, 28, 2, 2] (1, 3) [-1, 1, 2, 1, 3, 3, 4, 40, 1, 3, 3, 1, 3, 3, 4, 40, 1, 3, 3, 1, 3, 3, 4, 40] (2, 0) [0, 9, 6, 1, 23, 1, 2, 1, 5, 9, 6, 1, 23, 1, 2, 1, 5, 9, 6, 1, 23, 1, 2, 1] (2, 1) [-1, 1, 16, 1, 1, 8, 2, 1, 1, 23, 17, 1, 1, 8, 2, 1, 1, 23, 17, 1, 1, 8, 2, 1] (2, 2) [-1, 6, 12, 2, 1, 1, 1, 6, 2, 3, 1, 5, 12, 2, 1, 1, 1, 6, 2, 3, 1, 5, 12, 2] (2, 3) [-1, 1, 5, 204, 1, 4, 1, 4, 6, 204, 1, 4, 1, 4, 6, 204, 1, 4, 1, 4, 6, 204, 1, 4] (3, 0) [0, 4, 1, 5, 4, 1, 2, 1, 28, 1, 1, 4, 1, 5, 4, 1, 2, 1, 28, 1, 1, 4, 1, 5] (3, 1) [0, 9, 2, 7, 3, 4, 2, 2, 3, 9, 2, 7, 3, 4, 2, 2, 3, 9, 2, 7, 3, 4, 2, 2] (3, 2) [-1, 1, 2, 2, 2, 13, 3, 1, 11, 3, 3, 2, 2, 13, 3, 1, 11, 3, 3, 2, 2, 13, 3, 1] (3, 3) [0, 3, 2, 40, 1, 1, 3, 3, 5, 3, 2, 40, 1, 1, 3, 3, 5, 3, 2, 40, 1, 1, 3, 3] (4, 0) [-1, 1, 4, 7, 1, 2, 5, 1, 1, 26, 5, 7, 1, 2, 5, 1, 1, 26, 5, 7, 1, 2, 5, 1] (4, 1) [0, 2, 3, 1, 3, 1, 4, 2, 6, 1, 3, 1, 1, 2, 3, 1, 3, 1, 4, 2, 6, 1, 3, 1] (4, 2) [0, 68, 3, 1, 1, 1, 1, 1, 18, 68, 3, 1, 1, 1, 1, 1, 18, 68, 3, 1, 1, 1, 1, 1] (4, 3) [-1, 1, 2, 7, 1, 10, 1, 1, 27, 2, 3, 7, 1, 10, 1, 1, 27, 2, 3, 7, 1, 10, 1, 1] (5, 0) [-1, 2, 1, 3, 2, 1, 7, 3, 2, 2, 1, 4, 1, 1, 1, 3, 2, 1, 7, 3, 2, 2, 1, 4] (5, 1) [0, 4, 1, 3, 1, 3, 35, 1, 10, 4, 1, 3, 1, 3, 35, 1, 10, 4, 1, 3, 1, 3, 35, 1] (5, 2) [-1, 13, 1, 5, 1, 9, 1, 1, 3, 4, 1, 12, 1, 5, 1, 9, 1, 1, 3, 4, 1, 12, 1, 5] (5, 3) [0, 1, 1, 1, 2, 1, 1, 9, 5, 2, 17, 1, 1, 1, 2, 1, 1, 9, 5, 2, 17, 1, 1, 1] (6, 0) [-1, 1, 14, 2, 1, 1, 12, 1, 3, 2, 1, 2, 15, 2, 1, 1, 12, 1, 3, 2, 1, 2, 15, 2] (6, 1) [-1, 4, 6, 1, 55, 22, 1, 3, 6, 1, 55, 22, 1, 3, 6, 1, 55, 22, 1, 3, 6, 1, 55, 22] (6, 2) [0, 1, 1, 33, 1, 1, 8, 1, 4, 3, 1, 1, 1, 33, 1, 1, 8, 1, 4, 3, 1, 1, 1, 33] (6, 3) [0, 1, 8, 1, 1, 5, 8, 1, 2, 1, 2, 1, 1, 1, 8, 1, 1, 5, 8, 1, 2, 1, 2, 1] (7, 0) [0, 2, 11, 1, 1, 1, 3, 14, 2, 1, 2, 2, 11, 1, 1, 1, 3, 14, 2, 1, 2, 2, 11, 1] (7, 1) [0, 19, 1, 2, 1, 1, 10, 1, 1, 1, 1, 3, 1, 19, 1, 2, 1, 1, 10, 1, 1, 1, 1, 3] (7, 2) [0, 6, 1, 2, 2, 1, 1, 6, 5, 1, 7, 6, 1, 2, 2, 1, 1, 6, 5, 1, 7, 6, 1, 2] (7, 3) [-1, 4, 4, 4, 1, 1, 1, 4, 1, 8, 1, 1, 1, 3, 4, 4, 1, 1, 1, 4, 1, 8, 1, 1] (8, 0) [-1, 1, 1, 3, 18, 2, 1, 6, 1, 11, 2, 3, 18, 2, 1, 6, 1, 11, 2, 3, 18, 2, 1, 6] (8, 1) [-1, 2, 2, 1, 1, 1, 1, 10, 1, 101, 1, 1, 2, 1, 1, 1, 1, 10, 1, 101, 1, 1, 2, 1] (8, 2) [0, 1, 5, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 4, 2, 1, 5, 1, 1, 2, 2, 1, 1, 2] (8, 3) [0, 4, 3, 1, 8, 47, 5, 4, 3, 1, 8, 47, 5, 4, 3, 1, 8, 47, 5, 4, 3, 1, 8, 47] (9, 0) [0, 1, 2, 1, 6, 1, 2, 61, 6, 1, 2, 1, 6, 1, 2, 61, 6, 1, 2, 1, 6, 1, 2, 61] (9, 1) [-1, 1, 7, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 20, 8, 1, 1, 1, 1, 2, 1, 1, 1, 1] (9, 2) [0, 2, 1, 13, 1, 15, 1, 2, 4, 1, 2, 2, 1, 13, 1, 15, 1, 2, 4, 1, 2, 2, 1, 13] (9, 3) [0, 1, 4, 1, 43, 9, 2, 3, 1, 1, 4, 1, 43, 9, 2, 3, 1, 1, 4, 1, 43, 9, 2, 3] (10, 0) [-1, 7, 1, 2, 1, 306, 1, 2, 1, 6, 1, 2, 1, 306, 1, 2, 1, 6, 1, 2, 1, 306, 1, 2] (10, 1) [-1, 2, 1, 8, 6, 10, 2, 3, 1, 1, 1, 1, 1, 8, 6, 10, 2, 3, 1, 1, 1, 1, 1, 8] (10, 2) [0, 1, 2, 2, 1, 1, 2, 2, 1, 15, 15, 1, 2, 2, 1, 1, 2, 2, 1, 15, 15, 1, 2, 2] (10, 3) [0, 6, 8, 1, 1, 1, 1, 1, 3, 2, 10, 6, 8, 1, 1, 1, 1, 1, 3, 2, 10, 6, 8, 1] (11, 0) [0, 1, 6, 61, 2, 1, 6, 1, 2, 1, 6, 61, 2, 1, 6, 1, 2, 1, 6, 61, 2, 1, 6, 1] (11, 1) [-1, 5, 1, 1, 3, 2, 9, 43, 1, 4, 1, 1, 3, 2, 9, 43, 1, 4, 1, 1, 3, 2, 9, 43] (11, 2) [0, 1, 2, 2, 1, 4, 2, 1, 15, 1, 13, 1, 2, 2, 1, 4, 2, 1, 15, 1, 13, 1, 2, 2] (11, 3) [-1, 1, 19, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 8, 20, 2, 1, 1, 1, 1, 2, 1, 1, 1] (12, 0) [0, 3, 2, 11, 1, 6, 1, 2, 18, 3, 2, 11, 1, 6, 1, 2, 18, 3, 2, 11, 1, 6, 1, 2] (12, 1) [-1, 1, 3, 5, 47, 8, 1, 3, 4, 5, 47, 8, 1, 3, 4, 5, 47, 8, 1, 3, 4, 5, 47, 8] (12, 2) [-1, 1, 1, 1, 1, 5, 1, 2, 4, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 5, 1, 2, 4, 1] (12, 3) [-1, 2, 101, 1, 10, 1, 1, 1, 1, 2, 1, 1, 101, 1, 10, 1, 1, 1, 1, 2, 1, 1, 101, 1] (13, 0) [0, 1, 11, 2, 2, 1, 2, 14, 3, 1, 1, 1, 11, 2, 2, 1, 2, 14, 3, 1, 1, 1, 11, 2] (13, 1) [-1, 1, 2, 1, 1, 1, 8, 1, 4, 1, 1, 1, 4, 4, 3, 1, 1, 1, 8, 1, 4, 1, 1, 1] (13, 2) [-1, 1, 1, 1, 6, 7, 1, 5, 6, 1, 1, 2, 2, 1, 6, 7, 1, 5, 6, 1, 1, 2, 2, 1] (13, 3) [-1, 1, 18, 1, 3, 1, 1, 1, 1, 10, 1, 1, 2, 1, 19, 1, 3, 1, 1, 1, 1, 10, 1, 1] (14, 0) [0, 2, 15, 2, 1, 2, 3, 1, 12, 1, 1, 2, 15, 2, 1, 2, 3, 1, 12, 1, 1, 2, 15, 2] (14, 1) [0, 8, 1, 1, 1, 2, 1, 2, 1, 8, 5, 1, 1, 8, 1, 1, 1, 2, 1, 2, 1, 8, 5, 1] (14, 2) [0, 1, 1, 1, 3, 4, 1, 8, 1, 1, 33, 1, 1, 1, 3, 4, 1, 8, 1, 1, 33, 1, 1, 1] (14, 3) [0, 1, 22, 55, 1, 6, 3, 1, 22, 55, 1, 6, 3, 1, 22, 55, 1, 6, 3, 1, 22, 55, 1, 6] (15, 0) [0, 1, 2, 3, 1, 1, 1, 4, 1, 2, 2, 3, 7, 1, 2, 3, 1, 1, 1, 4, 1, 2, 2, 3] (15, 1) [0, 1, 1, 2, 1, 1, 1, 17, 2, 5, 9, 1, 1, 2, 1, 1, 1, 17, 2, 5, 9, 1, 1, 2] (15, 2) [0, 1, 12, 1, 4, 3, 1, 1, 9, 1, 5, 1, 12, 1, 4, 3, 1, 1, 9, 1, 5, 1, 12, 1] (15, 3) [0, 1, 3, 1, 4, 10, 1, 35, 3, 1, 3, 1, 4, 10, 1, 35, 3, 1, 3, 1, 4, 10, 1, 35] (16, 0) [-1, 1, 4, 26, 1, 1, 5, 2, 1, 7, 5, 26, 1, 1, 5, 2, 1, 7, 5, 26, 1, 1, 5, 2] (16, 1) [0, 3, 2, 27, 1, 1, 10, 1, 7, 3, 2, 27, 1, 1, 10, 1, 7, 3, 2, 27, 1, 1, 10, 1] (16, 2) [0, 18, 1, 1, 1, 1, 1, 3, 68, 18, 1, 1, 1, 1, 1, 3, 68, 18, 1, 1, 1, 1, 1, 3] (16, 3) [-1, 4, 2, 1, 1, 3, 1, 6, 2, 4, 1, 3, 1, 3, 2, 1, 1, 3, 1, 6, 2, 4, 1, 3] (17, 0) [0, 5, 1, 4, 1, 1, 28, 1, 2, 1, 4, 5, 1, 4, 1, 1, 28, 1, 2, 1, 4, 5, 1, 4] (17, 1) [0, 2, 3, 5, 3, 3, 1, 1, 40, 2, 3, 5, 3, 3, 1, 1, 40, 2, 3, 5, 3, 3, 1, 1] (17, 2) [0, 2, 2, 3, 3, 11, 1, 3, 13, 2, 2, 3, 3, 11, 1, 3, 13, 2, 2, 3, 3, 11, 1, 3] (17, 3) [0, 2, 9, 3, 2, 2, 4, 3, 7, 2, 9, 3, 2, 2, 4, 3, 7, 2, 9, 3, 2, 2, 4, 3] (18, 0) [-1, 1, 4, 1, 2, 1, 23, 1, 6, 9, 5, 1, 2, 1, 23, 1, 6, 9, 5, 1, 2, 1, 23, 1] (18, 1) [-1, 1, 3, 1, 4, 1, 204, 6, 4, 1, 4, 1, 204, 6, 4, 1, 4, 1, 204, 6, 4, 1, 4, 1] (18, 2) [0, 1, 3, 2, 6, 1, 1, 1, 2, 12, 5, 1, 3, 2, 6, 1, 1, 1, 2, 12, 5, 1, 3, 2] (18, 3) [-1, 1, 22, 1, 1, 2, 8, 1, 1, 17, 23, 1, 1, 2, 8, 1, 1, 17, 23, 1, 1, 2, 8, 1] (19, 0) [0, 1, 2, 3, 2, 1, 122, 3, 2, 1, 2, 3, 2, 1, 122, 3, 2, 1, 2, 3, 2, 1, 122, 3] (19, 1) [0, 3, 1, 3, 3, 1, 40, 4, 3, 3, 1, 3, 3, 1, 40, 4, 3, 3, 1, 3, 3, 1, 40, 4] (19, 2) [0, 1, 7, 2, 1, 9, 2, 2, 28, 1, 7, 2, 1, 9, 2, 2, 28, 1, 7, 2, 1, 9, 2, 2] (19, 3) [-1, 1, 3, 1, 2, 1, 1, 3, 1, 1, 1, 87, 4, 1, 2, 1, 1, 3, 1, 1, 1, 87, 4, 1]