# label = 2.2.5.1-81.1-a
# Base field F = Number Field in a with defining polynomial x^2 - x - 1
# Quaternion algebra given by i^2 = -1, j^2 = -1
# Order with basis over the integers given by [1, 3*i, 1/2*a + 1/2 + (1/2*a + 1)*i + 3/2*j, (-1/2*a - 1)*i + (1/2*a + 1/2)*j + 1/2*k]

# Nmax = 10000

[(1, [3*i, 1/2*a + 1/2 + (1/2*a + 1)*i + 3/2*j, (-1/2*a - 1)*i + (1/2*a + 1/2)*j + 1/2*k]), (-1, [(9*a - 6)*i, 1/2*a + 1/2 + (1/2*a + 1)*i + 3/2*j, -1/2*a + (-351/11*a + 117/11)*i + (-7/11*a + 1/22)*j + (-3/22*a + 1/22)*k])]
[((3,), 29*a + 59 + (39/2*a + 113/2)*i + 159/2*j + (-3/2*a)*k)]

# map: (a |-> -0.62) -> -1, (a |-> 1.62) -> -1, Fractional ideal (3) -> -1
[a + 5, 15/2*a - 1 + (143/2*a + 155)*i + (-155/2*a - 77)*j + (-1/2*a - 75)*k, [(5, [(a - 3, 3, 1.575)]), (41, [(a - 7, -3, 0.5500), (-a - 6, -3, 0.5500)]), (149, [(4*a - 15, -3, 0.2885), (-4*a - 11, -3, 0.2885)]), (176, [(4*a - 16, -6, 1.062), (-4*a - 12, -6, 1.062)]), (209, [(a - 15, -6, 0.9744), (-a - 14, -6, 0.9744)]), (269, [(4*a - 19, -3, 0.2147), (-4*a - 15, -3, 0.2147)]), (281, [(7*a - 22, 9, 1.891), (-7*a - 15, 9, 1.891)]), (320, [(8*a - 24, 12, 3.150)]), (341, [(a - 19, -6, 0.7629), (-a - 18, -6, 0.7629)]), (389, [(5*a - 23, 15, 4.464), (-5*a - 18, 15, 4.464)]), (449, [(8*a - 27, 9, 1.496), (-8*a - 19, 9, 1.496)]), (464, [(4*a - 24, 12, 2.616), (-4*a - 20, 12, 2.616)]), (569, [(5*a - 27, -9, 1.329), (-5*a - 22, -9, 1.329)]), (641, [(7*a - 30, 3, 0.1391), (-7*a - 23, 3, 0.1391)]), (701, [(a - 27, 9, 1.197), (-a - 26, 9, 1.197)]), (704, [(8*a - 32, -6, 0.5309), (-8*a - 24, -6, 0.5309)]), (821, [(4*a - 31, -9, 1.106), (-4*a - 27, -9, 1.106)]), (845, [(-13*a - 26, -6, 0.4846)]), (869, [(7*a - 34, -6, 0.4779), (-7*a - 27, -6, 0.4779)]), (881, [(8*a - 35, 3, 0.1187), (-8*a - 27, 3, 0.1187)]), (905, [(11*a - 38, 6, 0.4683), (-11*a - 27, 6, 0.4683)]), (929, [(a - 31, 9, 1.040), (-a - 30, 9, 1.040)]), (944, [(8*a - 36, -6, 0.4585), (-8*a - 28, -6, 0.4585)]), (1121, [(-13*a - 30, -18, 3.787), (13*a - 43, -18, 3.787)]), (1136, [(4*a - 36, -12, 1.672), (-4*a - 32, -12, 1.672)]), (1145, [(8*a - 39, 0, 0), (-8*a - 31, 0, 0)]), (1181, [(11*a - 42, -9, 0.9223), (-11*a - 31, -9, 0.9223)]), (1301, [(5*a - 39, 3, 0.09764), (-5*a - 34, 3, 0.09764)]), (1349, [(4*a - 39, -6, 0.3835), (-4*a - 35, -6, 0.3835)]), (1421, [(7*a - 42, 6, 0.3737), (-7*a - 35, 6, 0.3737)]), (1424, [(4*a - 40, 6, 0.3733), (-4*a - 36, 6, 0.3733)]), (1445, [(-17*a - 34, 12, 1.482)]), (1481, [(-a - 38, 15, 2.288), (a - 39, 15, 2.288)]), (1520, [(8*a - 44, -12, 1.445), (-8*a - 36, -12, 1.445)]), (1529, [(16*a - 51, -12, 1.441), (-16*a - 35, -12, 1.441)]), (1616, [(16*a - 52, 0, 0), (-16*a - 36, 0, 0)]), (1661, [(4*a - 43, 24, 5.530), (-4*a - 39, 24, 5.530)]), (1745, [(7*a - 46, -18, 3.035), (-7*a - 39, -18, 3.035)]), (1769, [(8*a - 47, 6, 0.3349), (-8*a - 39, 6, 0.3349), (13*a - 51, 0, 0), (-13*a - 38, 0, 0)]), (1829, [(11*a - 50, -12, 1.318), (-11*a - 39, -12, 1.318)]), (1856, [(8*a - 48, 0, 0), (-8*a - 40, 0, 0)]), (1889, [(16*a - 55, 3, 0.08103), (-16*a - 39, 3, 0.08103)]), (1901, [(-19*a - 39, 9, 0.7270), (19*a - 58, 9, 0.7270)]), (1949, [(5*a - 47, 9, 0.7180), (-5*a - 42, 9, 0.7180)]), (2096, [(4*a - 48, 18, 2.769), (-4*a - 44, 18, 2.769)]), (2129, [(8*a - 51, -15, 1.908), (-8*a - 43, -15, 1.908)]), (2141, [(-13*a - 42, -15, 1.903), (13*a - 55, -15, 1.903)]), (2189, [(-17*a - 42, -12, 1.204), (17*a - 59, -12, 1.204)]), (2201, [(11*a - 54, 6, 0.3003), (-11*a - 43, 6, 0.3003)]), (2309, [(20*a - 63, 9, 0.6596), (-20*a - 43, 9, 0.6596)]), (2321, [(5*a - 51, 12, 1.170), (-5*a - 46, 12, 1.170)]), (2381, [(4*a - 51, -21, 3.537), (-4*a - 47, -21, 3.537)]), (2480, [(4*a - 52, -12, 1.132), (-4*a - 48, -12, 1.132)]), (2489, [(7*a - 54, -12, 1.129), (-7*a - 47, -12, 1.129)]), (2549, [(-a - 50, 9, 0.6278), (a - 51, 9, 0.6278)]), (2609, [(-17*a - 46, 3, 0.06895), (17*a - 63, 3, 0.06895)]), (2624, [(8*a - 56, 6, 0.2750), (-8*a - 48, 6, 0.2750)]), (2705, [(16*a - 63, -6, 0.2709), (-16*a - 47, -6, 0.2709)]), (2741, [(-19*a - 47, -15, 1.682), (19*a - 66, -15, 1.682)]), (2789, [(4*a - 55, -9, 0.6002), (-4*a - 51, -9, 0.6002)]), (2864, [(20*a - 68, -18, 2.369), (-20*a - 48, -18, 2.369)]), (2909, [(7*a - 58, 21, 3.200), (-7*a - 51, 21, 3.200)]), (2945, [(8*a - 59, 12, 1.038), (-8*a - 51, 12, 1.038)]), (2969, [(-a - 54, -3, 0.06463), (a - 55, -3, 0.06463)]), (2981, [(-13*a - 50, -12, 1.032), (13*a - 63, -12, 1.032)]), (3041, [(11*a - 62, -15, 1.597), (-11*a - 51, -15, 1.597)]), (3056, [(8*a - 60, 12, 1.019), (-8*a - 52, 12, 1.019)]), (3161, [(16*a - 67, 12, 1.002), (-16*a - 51, 12, 1.002), (5*a - 59, 0, 0), (-5*a - 54, 0, 0)]), (3209, [(-19*a - 51, -3, 0.06217), (19*a - 70, -3, 0.06217)]), (3221, [(20*a - 71, 15, 1.551), (-20*a - 51, 15, 1.551)]), (3245, [(-23*a - 51, -12, 0.9892), (23*a - 74, -12, 0.9892)]), (3344, [(20*a - 72, -12, 0.9744), (-20*a - 52, -12, 0.9744)]), (3401, [(8*a - 63, 6, 0.2416), (-8*a - 55, 6, 0.2416)]), (3449, [(-13*a - 54, 15, 1.499), (13*a - 67, 15, 1.499)]), (3509, [(11*a - 66, 24, 3.805), (-11*a - 55, 24, 3.805)]), (3545, [(17*a - 71, 0, 0), (-17*a - 54, 0, 0)]), (3629, [(5*a - 63, -12, 0.9354), (-5*a - 58, -12, 0.9354)]), (3641, [(25*a - 79, 6, 0.2335), (-25*a - 54, 6, 0.2335)]), (3701, [(4*a - 63, 21, 2.837), (-4*a - 59, 21, 2.837)]), (3761, [(-23*a - 55, -15, 1.436), (23*a - 78, -15, 1.436)]), (3776, [(16*a - 72, 6, 0.2292), (-16*a - 56, 6, 0.2292)]), (3824, [(4*a - 64, 24, 3.645), (-4*a - 60, 24, 3.645)]), (3845, [(7*a - 66, 18, 2.045), (-7*a - 59, 18, 2.045)]), (3905, [(-a - 62, 12, 0.9017), (a - 63, 12, 0.9017)]), (3920, [(-28*a - 56, 24, 3.600)]), (4016, [(8*a - 68, -18, 2.001), (-8*a - 60, -18, 2.001)]), (4061, [(-17*a - 58, -18, 1.990), (17*a - 75, -18, 1.990)]), (4169, [(16*a - 75, 12, 0.8727), (-16*a - 59, 12, 0.8727)]), (4205, [(29*a - 87, 6, 0.2172)]), (4241, [(-19*a - 59, 15, 1.352), (19*a - 78, 15, 1.352)]), (4349, [(-28*a - 59, 3, 0.05340), (28*a - 87, 3, 0.05340)]), (4361, [(7*a - 70, -12, 0.8533), (-7*a - 63, -12, 0.8533)]), (4409, [(8*a - 71, 3, 0.05304), (-8*a - 63, 3, 0.05304)]), (4421, [(-a - 66, 15, 1.324), (a - 67, 15, 1.324)]), (4481, [(-13*a - 62, -15, 1.315), (13*a - 75, -15, 1.315)]), (4541, [(11*a - 74, 12, 0.8362), (-11*a - 63, 12, 0.8362)]), (4544, [(8*a - 72, -24, 3.344), (-8*a - 64, -24, 3.344)]), (4661, [(5*a - 71, 12, 0.8254), (-5*a - 66, 12, 0.8254)]), (4721, [(16*a - 79, -3, 0.05126), (-16*a - 63, -3, 0.05126)]), (4769, [(25*a - 87, 12, 0.8160), (-25*a - 62, 12, 0.8160)]), (4829, [(20*a - 83, -12, 0.8109), (-20*a - 63, -12, 0.8109)]), (4880, [(4*a - 72, 12, 0.8066), (-4*a - 68, 12, 0.8066)]), (4889, [(-23*a - 63, -15, 1.259), (23*a - 86, -15, 1.259)]), (4949, [(28*a - 91, 0, 0), (-28*a - 63, 0, 0)]), (4976, [(20*a - 84, 12, 0.7988), (-20*a - 64, 12, 0.7988)]), (5045, [(13*a - 79, 0, 0), (-13*a - 66, 0, 0)]), (5105, [(11*a - 78, -24, 3.155), (-11*a - 67, -24, 3.155)]), (5189, [(-17*a - 66, -15, 1.222), (17*a - 83, -15, 1.222)]), (5309, [(4*a - 75, 3, 0.04833), (-4*a - 71, 3, 0.04833)]), (5381, [(25*a - 91, -3, 0.04801), (-25*a - 66, -3, 0.04801)]), (5429, [(29*a - 95, 6, 0.1912), (-29*a - 66, 6, 0.1912), (20*a - 87, 0, 0), (-20*a - 67, 0, 0)]), (5456, [(16*a - 84, 12, 0.7629), (-16*a - 68, 12, 0.7629)]), (5489, [(7*a - 78, 12, 0.7606), (-7*a - 71, 12, 0.7606)]), (5501, [(-23*a - 67, 3, 0.04748), (23*a - 90, 3, 0.04748)]), (5549, [(-a - 74, -12, 0.7564), (a - 75, -12, 0.7564)]), (5609, [(-32*a - 67, 6, 0.1881), (32*a - 99, 6, 0.1881)]), (5696, [(8*a - 80, -6, 0.1867), (-8*a - 72, -6, 0.1867)]), (5744, [(-28*a - 68, -24, 2.974), (28*a - 96, -24, 2.974)]), (5801, [(-17*a - 70, 3, 0.04624), (17*a - 87, 3, 0.04624)]), (5909, [(4*a - 79, -18, 1.649), (-4*a - 75, -18, 1.649)]), (5921, [(16*a - 87, 0, 0), (-16*a - 71, 0, 0)]), (6029, [(-19*a - 71, -15, 1.134), (19*a - 90, -15, 1.134)]), (6080, [(16*a - 88, 12, 0.7227), (-16*a - 72, 12, 0.7227)]), (6089, [(29*a - 99, 15, 1.128), (-29*a - 70, 15, 1.128)]), (6101, [(7*a - 82, -27, 3.652), (-7*a - 75, -27, 3.652)]), (6161, [(-a - 78, 24, 2.872), (a - 79, 24, 2.872), (8*a - 83, 6, 0.1795), (-8*a - 75, 6, 0.1795)]), (6245, [(28*a - 99, 0, 0), (-28*a - 71, 0, 0)]), (6269, [(-13*a - 74, 33, 5.382), (13*a - 87, 33, 5.382)]), (6281, [(31*a - 102, -6, 0.1778), (-31*a - 71, -6, 0.1778)]), (6320, [(8*a - 84, 12, 0.7088), (-8*a - 76, 12, 0.7088)]), (6329, [(11*a - 86, -3, 0.04427), (-11*a - 75, -3, 0.04427)]), (6416, [(-28*a - 72, -18, 1.583), (28*a - 100, -18, 1.583)]), (6449, [(5*a - 83, 3, 0.04385), (-5*a - 78, 3, 0.04385)]), (6464, [(-32*a - 72, 36, 6.308), (32*a - 104, 36, 6.308)]), (6569, [(16*a - 91, 9, 0.3911), (-16*a - 75, 9, 0.3911)]), (6689, [(-19*a - 75, -3, 0.04306), (19*a - 94, -3, 0.04306)]), (6701, [(25*a - 99, -9, 0.3872), (-25*a - 74, -9, 0.3872)]), (6704, [(4*a - 84, -18, 1.548), (-4*a - 80, -18, 1.548)]), (6809, [(8*a - 87, -18, 1.536), (-8*a - 79, -18, 1.536)]), (6821, [(-23*a - 75, 6, 0.1706), (23*a - 98, 6, 0.1706)]), (6845, [(37*a - 111, 6, 0.1703)]), (6896, [(20*a - 96, 36, 6.107), (-20*a - 76, 36, 6.107)]), (6929, [(-13*a - 78, 6, 0.1692), (13*a - 91, 6, 0.1692)]), (6941, [(-28*a - 75, 12, 0.6764), (28*a - 103, 12, 0.6764)]), (6989, [(11*a - 90, -18, 1.517), (-11*a - 79, -18, 1.517), (31*a - 106, 18, 1.517), (-31*a - 75, 18, 1.517)]), (7001, [(-32*a - 75, -15, 1.052), (32*a - 107, -15, 1.052)]), (7109, [(5*a - 87, -15, 1.044), (-5*a - 82, -15, 1.044)]), (7121, [(-17*a - 78, 15, 1.043), (17*a - 95, 15, 1.043)]), (7205, [(4*a - 87, -24, 2.655), (-4*a - 83, -24, 2.655)]), (7376, [(4*a - 88, -12, 0.6561), (-4*a - 84, -12, 0.6561)]), (7409, [(25*a - 103, -30, 4.091), (-25*a - 78, -30, 4.091)]), (7421, [(7*a - 90, 30, 4.088), (-7*a - 83, 30, 4.088), (20*a - 99, -12, 0.6541), (-20*a - 79, -12, 0.6541)]), (7481, [(-a - 86, -3, 0.04072), (a - 87, -3, 0.04072)]), (7505, [(29*a - 107, -12, 0.6504), (-29*a - 78, -12, 0.6504)]), (7529, [(-23*a - 79, 21, 1.989), (23*a - 102, 21, 1.989)]), (7601, [(37*a - 115, 24, 2.585), (-37*a - 78, 24, 2.585)]), (7664, [(8*a - 92, 12, 0.6437), (-8*a - 84, 12, 0.6437)]), (7745, [(-32*a - 79, 6, 0.1601), (32*a - 111, 6, 0.1601)]), (7781, [(35*a - 114, 0, 0), (-35*a - 79, 0, 0)]), (7829, [(-17*a - 82, -3, 0.03980), (17*a - 99, -3, 0.03980)]), (7856, [(-28*a - 80, 6, 0.1589), (28*a - 108, 6, 0.1589)]), (7901, [(4*a - 91, -9, 0.3566), (-4*a - 87, -9, 0.3566)]), (7961, [(16*a - 99, -12, 0.6315), (-16*a - 83, -12, 0.6315)]), (8105, [(-19*a - 83, -6, 0.1565), (19*a - 102, -6, 0.1565)]), (8129, [(7*a - 94, 0, 0), (-7*a - 87, 0, 0)]), (8144, [(16*a - 100, 0, 0), (-16*a - 84, 0, 0)]), (8189, [(-a - 90, 12, 0.6227), (a - 91, 12, 0.6227)]), (8201, [(8*a - 95, -12, 0.6222), (-8*a - 87, -12, 0.6222)]), (8261, [(29*a - 111, 0, 0), (-29*a - 82, 0, 0)]), (8336, [(20*a - 104, 6, 0.1543), (-20*a - 84, 6, 0.1543)]), (8345, [(-13*a - 86, -24, 2.467), (13*a - 99, -24, 2.467)]), (8384, [(8*a - 96, 6, 0.1539), (-8*a - 88, 6, 0.1539)]), (8405, [(-41*a - 82, 30, 3.841)]), (8429, [(-28*a - 83, 9, 0.3452), (28*a - 111, 9, 0.3452)]), (8501, [(31*a - 114, -3, 0.03820), (-31*a - 83, -3, 0.03820)]), (8609, [(-40*a - 83, -15, 0.9489), (40*a - 123, -15, 0.9489)]), (8624, [(-28*a - 84, 12, 0.6068), (28*a - 112, 12, 0.6068)]), (8705, [(16*a - 103, 24, 2.416), (-16*a - 87, 24, 2.416)]), (8720, [(-32*a - 84, 12, 0.6034), (32*a - 116, 12, 0.6034)]), (8816, [(4*a - 96, 12, 0.6001), (-4*a - 92, 12, 0.6001), (-40*a - 84, -12, 0.6001), (40*a - 124, -12, 0.6001)]), (8861, [(-19*a - 87, -3, 0.03741), (19*a - 106, -3, 0.03741)]), (8909, [(20*a - 107, -18, 1.343), (-20*a - 87, -18, 1.343)]), (8921, [(25*a - 111, -18, 1.342), (-25*a - 86, -18, 1.342)]), (8945, [(8*a - 99, -6, 0.1489), (-8*a - 91, -6, 0.1489)]), (9041, [(-23*a - 87, -3, 0.03704), (23*a - 110, -3, 0.03704)]), (9101, [(-13*a - 90, -6, 0.1477), (13*a - 103, -6, 0.1477)]), (9161, [(11*a - 102, -9, 0.3312), (-11*a - 91, -9, 0.3312)]), (9209, [(37*a - 123, 9, 0.3303), (-37*a - 86, 9, 0.3303)]), (9221, [(-28*a - 87, -15, 0.9169), (28*a - 115, -15, 0.9169)]), (9281, [(5*a - 99, -9, 0.3290), (-5*a - 94, -9, 0.3290)]), (9305, [(31*a - 118, 0, 0), (-31*a - 87, 0, 0)]), (9329, [(32*a - 119, 0, 0), (-32*a - 87, 0, 0)]), (9341, [(-17*a - 90, 9, 0.3280), (17*a - 107, 9, 0.3280)]), (9389, [(35*a - 122, 30, 3.635), (-35*a - 87, 30, 3.635), (4*a - 99, 0, 0), (-4*a - 95, 0, 0)]), (9449, [(-40*a - 87, 6, 0.1449), (40*a - 127, 6, 0.1449)]), (9461, [(-43*a - 87, -33, 4.381), (43*a - 130, -33, 4.381)]), (9536, [(-32*a - 88, -12, 0.5770), (32*a - 120, -12, 0.5770)]), (9584, [(4*a - 100, 0, 0), (-4*a - 96, 0, 0)]), (9641, [(7*a - 102, -24, 2.296), (-7*a - 95, -24, 2.296)]), (9680, [(-44*a - 88, -24, 2.291)]), (9701, [(20*a - 111, 12, 0.5721), (-20*a - 91, 12, 0.5721), (a - 99, 0, 0), (-a - 98, 0, 0)]), (9845, [(-23*a - 91, 12, 0.5679), (23*a - 114, 12, 0.5679)]), (9869, [(29*a - 119, -18, 1.276), (-29*a - 90, -18, 1.276)]), (9920, [(8*a - 104, -36, 5.092), (-8*a - 96, -36, 5.092)])]]

# map: (a |-> -0.62) -> -1, (a |-> 1.62) -> -1, Fractional ideal (3) -> 1
[1, None, [(16, [(-4, -1, 1.761)]), (49, [(-7, 1, 1.006)]), (61, [(3*a - 10, 1, 0.9019), (-3*a - 7, 1, 0.9019)]), (64, [(-8, 1, 0.8805)]), (109, [(a - 11, -2, 2.699), (-a - 10, -2, 2.699)]), (121, [(-11, 2, 2.561)]), (145, [(3*a - 14, -1, 0.5850), (-3*a - 11, -1, 0.5850)]), (241, [(-5*a - 14, 0, 0), (5*a - 19, 0, 0)]), (304, [(4*a - 20, 2, 1.616), (-4*a - 16, 2, 1.616)]), (361, [(-19, -2, 1.483)]), (409, [(-3*a - 19, 0, 0), (3*a - 22, 0, 0)]), (421, [(-4*a - 19, 0, 0), (4*a - 23, 0, 0)]), (445, [(7*a - 26, -1, 0.3339), (-7*a - 19, -1, 0.3339)]), (496, [(8*a - 28, -2, 1.265), (-8*a - 20, -2, 1.265)]), (505, [(a - 23, 1, 0.3135), (-a - 22, 1, 0.3135)]), (529, [(-23, -3, 2.756)]), (589, [(3*a - 26, 2, 1.161), (-3*a - 23, 2, 1.161)]), (601, [(9*a - 31, -1, 0.2873), (-9*a - 22, -1, 0.2873)]), (649, [(8*a - 31, -2, 1.106), (-8*a - 23, -2, 1.106)]), (661, [(11*a - 34, 3, 2.466), (-11*a - 23, 3, 2.466)]), (781, [(5*a - 31, -2, 1.008), (-5*a - 26, -2, 1.008)]), (829, [(-9*a - 26, 0, 0), (9*a - 35, 0, 0)]), (880, [(4*a - 32, -2, 0.9498), (-4*a - 28, -2, 0.9498)]), (961, [(-31, 0, 0)]), (1045, [(3*a - 34, 4, 3.486), (-3*a - 31, 4, 3.486)]), (1069, [(4*a - 35, -3, 1.939), (-4*a - 31, -3, 1.939)]), (1129, [(7*a - 38, 2, 0.8386), (-7*a - 31, 2, 0.8386)]), (1189, [(a - 35, -1, 0.2043), (-a - 34, -1, 0.2043), (12*a - 43, 1, 0.2043), (-12*a - 31, 1, 0.2043)]), (1201, [(-15*a - 31, 1, 0.2033), (15*a - 46, 1, 0.2033)]), (1216, [(-8*a - 32, 0, 0), (8*a - 40, 0, 0)]), (1264, [(12*a - 44, 4, 3.170), (-12*a - 32, 4, 3.170)]), (1321, [(3*a - 38, 1, 0.1938), (-3*a - 35, 1, 0.1938)]), (1381, [(9*a - 43, -4, 3.033), (-9*a - 34, -4, 3.033)]), (1429, [(-13*a - 34, 3, 1.677), (13*a - 47, 3, 1.677)]), (1441, [(8*a - 43, 2, 0.7422), (-8*a - 35, 2, 0.7422)]), (1489, [(11*a - 46, -2, 0.7302), (-11*a - 35, -2, 0.7302)]), (1501, [(-12*a - 35, 0, 0), (12*a - 47, 0, 0)]), (1609, [(5*a - 43, 2, 0.7024), (-5*a - 38, 2, 0.7024)]), (1705, [(9*a - 47, 2, 0.6824), (-9*a - 38, 2, 0.6824)]), (1801, [(-17*a - 38, -3, 1.494), (17*a - 55, -3, 1.494)]), (1849, [(-43, -5, 4.095)]), (1969, [(-3*a - 43, 0, 0), (3*a - 46, 0, 0)]), (1984, [(16*a - 56, -2, 0.6326), (-16*a - 40, -2, 0.6326)]), (2005, [(4*a - 47, 1, 0.1573), (-4*a - 43, 1, 0.1573)]), (2101, [(-7*a - 43, 0, 0), (7*a - 50, 0, 0)]), (2161, [(-a - 46, 2, 0.6061), (a - 47, 2, 0.6061)]), (2209, [(-47, -1, 0.1499)]), (2221, [(12*a - 55, 4, 2.391), (-12*a - 43, 4, 2.391)]), (2224, [(-8*a - 44, 0, 0), (8*a - 52, 0, 0)]), (2269, [(-15*a - 43, 3, 1.331), (15*a - 58, 3, 1.331)]), (2281, [(16*a - 59, 2, 0.5900), (-16*a - 43, 2, 0.5900)]), (2305, [(-19*a - 43, 5, 3.668), (19*a - 62, 5, 3.668)]), (2341, [(3*a - 50, -4, 2.329), (-3*a - 47, -4, 2.329)]), (2416, [(20*a - 64, -4, 2.293), (-20*a - 44, -4, 2.293)]), (2449, [(9*a - 55, 2, 0.5694), (-9*a - 46, 2, 0.5694)]), (2521, [(8*a - 55, 5, 3.507), (-8*a - 47, 5, 3.507)]), (2545, [(-13*a - 46, -5, 3.491), (13*a - 59, -5, 3.491)]), (2605, [(11*a - 58, -5, 3.450), (-11*a - 47, -5, 3.450)]), (2629, [(-12*a - 47, 0, 0), (12*a - 59, 0, 0)]), (2641, [(-21*a - 46, -2, 0.5483), (21*a - 67, -2, 0.5483)]), (2689, [(-15*a - 47, 0, 0), (15*a - 62, 0, 0)]), (2704, [(-52, -4, 2.167)]), (2749, [(20*a - 67, -1, 0.1343), (-20*a - 47, -1, 0.1343)]), (2761, [(-23*a - 47, 0, 0), (23*a - 70, 0, 0)]), (2869, [(9*a - 59, -2, 0.5260), (-9*a - 50, -2, 0.5260)]), (2896, [(4*a - 56, 4, 2.094), (-4*a - 52, 4, 2.094)]), (3061, [(-17*a - 50, 3, 1.146), (17*a - 67, 3, 1.146)]), (3109, [(-21*a - 50, 5, 3.158), (21*a - 71, 5, 3.158)]), (3136, [(-56, 2, 0.5031)]), (3181, [(3*a - 58, -2, 0.4996), (-3*a - 55, -2, 0.4996)]), (3184, [(12*a - 64, -2, 0.4993), (-12*a - 52, -2, 0.4993)]), (3229, [(4*a - 59, -4, 1.983), (-4*a - 55, -4, 1.983)]), (3280, [(16*a - 68, -4, 1.968), (-16*a - 52, -4, 1.968)]), (3361, [(7*a - 62, -2, 0.4860), (-7*a - 55, -2, 0.4860)]), (3376, [(24*a - 76, 4, 1.940), (-24*a - 52, 4, 1.940)]), (3421, [(-a - 58, 2, 0.4817), (a - 59, 2, 0.4817)]), (3481, [(-59, 0, 0)]), (3520, [(8*a - 64, 2, 0.4749), (-8*a - 56, 2, 0.4749)]), (3541, [(12*a - 67, 1, 0.1184), (-12*a - 55, 1, 0.1184)]), (3649, [(3*a - 62, -1, 0.1166), (-3*a - 59, -1, 0.1166), (16*a - 71, 1, 0.1166), (-16*a - 55, 1, 0.1166)]), (3664, [(-12*a - 56, 0, 0), (12*a - 68, 0, 0)]), (3709, [(-19*a - 55, 5, 2.892), (19*a - 74, 5, 2.892)]), (3769, [(24*a - 79, -3, 1.033), (-24*a - 55, -3, 1.033)]), (3781, [(27*a - 82, -4, 1.833), (-27*a - 55, -4, 1.833)]), (3805, [(9*a - 67, -1, 0.1142), (-9*a - 58, -1, 0.1142)]), (3889, [(8*a - 67, -3, 1.017), (-8*a - 59, -3, 1.017)]), (3904, [(24*a - 80, -6, 4.058), (-24*a - 56, -6, 4.058)]), (3949, [(-13*a - 58, 0, 0), (13*a - 71, 0, 0)]), (4009, [(11*a - 70, 2, 0.4450), (-11*a - 59, 2, 0.4450)]), (4045, [(12*a - 71, 3, 0.9968), (-12*a - 59, 3, 0.9968)]), (4129, [(5*a - 67, 1, 0.1096), (-5*a - 62, 1, 0.1096)]), (4141, [(-15*a - 59, 5, 2.737), (15*a - 74, 5, 2.737), (-21*a - 58, -5, 2.737), (21*a - 79, -5, 2.737)]), (4189, [(-25*a - 58, 0, 0), (25*a - 83, 0, 0)]), (4261, [(20*a - 79, 3, 0.9712), (-20*a - 59, 3, 0.9712)]), (4309, [(-23*a - 59, 6, 3.863), (23*a - 82, 6, 3.863)]), (4321, [(9*a - 71, -5, 2.679), (-9*a - 62, -5, 2.679), (24*a - 83, -3, 0.9644), (-24*a - 59, -3, 0.9644)]), (4336, [(-4*a - 64, 0, 0), (4*a - 68, 0, 0)]), (4345, [(-27*a - 59, 0, 0), (27*a - 86, 0, 0)]), (4489, [(-67, -3, 0.9462)]), (4609, [(-17*a - 62, -2, 0.4150), (17*a - 79, -2, 0.4150)]), (4624, [(-68, 2, 0.4144)]), (4681, [(3*a - 70, -4, 1.647), (-3*a - 67, -4, 1.647)]), (4705, [(-21*a - 62, 3, 0.9242), (21*a - 83, 3, 0.9242)]), (4720, [(12*a - 76, 6, 3.691), (-12*a - 64, 6, 3.691)]), (4741, [(4*a - 71, 4, 1.637), (-4*a - 67, 4, 1.637)]), (4801, [(29*a - 91, -1, 0.1017), (-29*a - 62, -1, 0.1017)]), (4909, [(7*a - 74, -8, 6.434), (-7*a - 67, -8, 6.434)]), (4969, [(-a - 70, 5, 2.498), (a - 71, 5, 2.498)]), (5041, [(-71, 2, 0.3968)]), (5056, [(-24*a - 64, 0, 0), (24*a - 88, 0, 0)]), (5104, [(8*a - 76, 2, 0.3944), (-8*a - 68, 2, 0.3944), (-28*a - 64, 2, 0.3944), (28*a - 92, 2, 0.3944)]), (5149, [(12*a - 79, -6, 3.534), (-12*a - 67, -6, 3.534)]), (5245, [(3*a - 74, 1, 0.09726), (-3*a - 71, 1, 0.09726)]), (5269, [(-15*a - 67, 6, 3.493), (15*a - 82, 6, 3.493)]), (5296, [(12*a - 80, 2, 0.3872), (-12*a - 68, 2, 0.3872)]), (5305, [(16*a - 83, -5, 2.418), (-16*a - 67, -5, 2.418)]), (5401, [(-19*a - 67, 0, 0), (19*a - 86, 0, 0)]), (5449, [(9*a - 79, 1, 0.09542), (-9*a - 70, 1, 0.09542)]), (5521, [(24*a - 91, 3, 0.8532), (-24*a - 67, 3, 0.8532)]), (5545, [(8*a - 79, -5, 2.365), (-8*a - 71, -5, 2.365)]), (5569, [(27*a - 94, 4, 1.510), (-27*a - 67, 4, 1.510)]), (5581, [(-28*a - 67, 1, 0.09429), (28*a - 95, 1, 0.09429)]), (5584, [(-20*a - 68, 0, 0), (20*a - 88, 0, 0)]), (5605, [(31*a - 98, 2, 0.3763), (-31*a - 67, 2, 0.3763)]), (5641, [(-13*a - 70, 0, 0), (13*a - 83, 0, 0)]), (5680, [(-24*a - 68, 0, 0), (24*a - 92, 0, 0)]), (5701, [(-11*a - 71, 0, 0), (11*a - 82, 0, 0)]), (5749, [(12*a - 83, -4, 1.486), (-12*a - 71, -4, 1.486)]), (5821, [(5*a - 79, -6, 3.324), (-5*a - 74, -6, 3.324)]), (5881, [(-15*a - 71, 2, 0.3674), (15*a - 86, 2, 0.3674)]), (6061, [(9*a - 83, 2, 0.3619), (-9*a - 74, 2, 0.3619), (20*a - 91, -6, 3.257), (-20*a - 71, -6, 3.257)]), (6064, [(-4*a - 76, 0, 0), (4*a - 80, 0, 0)]), (6121, [(-33*a - 70, 0, 0), (33*a - 103, 0, 0)]), (6145, [(-23*a - 71, 5, 2.246), (23*a - 94, 5, 2.246)]), (6169, [(24*a - 95, -4, 1.435), (-24*a - 71, -4, 1.435)]), (6229, [(27*a - 98, -1, 0.08925), (-27*a - 71, -1, 0.08925)]), (6241, [(-79, 2, 0.3567)]), (6289, [(-32*a - 71, 0, 0), (32*a - 103, 0, 0)]), (6301, [(35*a - 106, -8, 5.679), (-35*a - 71, -8, 5.679)]), (6445, [(17*a - 91, 3, 0.7897), (-17*a - 74, 3, 0.7897)]), (6469, [(3*a - 82, 4, 1.401), (-3*a - 79, 4, 1.401)]), (6541, [(4*a - 83, -2, 0.3484), (-4*a - 79, -2, 0.3484)]), (6589, [(-21*a - 74, 6, 3.124), (21*a - 95, 6, 3.124)]), (6745, [(7*a - 86, -2, 0.3431), (-7*a - 79, -2, 0.3431)]), (6781, [(29*a - 103, -4, 1.369), (-29*a - 74, -4, 1.369)]), (6805, [(-a - 82, -1, 0.08539), (a - 83, -1, 0.08539)]), (6829, [(33*a - 107, -3, 0.7672), (-33*a - 74, -3, 0.7672)]), (6889, [(-83, 9, 6.874)]), (6976, [(8*a - 88, 2, 0.3373), (-8*a - 80, 2, 0.3373)]), (7024, [(24*a - 100, 2, 0.3362), (-24*a - 76, 2, 0.3362)]), (7045, [(12*a - 91, -5, 2.098), (-12*a - 79, -5, 2.098)]), (7129, [(-3*a - 83, 0, 0), (3*a - 86, 0, 0)]), (7201, [(-15*a - 79, -4, 1.328), (15*a - 94, -4, 1.328)]), (7216, [(12*a - 92, -2, 0.3317), (-12*a - 80, -2, 0.3317), (-36*a - 76, -6, 2.985), (36*a - 112, -6, 2.985)]), (7249, [(-16*a - 79, 0, 0), (16*a - 95, 0, 0)]), (7489, [(-8*a - 83, 0, 0), (8*a - 91, 0, 0)]), (7561, [(-24*a - 79, 0, 0), (24*a - 103, 0, 0)]), (7621, [(-13*a - 82, 4, 1.291), (13*a - 95, 4, 1.291)]), (7645, [(27*a - 106, -10, 8.056), (-27*a - 79, -10, 8.056)]), (7669, [(-28*a - 79, 4, 1.287), (28*a - 107, 4, 1.287)]), (7681, [(11*a - 94, -3, 0.7234), (-11*a - 83, -3, 0.7234)]), (7729, [(31*a - 110, 2, 0.3205), (-31*a - 79, 2, 0.3205)]), (7741, [(12*a - 95, 2, 0.3202), (-12*a - 83, 2, 0.3202)]), (7744, [(-88, 0, 0)]), (7789, [(-36*a - 79, -1, 0.07981), (36*a - 115, -1, 0.07981)]), (7801, [(5*a - 91, -3, 0.7178), (-5*a - 86, -3, 0.7178), (-39*a - 79, -1, 0.07975), (39*a - 118, -1, 0.07975)]), (7909, [(-15*a - 83, -6, 2.851), (15*a - 98, -6, 2.851)]), (7984, [(-36*a - 80, -2, 0.3153), (36*a - 116, -2, 0.3153)]), (8005, [(-21*a - 82, 5, 1.968), (21*a - 103, 5, 1.968)]), (8089, [(-9*a - 86, 5, 1.958), (9*a - 95, 5, 1.958)]), (8149, [(20*a - 103, -1, 0.07803), (-20*a - 83, -1, 0.07803), (25*a - 107, -1, 0.07803), (-25*a - 82, -1, 0.07803)]), (8269, [(-23*a - 83, 3, 0.6972), (23*a - 106, 3, 0.6972)]), (8281, [(-91, -4, 1.239)]), (8305, [(24*a - 107, -2, 0.3092), (-24*a - 83, -2, 0.3092)]), (8341, [(33*a - 115, 4, 1.234), (-33*a - 82, 4, 1.234)]), (8389, [(37*a - 119, 1, 0.07691), (-37*a - 82, 1, 0.07691)]), (8401, [(27*a - 110, 2, 0.3074), (-27*a - 83, 2, 0.3074)]), (8521, [(-32*a - 83, 3, 0.6868), (32*a - 115, 3, 0.6868)]), (8545, [(3*a - 94, 5, 1.905), (-3*a - 91, 5, 1.905)]), (8569, [(-17*a - 86, 4, 1.218), (17*a - 103, 4, 1.218), (-35*a - 83, 0, 0), (35*a - 118, 0, 0)]), (8581, [(-36*a - 83, 3, 0.6844), (36*a - 119, 3, 0.6844)]), (8605, [(-39*a - 83, 3, 0.6834), (39*a - 122, 3, 0.6834)]), (8629, [(4*a - 95, -1, 0.07583), (-4*a - 91, -1, 0.07583)]), (8656, [(-12*a - 88, 0, 0), (12*a - 100, 0, 0)]), (8761, [(-21*a - 86, -4, 1.204), (21*a - 107, -4, 1.204)]), (8869, [(7*a - 98, -6, 2.693), (-7*a - 91, -6, 2.693)]), (8896, [(16*a - 104, 2, 0.2987), (-16*a - 88, 2, 0.2987)]), (8929, [(-a - 94, 1, 0.07454), (a - 95, 1, 0.07454)]), (9049, [(29*a - 115, 2, 0.2962), (-29*a - 86, 2, 0.2962)]), (9136, [(8*a - 100, 6, 2.653), (-8*a - 92, 6, 2.653)]), (9145, [(33*a - 119, -6, 2.652), (-33*a - 86, -6, 2.652)]), (9229, [(12*a - 103, 2, 0.2933), (-12*a - 91, 2, 0.2933)]), (9241, [(-41*a - 86, 5, 1.832), (41*a - 127, 5, 1.832)]), (9280, [(24*a - 112, -6, 2.632), (-24*a - 88, -6, 2.632)]), (9301, [(-3*a - 95, 0, 0), (3*a - 98, 0, 0)]), (9421, [(-15*a - 91, 2, 0.2903), (15*a - 106, 2, 0.2903)]), (9424, [(-28*a - 88, 0, 0), (28*a - 116, 0, 0)]), (9481, [(16*a - 107, -2, 0.2894), (-16*a - 91, -2, 0.2894)]), (9601, [(9*a - 103, 5, 1.797), (-9*a - 94, 5, 1.797)]), (9649, [(-19*a - 91, 0, 0), (19*a - 110, 0, 0)]), (9664, [(-40*a - 88, 0, 0), (40*a - 128, 0, 0)]), (9721, [(8*a - 103, -6, 2.572), (-8*a - 95, -6, 2.572)]), (9889, [(-13*a - 94, 6, 2.550), (13*a - 107, 6, 2.550), (24*a - 115, -2, 0.2833), (-24*a - 91, -2, 0.2833)]), (9904, [(20*a - 112, -4, 1.132), (-20*a - 92, -4, 1.132)]), (9949, [(11*a - 106, -1, 0.07062), (-11*a - 95, -1, 0.07062)])]]

# map: (a |-> -0.62) -> 1, (a |-> 1.62) -> 1, Fractional ideal (3) -> -1
[-a - 2, -23/2*a - 23/2 + (-25/2*a - 45/2)*i + (-7/2*a - 63/2)*j + (-1/2*a + 1/2)*k, [(29, [(a + 5, -3, 1.962), (-a + 6, -3, 1.962)]), (80, [(-4*a + 12, 0, 0)]), (89, [(a + 9, -3, 1.120), (-a + 10, -3, 1.120)]), (101, [(4*a + 9, 3, 1.051), (-4*a + 13, 3, 1.051)]), (176, [(4*a + 12, -6, 3.186), (-4*a + 16, -6, 3.186)]), (209, [(-5*a + 18, 0, 0), (5*a + 13, 0, 0)]), (245, [(-7*a + 21, 0, 0)]), (305, [(a + 17, -6, 2.420), (-a + 18, -6, 2.420)]), (320, [(-8*a + 24, 0, 0)]), (341, [(4*a + 17, 6, 2.289), (-4*a + 21, 6, 2.289)]), (401, [(7*a + 18, -3, 0.5276), (-7*a + 25, -3, 0.5276)]), (461, [(a + 21, 3, 0.4921), (-a + 22, 3, 0.4921)]), (509, [(4*a + 21, 3, 0.4683), (-4*a + 25, 3, 0.4683)]), (521, [(5*a + 21, -3, 0.4629), (-5*a + 26, -3, 0.4629)]), (545, [(8*a + 21, -6, 1.810), (-8*a + 29, -6, 1.810)]), (605, [(-11*a + 33, 0, 0)]), (656, [(4*a + 24, 6, 1.650), (-4*a + 28, 6, 1.650)]), (704, [(8*a + 24, 6, 1.593), (-8*a + 32, 6, 1.593)]), (761, [(8*a + 25, -3, 0.3830), (-8*a + 33, -3, 0.3830)]), (809, [(7*a + 26, -3, 0.3715), (-7*a + 33, -3, 0.3715)]), (869, [(-a + 30, 0, 0), (a + 29, 0, 0)]), (941, [(4*a + 29, -3, 0.3444), (-4*a + 33, -3, 0.3444)]), (944, [(8*a + 28, 6, 1.376), (-8*a + 36, 6, 1.376)]), (1049, [(-13*a + 42, 9, 2.936), (13*a + 29, 9, 2.936)]), (1061, [(7*a + 30, -9, 2.919), (-7*a + 37, -9, 2.919)]), (1109, [(11*a + 30, 3, 0.3173), (-11*a + 41, 3, 0.3173)]), (1121, [(a + 33, -6, 1.262), (-a + 34, -6, 1.262)]), (1136, [(-4*a + 36, 0, 0), (4*a + 32, 0, 0)]), (1205, [(4*a + 33, -12, 4.870), (-4*a + 37, -12, 4.870)]), (1229, [(5*a + 33, -9, 2.712), (-5*a + 38, -9, 2.712)]), (1289, [(8*a + 33, 3, 0.2943), (-8*a + 41, 3, 0.2943)]), (1349, [(-13*a + 46, 6, 1.151), (13*a + 33, 6, 1.151)]), (1361, [(16*a + 33, 3, 0.2864), (-16*a + 49, 3, 0.2864)]), (1409, [(11*a + 34, 3, 0.2815), (-11*a + 45, 3, 0.2815)]), (1520, [(8*a + 36, 12, 4.336), (-8*a + 44, 12, 4.336)]), (1529, [(5*a + 37, -6, 1.081), (-5*a + 42, -6, 1.081)]), (1601, [(8*a + 37, -3, 0.2641), (-8*a + 45, -3, 0.2641)]), (1661, [(7*a + 38, -6, 1.037), (-7*a + 45, -6, 1.037)]), (1709, [(-17*a + 54, -3, 0.2556), (17*a + 37, -3, 0.2556)]), (1721, [(a + 41, 3, 0.2547), (-a + 42, 3, 0.2547)]), (1805, [(-19*a + 57, 0, 0)]), (1829, [(4*a + 41, -6, 0.9882), (-4*a + 45, -6, 0.9882)]), (1856, [(-8*a + 48, 0, 0), (8*a + 40, 0, 0)]), (2009, [(-7*a + 49, 0, 0), (7*a + 42, 0, 0)]), (2045, [(-13*a + 54, 6, 0.9346), (13*a + 41, 6, 0.9346)]), (2069, [(a + 45, 9, 2.091), (-a + 46, 9, 2.091)]), (2081, [(16*a + 41, 9, 2.085), (-16*a + 57, 9, 2.085)]), (2096, [(4*a + 44, -6, 0.9231), (-4*a + 48, -6, 0.9231)]), (2105, [(-11*a + 53, 0, 0), (11*a + 42, 0, 0)]), (2189, [(4*a + 45, -12, 3.613), (-4*a + 49, -12, 3.613)]), (2201, [(-19*a + 61, 0, 0), (19*a + 42, 0, 0)]), (2321, [(8*a + 45, -6, 0.8772), (-8*a + 53, -6, 0.8772)]), (2384, [(16*a + 44, 12, 3.462), (-16*a + 60, 12, 3.462)]), (2441, [(-13*a + 58, 3, 0.2139), (13*a + 45, 3, 0.2139)]), (2480, [(4*a + 48, 12, 3.395), (-4*a + 52, 12, 3.395)]), (2489, [(16*a + 45, -6, 0.8471), (-16*a + 61, -6, 0.8471)]), (2501, [(11*a + 46, 12, 3.380), (-11*a + 57, 12, 3.380), (-17*a + 62, 0, 0), (17*a + 45, 0, 0)]), (2621, [(5*a + 49, -3, 0.2064), (-5*a + 54, -3, 0.2064)]), (2624, [(8*a + 48, 6, 0.8250), (-8*a + 56, 6, 0.8250)]), (2645, [(-23*a + 69, 0, 0)]), (2729, [(8*a + 49, -3, 0.2023), (-8*a + 57, -3, 0.2023)]), (2801, [(7*a + 50, 3, 0.1996), (-7*a + 57, 3, 0.1996)]), (2861, [(a + 53, 3, 0.1975), (-a + 54, 3, 0.1975)]), (2864, [(20*a + 48, -6, 0.7897), (-20*a + 68, -6, 0.7897)]), (2945, [(-17*a + 66, 0, 0), (17*a + 49, 0, 0)]), (2981, [(20*a + 49, 6, 0.7741), (-20*a + 69, 6, 0.7741)]), (3005, [(4*a + 53, -6, 0.7710), (-4*a + 57, -6, 0.7710)]), (3056, [(8*a + 52, 12, 3.058), (-8*a + 60, 12, 3.058)]), (3089, [(-19*a + 69, -3, 0.1901), (19*a + 50, -3, 0.1901)]), (3245, [(7*a + 54, 12, 2.968), (-7*a + 61, 12, 2.968)]), (3305, [(a + 57, 6, 0.7351), (-a + 58, 6, 0.7351)]), (3329, [(-13*a + 66, 3, 0.1831), (13*a + 53, 3, 0.1831)]), (3344, [(-4*a + 60, 0, 0), (4*a + 56, 0, 0)]), (3389, [(11*a + 54, 3, 0.1815), (-11*a + 65, 3, 0.1815)]), (3401, [(16*a + 53, -6, 0.7247), (-16*a + 69, -6, 0.7247)]), (3461, [(4*a + 57, -3, 0.1796), (-4*a + 61, -3, 0.1796)]), (3581, [(-19*a + 73, -3, 0.1766), (19*a + 54, -3, 0.1766)]), (3629, [(-23*a + 77, -6, 0.7016), (23*a + 54, -6, 0.7016)]), (3641, [(8*a + 57, 6, 0.7004), (-8*a + 65, 6, 0.7004)]), (3776, [(16*a + 56, 6, 0.6878), (-16*a + 72, 6, 0.6878)]), (3821, [(-13*a + 70, -15, 4.273), (13*a + 57, -15, 4.273)]), (3824, [(-4*a + 64, 0, 0), (4*a + 60, 0, 0)]), (3881, [(11*a + 58, -9, 1.526), (-11*a + 69, -9, 1.526)]), (3905, [(-16*a + 73, 0, 0), (16*a + 57, 0, 0)]), (3929, [(-17*a + 74, 9, 1.517), (17*a + 57, 9, 1.517)]), (3989, [(20*a + 57, 3, 0.1673), (-20*a + 77, 3, 0.1673)]), (4001, [(5*a + 61, -15, 4.176), (-5*a + 66, -15, 4.176)]), (4016, [(8*a + 60, -6, 0.6669), (-8*a + 68, -6, 0.6669)]), (4049, [(25*a + 57, -9, 1.494), (-25*a + 82, -9, 1.494)]), (4061, [(-28*a + 85, 0, 0), (28*a + 57, 0, 0)]), (4145, [(8*a + 61, -6, 0.6564), (-8*a + 69, -6, 0.6564)]), (4169, [(-23*a + 81, 12, 2.618), (23*a + 58, 12, 2.618)]), (4229, [(7*a + 62, -3, 0.1625), (-7*a + 69, -3, 0.1625)]), (4289, [(a + 65, -9, 1.452), (-a + 66, -9, 1.452)]), (4304, [(16*a + 60, 12, 2.577), (-16*a + 76, 12, 2.577)]), (4469, [(4*a + 65, 6, 0.6322), (-4*a + 69, 6, 0.6322), (-17*a + 78, 0, 0), (17*a + 61, 0, 0)]), (4496, [(-28*a + 88, -6, 0.6303), (28*a + 60, -6, 0.6303)]), (4541, [(20*a + 61, 6, 0.6272), (-20*a + 81, 6, 0.6272)]), (4544, [(8*a + 64, -12, 2.508), (-8*a + 72, -12, 2.508)]), (4649, [(29*a + 61, 3, 0.1550), (-29*a + 90, 3, 0.1550)]), (4661, [(-19*a + 81, 0, 0), (19*a + 62, 0, 0)]), (4769, [(7*a + 66, 6, 0.6120), (-7*a + 73, 6, 0.6120)]), (4805, [(-31*a + 93, 0, 0)]), (4829, [(a + 69, -6, 0.6082), (-a + 70, -6, 0.6082)]), (4901, [(-13*a + 78, 0, 0), (13*a + 65, 0, 0)]), (4961, [(-11*a + 77, 0, 0), (11*a + 66, 0, 0)]), (4976, [(20*a + 64, -12, 2.396), (-20*a + 84, -12, 2.396)]), (5009, [(16*a + 65, 15, 3.732), (-16*a + 81, 15, 3.732)]), (5021, [(4*a + 69, 15, 3.728), (-4*a + 73, 15, 3.728)]), (5081, [(5*a + 69, -9, 1.334), (-5*a + 74, -9, 1.334)]), (5249, [(8*a + 69, -12, 2.333), (-8*a + 77, -12, 2.333), (-19*a + 85, 0, 0), (19*a + 66, 0, 0)]), (5261, [(-28*a + 93, -15, 3.642), (28*a + 65, -15, 3.642)]), (5345, [(-23*a + 89, 0, 0), (23*a + 66, 0, 0)]), (5441, [(31*a + 66, 9, 1.289), (-31*a + 97, 9, 1.289)]), (5456, [(4*a + 72, -12, 2.289), (-4*a + 76, -12, 2.289)]), (5489, [(-13*a + 82, 0, 0), (13*a + 69, 0, 0)]), (5549, [(-11*a + 81, 0, 0), (11*a + 70, 0, 0)]), (5609, [(16*a + 69, 6, 0.5643), (-16*a + 85, 6, 0.5643)]), (5645, [(-17*a + 86, 6, 0.5625), (17*a + 69, 6, 0.5625)]), (5669, [(5*a + 73, -3, 0.1403), (-5*a + 78, -3, 0.1403)]), (5696, [(8*a + 72, -6, 0.5600), (-8*a + 80, -6, 0.5600)]), (5741, [(20*a + 69, 3, 0.1394), (-20*a + 89, 3, 0.1394)]), (5744, [(-28*a + 96, -12, 2.231), (28*a + 68, -12, 2.231)]), (5849, [(8*a + 73, 9, 1.243), (-8*a + 81, 9, 1.243)]), (5861, [(25*a + 69, 9, 1.242), (-25*a + 94, 9, 1.242)]), (5909, [(-28*a + 97, -12, 2.199), (28*a + 69, -12, 2.199)]), (5921, [(29*a + 69, -6, 0.5492), (-29*a + 98, -6, 0.5492)]), (5945, [(7*a + 74, -18, 4.933), (-7*a + 81, -18, 4.933), (-32*a + 101, -6, 0.5481), (32*a + 69, -6, 0.5481)]), (5981, [(-23*a + 93, 9, 1.230), (23*a + 70, 9, 1.230)]), (6005, [(a + 77, -6, 0.5454), (-a + 78, -6, 0.5454)]), (6080, [(16*a + 72, -12, 2.168), (-16*a + 88, -12, 2.168)]), (6221, [(4*a + 77, 3, 0.1340), (-4*a + 81, 3, 0.1340)]), (6224, [(-20*a + 92, 0, 0), (20*a + 72, 0, 0)]), (6281, [(-17*a + 90, 0, 0), (17*a + 73, 0, 0)]), (6320, [(8*a + 76, -12, 2.126), (-8*a + 84, -12, 2.126)]), (6389, [(20*a + 73, 3, 0.1322), (-20*a + 93, 3, 0.1322)]), (6464, [(-32*a + 104, 0, 0), (32*a + 72, 0, 0)]), (6521, [(-19*a + 93, 3, 0.1308), (19*a + 74, 3, 0.1308)]), (6581, [(7*a + 78, 3, 0.1302), (-7*a + 85, 3, 0.1302)]), (6605, [(29*a + 73, 18, 4.680), (-29*a + 102, 18, 4.680)]), (6641, [(-32*a + 105, -6, 0.5186), (32*a + 73, -6, 0.5186), (-a + 82, 0, 0), (a + 81, 0, 0)]), (6704, [(4*a + 80, -6, 0.5162), (-4*a + 84, -6, 0.5162)]), (6761, [(-13*a + 90, 3, 0.1285), (13*a + 77, 3, 0.1285)]), (6809, [(31*a + 74, 6, 0.5122), (-31*a + 105, 6, 0.5122)]), (6821, [(11*a + 78, -12, 2.047), (-11*a + 89, -12, 2.047)]), (6869, [(4*a + 81, 9, 1.147), (-4*a + 85, 9, 1.147)]), (6896, [(-20*a + 96, 0, 0), (20*a + 76, 0, 0)]), (6905, [(16*a + 77, -12, 2.034), (-16*a + 93, -12, 2.034)]), (6941, [(5*a + 81, -12, 2.029), (-5*a + 86, -12, 2.029)]), (7145, [(-8*a + 89, 0, 0), (8*a + 81, 0, 0)]), (7184, [(-32*a + 108, -6, 0.4986), (32*a + 76, -6, 0.4986)]), (7205, [(-19*a + 97, 0, 0), (19*a + 78, 0, 0)]), (7229, [(25*a + 77, -3, 0.1243), (-25*a + 102, -3, 0.1243)]), (7301, [(-28*a + 105, 18, 4.452), (28*a + 77, 18, 4.452)]), (7349, [(-23*a + 101, -15, 3.081), (23*a + 78, -15, 3.081)]), (7409, [(37*a + 77, 6, 0.4910), (-37*a + 114, 6, 0.4910)]), (7445, [(-13*a + 94, 18, 4.408), (13*a + 81, 18, 4.408)]), (7505, [(11*a + 82, -12, 1.951), (-11*a + 93, -12, 1.951)]), (7541, [(31*a + 78, -15, 3.042), (-31*a + 109, -15, 3.042)]), (7589, [(35*a + 78, 9, 1.092), (-35*a + 113, 9, 1.092)]), (7601, [(16*a + 81, -12, 1.939), (-16*a + 97, -12, 1.939)]), (7649, [(-17*a + 98, -3, 0.1208), (17*a + 81, -3, 0.1208)]), (7664, [(-8*a + 92, 0, 0), (8*a + 84, 0, 0)]), (7781, [(20*a + 81, 12, 1.916), (-20*a + 101, 12, 1.916)]), (7841, [(8*a + 85, 9, 1.074), (-8*a + 93, 9, 1.074)]), (7856, [(-28*a + 108, -6, 0.4768), (28*a + 80, -6, 0.4768)]), (7949, [(7*a + 86, -9, 1.067), (-7*a + 93, -9, 1.067)]), (7961, [(25*a + 81, 6, 0.4737), (-25*a + 106, 6, 0.4737)]), (8009, [(a + 89, 15, 2.952), (-a + 90, 15, 2.952)]), (8045, [(-28*a + 109, -6, 0.4712), (28*a + 81, -6, 0.4712)]), (8069, [(29*a + 81, 3, 0.1176), (-29*a + 110, 3, 0.1176)]), (8081, [(-23*a + 105, 3, 0.1175), (23*a + 82, 3, 0.1175)]), (8129, [(-32*a + 113, 18, 4.219), (32*a + 81, 18, 4.219)]), (8189, [(37*a + 81, -12, 1.868), (-37*a + 118, -12, 1.868)]), (8201, [(-40*a + 121, 12, 1.867), (40*a + 81, 12, 1.867)]), (8261, [(4*a + 89, 12, 1.860), (-4*a + 93, 12, 1.860)]), (8369, [(35*a + 82, -15, 2.887), (-35*a + 117, -15, 2.887)]), (8381, [(-17*a + 102, 0, 0), (17*a + 85, 0, 0)]), (8384, [(8*a + 88, -6, 0.4616), (-8*a + 96, -6, 0.4616)]), (8624, [(-28*a + 112, 12, 1.820), (28*a + 84, 12, 1.820)]), (8669, [(-19*a + 105, -3, 0.1135), (19*a + 86, -3, 0.1135)]), (8681, [(7*a + 90, 3, 0.1134), (-7*a + 97, 3, 0.1134)]), (8741, [(a + 93, -9, 1.017), (-a + 94, -9, 1.017)]), (8816, [(4*a + 92, 12, 1.800), (-4*a + 96, 12, 1.800), (-40*a + 124, 12, 1.800), (40*a + 84, 12, 1.800)]), (8849, [(29*a + 85, 15, 2.808), (-29*a + 114, 15, 2.808)]), (8909, [(-13*a + 102, -12, 1.791), (13*a + 89, -12, 1.791)]), (8921, [(-32*a + 117, 0, 0), (32*a + 85, 0, 0)]), (8969, [(11*a + 90, -15, 2.789), (-11*a + 101, -15, 2.789)]), (9005, [(4*a + 93, 6, 0.4454), (-4*a + 97, 6, 0.4454)]), (9029, [(-41*a + 126, 3, 0.1112), (41*a + 85, 3, 0.1112)]), (9089, [(5*a + 93, 6, 0.4433), (-5*a + 98, 6, 0.4433), (16*a + 89, 6, 0.4433), (-16*a + 105, 6, 0.4433)]), (9101, [(31*a + 86, 12, 1.772), (-31*a + 117, 12, 1.772)]), (9104, [(20*a + 88, 6, 0.4429), (-20*a + 108, 6, 0.4429)]), (9245, [(-43*a + 129, 0, 0)]), (9329, [(8*a + 93, 6, 0.4376), (-8*a + 101, 6, 0.4376)]), (9449, [(-19*a + 109, -6, 0.4348), (19*a + 90, -6, 0.4348)]), (9521, [(25*a + 89, -9, 0.9745), (-25*a + 114, -9, 0.9745)]), (9536, [(-32*a + 120, 12, 1.731), (32*a + 88, 12, 1.731)]), (9584, [(4*a + 96, -12, 1.727), (-4*a + 100, -12, 1.727)]), (9629, [(-28*a + 117, 9, 0.9691), (28*a + 89, 9, 0.9691)]), (9641, [(-23*a + 113, 6, 0.4304), (23*a + 90, 6, 0.4304)]), (9689, [(-13*a + 106, 3, 0.1073), (13*a + 93, 3, 0.1073)]), (9749, [(11*a + 94, -15, 2.675), (-11*a + 105, -15, 2.675)]), (9845, [(37*a + 89, -12, 1.704), (-37*a + 126, -12, 1.704)]), (9869, [(5*a + 97, 12, 1.702), (-5*a + 102, 12, 1.702)]), (9881, [(-40*a + 129, -12, 1.701), (40*a + 89, -12, 1.701), (-16*a + 109, 0, 0), (16*a + 93, 0, 0)]), (9920, [(8*a + 96, 12, 1.697), (-8*a + 104, 12, 1.697)]), (9929, [(31*a + 90, 9, 0.9543), (-31*a + 121, 9, 0.9543)]), (9941, [(-17*a + 110, 3, 0.1060), (17*a + 93, 3, 0.1060)])]]

# map: (a |-> -0.62) -> 1, (a |-> 1.62) -> 1, Fractional ideal (3) -> 1
[-7, 1/2 + (-5*a + 3/2)*i + (-2*a - 7/2)*j + (-1/2)*k, [(1, [(1, 1, 0.5870)]), (64, [(8, -6, 2.642)]), (169, [(13, 0, 0)]), (181, [(a + 13, -6, 1.571), (-a + 14, -6, 1.571)]), (205, [(4*a + 13, 6, 1.476), (-4*a + 17, 6, 1.476)]), (229, [(3*a + 14, 6, 1.396), (-3*a + 17, 6, 1.396)]), (289, [(17, -6, 1.243)]), (304, [(4*a + 16, 0, 0), (-4*a + 20, 0, 0)]), (349, [(5*a + 17, 0, 0), (-5*a + 22, 0, 0)]), (496, [(8*a + 20, 0, 0), (-8*a + 28, 0, 0)]), (541, [(3*a + 22, 6, 0.9085), (-3*a + 25, 6, 0.9085)]), (589, [(7*a + 22, -12, 3.483), (-7*a + 29, -12, 3.483)]), (649, [(a + 25, 0, 0), (-a + 26, 0, 0)]), (709, [(4*a + 25, 6, 0.7936), (-4*a + 29, 6, 0.7936)]), (745, [(3*a + 26, 6, 0.7742), (-3*a + 29, 6, 0.7742)]), (769, [(9*a + 25, -12, 3.048), (-9*a + 34, -12, 3.048)]), (781, [(12*a + 25, -12, 3.025), (-12*a + 37, -12, 3.025)]), (784, [(28, 12, 3.019)]), (841, [(29, 6, 0.7287)]), (880, [(4*a + 28, -12, 2.849), (-4*a + 32, -12, 2.849)]), (976, [(12*a + 28, 0, 0), (-12*a + 40, 0, 0)]), (1009, [(8*a + 29, -6, 0.6653), (-8*a + 37, -6, 0.6653)]), (1021, [(9*a + 29, 0, 0), (-9*a + 38, 0, 0)]), (1045, [(12*a + 29, -12, 2.615), (-12*a + 41, -12, 2.615)]), (1216, [(8*a + 32, 12, 2.424), (-8*a + 40, 12, 2.424)]), (1249, [(3*a + 34, 6, 0.5979), (-3*a + 37, 6, 0.5979)]), (1264, [(12*a + 32, 12, 2.378), (-12*a + 44, 12, 2.378)]), (1345, [(7*a + 34, 6, 0.5762), (-7*a + 41, 6, 0.5762)]), (1369, [(37, 0, 0)]), (1405, [(a + 37, 6, 0.5638), (-a + 38, 6, 0.5638)]), (1441, [(15*a + 34, 0, 0), (-15*a + 49, 0, 0)]), (1501, [(4*a + 37, -12, 2.182), (-4*a + 41, -12, 2.182)]), (1549, [(3*a + 38, 0, 0), (-3*a + 41, 0, 0)]), (1621, [(9*a + 37, -6, 0.5249), (-9*a + 46, -6, 0.5249)]), (1669, [(12*a + 37, -6, 0.5173), (-12*a + 49, -6, 0.5173)]), (1681, [(41, -18, 4.639)]), (1705, [(16*a + 37, -12, 2.047), (-16*a + 53, -12, 2.047)]), (1741, [(11*a + 38, 0, 0), (-11*a + 49, 0, 0)]), (1744, [(4*a + 40, 0, 0), (-4*a + 44, 0, 0)]), (1789, [(-15*a + 53, -12, 1.998), (15*a + 38, -12, 1.998)]), (1861, [(5*a + 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