# label = 14.2.a.a
# Base field F = Number Field in a with defining polynomial x - 1
# Quaternion algebra given by i^2 = -2, j^2 = -1
# Order with basis over the integers given by [1, 7*i, 1/2 + 1/2*i + 1/2*j, (-5/2)*i + 1/2*k]

# Nmax = 5000

[(1/3, [7*i, 1/2 + 1/2*i + 1/2*j, (-5/2)*i + 1/2*k]), (-1/3, [7*i, 1/2 + 1/2*i + 1/2*j, (-5/2)*i + 1/2*k])]
[((2,), 5/2 + 13*i + 3/2*j + 1/2*k), ((7,), 1 + 13*i + j - k)]

# map: (1 |-> 1.0) -> -1, Fractional ideal (2) -> -1, Fractional ideal (7) -> 1
[1, None, [(-3, [(-3, 2/3, 1.531)]), (-19, [(-19, -2, 5.475)]), (-59, [(-59, 2, 3.107)]), (-83, [(-83, 2, 2.620)]), (-115, [(-115, -4, 8.902)]), (-131, [(-131, 2, 2.085)]), (-139, [(-139, -2, 2.024)]), (-187, [(-187, 4, 6.981)]), (-195, [(-195, 4, 6.836)]), (-227, [(-227, 2, 1.584)]), (-251, [(-251, 2, 1.506)]), (-283, [(-283, -2, 1.419)]), (-299, [(-299, 0, 0)]), (-307, [(-307, -6, 12.26)]), (-339, [(-339, 0, 0)]), (-355, [(-355, -4, 5.067)]), (-395, [(-395, 4, 4.803)]), (-411, [(-411, -4, 4.709)]), (-419, [(-419, 2, 1.166)]), (-451, [(-451, 4, 4.495)]), (-467, [(-467, 2, 1.104)]), (-523, [(-523, -6, 9.392)]), (-563, [(-563, -2, 1.006)]), (-579, [(-579, 4, 3.967)]), (-587, [(-587, -2, 0.9851)]), (-619, [(-619, -6, 8.633)]), (-635, [(-635, -4, 3.788)]), (-643, [(-643, 2, 0.9412)]), (-691, [(-691, 2, 0.9079)]), (-699, [(-699, 4, 3.611)]), (-731, [(-731, 0, 0)]), (-755, [(-755, 0, 0)]), (-787, [(-787, 2, 0.8507)]), (-803, [(-803, 4, 3.369)]), (-811, [(-811, 6, 7.542)]), (-843, [(-843, -4, 3.288)]), (-859, [(-859, 6, 7.329)]), (-899, [(-899, -4, 3.184)]), (-915, [(-915, -4, 3.156)]), (-923, [(-923, 0, 0)]), (-955, [(-955, -4, 3.089)]), (-971, [(-971, -2, 0.7659)]), (-979, [(-979, 0, 0)]), (-1011, [(-1011, -4, 3.002)]), (-1027, [(-1027, 4, 2.979)]), (-1067, [(-1067, 0, 0)]), (-1091, [(-1091, -2, 0.7225)]), (-1123, [(-1123, 10, 17.80)]), (-1139, [(-1139, 0, 0)]), (-1147, [(-1147, -4, 2.819)]), (-1195, [(-1195, 0, 0)]), (-1203, [(-1203, 8, 11.01)]), (-1235, [(-1235, -4, 2.716)]), (-1259, [(-1259, -6, 6.053)]), (-1291, [(-1291, 6, 5.978)]), (-1307, [(-1307, -6, 5.941)]), (-1315, [(-1315, 0, 0)]), (-1347, [(-1347, -4, 2.601)]), (-1363, [(-1363, -4, 2.586)]), (-1371, [(-1371, -4, 2.578)]), (-1403, [(-1403, -4, 2.549)]), (-1419, [(-1419, -8, 10.14)]), (-1427, [(-1427, -2, 0.6318)]), (-1459, [(-1459, 6, 5.623)]), (-1483, [(-1483, -2, 0.6197)]), (-1515, [(-1515, 4, 2.453)]), (-1531, [(-1531, 6, 5.490)]), (-1571, [(-1571, -2, 0.6021)]), (-1595, [(-1595, 0, 0)]), (-1627, [(-1627, 6, 5.325)]), (-1643, [(-1643, 4, 2.355)]), (-1651, [(-1651, 8, 9.398)]), (-1699, [(-1699, -10, 14.48)]), (-1707, [(-1707, 0, 0)]), (-1739, [(-1739, 0, 0)]), (-1763, [(-1763, 0, 0)]), (-1795, [(-1795, -8, 9.013)]), (-1811, [(-1811, -2, 0.5608)]), (-1819, [(-1819, 4, 2.238)]), (-1851, [(-1851, -8, 8.876)]), (-1867, [(-1867, 6, 4.971)]), (-1907, [(-1907, -2, 0.5465)]), (-1923, [(-1923, 0, 0)]), (-1931, [(-1931, -6, 4.888)]), (-1963, [(-1963, -4, 2.155)]), (-1979, [(-1979, -2, 0.5365)]), (-1987, [(-1987, 6, 4.819)]), (-2019, [(-2019, 0, 0)]), (-2035, [(-2035, 8, 8.465)]), (-2091, [(-2091, 8, 8.351)]), (-2099, [(-2099, 2, 0.5209)]), (-2131, [(-2131, 2, 0.5170)]), (-2147, [(-2147, 0, 0)]), (-2155, [(-2155, 8, 8.226)]), (-2203, [(-2203, -2, 0.5085)]), (-2211, [(-2211, 8, 8.121)]), (-2243, [(-2243, -6, 4.535)]), (-2267, [(-2267, 2, 0.5012)]), (-2315, [(-2315, 0, 0)]), (-2323, [(-2323, 0, 0)]), (-2355, [(-2355, 4, 1.967)]), (-2371, [(-2371, -2, 0.4901)]), (-2379, [(-2379, -4, 1.957)]), (-2411, [(-2411, 2, 0.4860)]), (-2427, [(-2427, -8, 7.751)]), (-2435, [(-2435, -4, 1.935)]), (-2467, [(-2467, -10, 12.01)]), (-2483, [(-2483, 4, 1.916)]), (-2491, [(-2491, -8, 7.651)]), (-2539, [(-2539, 2, 0.4736)]), (-2579, [(-2579, 2, 0.4700)]), (-2595, [(-2595, -4, 1.874)]), (-2603, [(-2603, 0, 0)]), (-2635, [(-2635, 8, 7.439)]), (-2651, [(-2651, -4, 1.854)]), (-2659, [(-2659, -10, 11.57)]), (-2707, [(-2707, -6, 4.128)]), (-2715, [(-2715, 4, 1.832)]), (-2747, [(-2747, 4, 1.821)]), (-2771, [(-2771, 4, 1.814)]), (-2803, [(-2803, 10, 11.27)]), (-2819, [(-2819, 2, 0.4495)]), (-2827, [(-2827, 8, 7.182)]), (-2859, [(-2859, -4, 1.785)]), (-2915, [(-2915, 8, 7.073)]), (-2931, [(-2931, -4, 1.763)]), (-2939, [(-2939, 6, 3.962)]), (-2971, [(-2971, 2, 0.4379)]), (-2987, [(-2987, 0, 0)]), (-2995, [(-2995, -12, 15.70)]), (-3027, [(-3027, 4, 1.735)]), (-3043, [(-3043, 0, 0)]), (-3083, [(-3083, -2, 0.4298)]), (-3099, [(-3099, 0, 0)]), (-3107, [(-3107, -4, 1.713)]), (-3139, [(-3139, -4, 1.704)]), (-3155, [(-3155, -4, 1.700)]), (-3163, [(-3163, -10, 10.61)]), (-3219, [(-3219, 8, 6.730)]), (-3251, [(-3251, 2, 0.4186)]), (-3307, [(-3307, -10, 10.38)]), (-3323, [(-3323, 6, 3.726)]), (-3331, [(-3331, -6, 3.722)]), (-3363, [(-3363, 4, 1.646)]), (-3379, [(-3379, 8, 6.569)]), (-3387, [(-3387, 8, 6.561)]), (-3419, [(-3419, -4, 1.633)]), (-3435, [(-3435, -4, 1.629)]), (-3443, [(-3443, 8, 6.508)]), (-3491, [(-3491, 2, 0.4039)]), (-3499, [(-3499, 10, 10.09)]), (-3531, [(-3531, 8, 6.426)]), (-3547, [(-3547, -6, 3.607)]), (-3587, [(-3587, 4, 1.594)]), (-3603, [(-3603, 12, 14.31)]), (-3611, [(-3611, 4, 1.589)]), (-3643, [(-3643, -2, 0.3954)]), (-3659, [(-3659, 6, 3.551)]), (-3667, [(-3667, 8, 6.306)]), (-3715, [(-3715, 12, 14.10)]), (-3723, [(-3723, 0, 0)]), (-3755, [(-3755, 8, 6.232)]), (-3779, [(-3779, -2, 0.3882)]), (-3811, [(-3811, -12, 13.92)]), (-3827, [(-3827, -4, 1.543)]), (-3835, [(-3835, -4, 1.542)]), (-3867, [(-3867, -8, 6.141)]), (-3883, [(-3883, -8, 6.128)]), (-3891, [(-3891, -4, 1.530)]), (-3923, [(-3923, 2, 0.3810)]), (-3939, [(-3939, 4, 1.521)]), (-3947, [(-3947, 6, 3.419)]), (-3979, [(-3979, -8, 6.054)]), (-3995, [(-3995, 0, 0)]), (-4003, [(-4003, 2, 0.3772)]), (-4035, [(-4035, -4, 1.503)]), (-4051, [(-4051, -2, 0.3750)]), (-4091, [(-4091, 2, 0.3731)]), (-4115, [(-4115, 0, 0)]), (-4147, [(-4147, -8, 5.930)]), (-4163, [(-4163, 4, 1.480)]), (-4171, [(-4171, 0, 0)]), (-4219, [(-4219, -2, 0.3674)]), (-4227, [(-4227, 4, 1.468)]), (-4259, [(-4259, 6, 3.291)]), (-4283, [(-4283, 6, 3.282)]), (-4315, [(-4315, 0, 0)]), (-4331, [(-4331, 8, 5.802)]), (-4339, [(-4339, -2, 0.3623)]), (-4371, [(-4371, 8, 5.776)]), (-4387, [(-4387, -8, 5.765)]), (-4395, [(-4395, -4, 1.440)]), (-4427, [(-4427, 0, 0)]), (-4443, [(-4443, 4, 1.432)]), (-4451, [(-4451, 2, 0.3577)]), (-4483, [(-4483, 10, 8.911)]), (-4499, [(-4499, -4, 1.423)]), (-4507, [(-4507, -2, 0.3555)]), (-4539, [(-4539, 8, 5.668)]), (-4555, [(-4555, 0, 0)]), (-4595, [(-4595, 4, 1.408)]), (-4611, [(-4611, -8, 5.623)]), (-4619, [(-4619, 0, 0)]), (-4651, [(-4651, -10, 8.749)]), (-4667, [(-4667, -4, 1.397)]), (-4723, [(-4723, -2, 0.3473)]), (-4731, [(-4731, 4, 1.388)]), (-4763, [(-4763, -8, 5.533)]), (-4787, [(-4787, -2, 0.3449)]), (-4819, [(-4819, 8, 5.501)]), (-4835, [(-4835, -4, 1.373)]), (-4843, [(-4843, -16, 21.95)]), (-4891, [(-4891, -8, 5.460)]), (-4899, [(-4899, 0, 0)]), (-4931, [(-4931, 2, 0.3399)]), (-4947, [(-4947, -8, 5.429)]), (-4955, [(-4955, -4, 1.356)]), (-4987, [(-4987, 10, 8.449)])]]

# map: (1 |-> 1.0) -> -1, Fractional ideal (2) -> 1, Fractional ideal (7) -> -1
[5, 5/2 + (-2)*i + 1/2*j + 1/2*k, [(-4, [(-4, -2, 1.325)]), (-7, [(-7, 2, 1.002)]), (-8, [(-8, 2, 0.9369)]), (-15, [(-15, -4, 1.368)]), (-23, [(-23, 0, 0)]), (-39, [(-39, 4, 0.8487)]), (-56, [(-56, -2, 0.7082)]), (-71, [(-71, 4, 0.6290)]), (-79, [(-79, -4, 0.5963)]), (-84, [(-84, 4, 2.313)]), (-88, [(-88, 4, 1.130)]), (-95, [(-95, -4, 0.5438)]), (-116, [(-116, 0, 0)]), (-119, [(-119, -4, 0.9717)]), (-120, [(-120, -4, 0.9676)]), (-127, [(-127, 8, 1.881)]), (-148, [(-148, -8, 3.485)]), (-151, [(-151, -8, 1.725)]), (-168, [(-168, 4, 1.636)]), (-183, [(-183, -4, 0.3918)]), (-184, [(-184, 8, 3.126)]), (-191, [(-191, 4, 0.3835)]), (-212, [(-212, 0, 0)]), (-228, [(-228, -4, 0.7020)]), (-231, [(-231, 0, 0)]), (-232, [(-232, 4, 0.6959)]), (-239, [(-239, 0, 0)]), (-247, [(-247, -12, 3.035)]), (-260, [(-260, 4, 0.6574)]), (-263, [(-263, 4, 0.3268)]), (-280, [(-280, -8, 5.068)]), (-287, [(-287, 4, 0.6257)]), (-295, [(-295, -4, 0.3086)]), (-296, [(-296, -4, 0.6161)]), (-303, [(-303, 4, 0.3045)]), (-308, [(-308, -4, 1.208)]), (-312, [(-312, -4, 0.6001)]), (-319, [(-319, 16, 4.748)]), (-340, [(-340, 8, 2.299)]), (-344, [(-344, -4, 0.5715)]), (-359, [(-359, -8, 1.119)]), (-372, [(-372, 8, 2.198)]), (-399, [(-399, -4, 0.5307)]), (-407, [(-407, -8, 1.051)]), (-408, [(-408, 8, 2.099)]), (-415, [(-415, 4, 0.2602)]), (-420, [(-420, -4, 1.034)]), (-424, [(-424, -12, 4.633)]), (-431, [(-431, 0, 0)]), (-436, [(-436, 0, 0)]), (-452, [(-452, 4, 0.4986)]), (-455, [(-455, 4, 0.4969)]), (-456, [(-456, 4, 0.4964)]), (-463, [(-463, 4, 0.2463)]), (-471, [(-471, 4, 0.2442)]), (-487, [(-487, -8, 0.9607)]), (-511, [(-511, 4, 0.4689)]), (-519, [(-519, 12, 2.094)]), (-520, [(-520, -4, 0.4648)]), (-527, [(-527, 0, 0)]), (-532, [(-532, 4, 0.9191)]), (-536, [(-536, 4, 0.4578)]), (-543, [(-543, -12, 2.047)]), (-548, [(-548, -8, 1.811)]), (-564, [(-564, -8, 1.785)]), (-568, [(-568, -4, 0.4448)]), (-583, [(-583, 8, 0.8780)]), (-596, [(-596, -8, 1.737)]), (-599, [(-599, 4, 0.2166)]), (-616, [(-616, 8, 3.417)]), (-623, [(-623, -4, 0.4247)]), (-631, [(-631, 4, 0.2110)]), (-632, [(-632, 4, 0.4216)]), (-644, [(-644, 4, 0.8354)]), (-655, [(-655, -12, 1.864)]), (-660, [(-660, -8, 1.650)]), (-679, [(-679, -12, 3.661)]), (-680, [(-680, 0, 0)]), (-687, [(-687, 12, 1.820)]), (-695, [(-695, 12, 1.809)]), (-708, [(-708, -4, 0.3984)]), (-728, [(-728, 0, 0)]), (-743, [(-743, 0, 0)]), (-744, [(-744, 0, 0)]), (-751, [(-751, 0, 0)]), (-760, [(-760, -4, 0.3845)]), (-767, [(-767, 4, 0.1914)]), (-772, [(-772, -4, 0.3815)]), (-788, [(-788, 8, 1.510)]), (-791, [(-791, 4, 0.3769)]), (-799, [(-799, -8, 0.7500)]), (-807, [(-807, -4, 0.1866)]), (-820, [(-820, 16, 5.923)]), (-823, [(-823, 12, 1.663)]), (-840, [(-840, -4, 0.7315)]), (-856, [(-856, -12, 3.261)]), (-863, [(-863, -12, 1.624)]), (-868, [(-868, 8, 2.878)]), (-872, [(-872, -4, 0.3590)]), (-879, [(-879, 4, 0.1788)]), (-884, [(-884, 8, 1.426)]), (-903, [(-903, 8, 1.411)]), (-904, [(-904, 4, 0.3526)]), (-911, [(-911, -8, 0.7024)]), (-919, [(-919, 4, 0.1748)]), (-932, [(-932, 0, 0)]), (-935, [(-935, -8, 0.6933)]), (-952, [(-952, -4, 0.6871)]), (-959, [(-959, 0, 0)]), (-967, [(-967, -16, 2.727)]), (-984, [(-984, 0, 0)]), (-991, [(-991, -4, 0.1684)]), (-996, [(-996, 12, 3.023)]), (-1012, [(-1012, -16, 5.331)]), (-1015, [(-1015, 8, 1.331)]), (-1016, [(-1016, 8, 1.330)]), (-1023, [(-1023, -8, 0.6628)]), (-1031, [(-1031, -4, 0.1651)]), (-1047, [(-1047, 4, 0.1638)]), (-1064, [(-1064, -4, 0.6499)]), (-1079, [(-1079, 4, 0.1613)]), (-1087, [(-1087, 24, 5.787)]), (-1092, [(-1092, -4, 0.6415)]), (-1096, [(-1096, 0, 0)]), (-1103, [(-1103, 8, 0.6383)]), (-1108, [(-1108, 0, 0)]), (-1124, [(-1124, -8, 1.265)]), (-1128, [(-1128, -8, 1.262)]), (-1135, [(-1135, -12, 1.416)]), (-1159, [(-1159, 4, 0.1557)]), (-1191, [(-1191, -12, 1.382)]), (-1192, [(-1192, 12, 2.763)]), (-1199, [(-1199, 8, 0.6122)]), (-1204, [(-1204, -4, 0.6110)]), (-1208, [(-1208, 0, 0)]), (-1220, [(-1220, -4, 0.3035)]), (-1236, [(-1236, 0, 0)]), (-1239, [(-1239, 4, 0.3011)]), (-1240, [(-1240, 16, 4.816)]), (-1247, [(-1247, 8, 0.6003)]), (-1255, [(-1255, -12, 1.346)]), (-1268, [(-1268, 8, 1.191)]), (-1271, [(-1271, -8, 0.5947)]), (-1288, [(-1288, -4, 0.5907)]), (-1295, [(-1295, 0, 0)]), (-1303, [(-1303, 8, 0.5873)]), (-1304, [(-1304, -4, 0.2935)]), (-1311, [(-1311, -8, 0.5855)]), (-1316, [(-1316, 0, 0)]), (-1320, [(-1320, 16, 4.668)]), (-1327, [(-1327, 12, 1.309)]), (-1348, [(-1348, 4, 0.2887)]), (-1351, [(-1351, -12, 2.595)]), (-1367, [(-1367, 4, 0.1433)]), (-1380, [(-1380, -8, 1.141)]), (-1383, [(-1383, -12, 1.283)]), (-1407, [(-1407, 0, 0)]), (-1415, [(-1415, 4, 0.1409)]), (-1416, [(-1416, -4, 0.2817)]), (-1423, [(-1423, 0, 0)]), (-1428, [(-1428, 8, 2.244)]), (-1432, [(-1432, 12, 2.521)]), (-1439, [(-1439, 0, 0)]), (-1460, [(-1460, -8, 1.110)]), (-1463, [(-1463, -8, 1.109)]), (-1464, [(-1464, -12, 2.493)]), (-1471, [(-1471, 20, 3.455)]), (-1479, [(-1479, -8, 0.5513)]), (-1492, [(-1492, -16, 4.391)]), (-1495, [(-1495, 8, 0.5483)]), (-1527, [(-1527, -4, 0.1356)]), (-1528, [(-1528, -20, 6.779)]), (-1535, [(-1535, -4, 0.1353)]), (-1540, [(-1540, 8, 2.161)]), (-1544, [(-1544, 4, 0.2698)]), (-1551, [(-1551, 8, 0.5383)]), (-1556, [(-1556, 8, 1.075)]), (-1572, [(-1572, 12, 2.406)]), (-1576, [(-1576, -4, 0.2670)]), (-1583, [(-1583, 12, 1.199)]), (-1591, [(-1591, 16, 2.126)]), (-1604, [(-1604, 4, 0.2647)]), (-1607, [(-1607, -12, 1.190)]), (-1624, [(-1624, 4, 0.5261)]), (-1631, [(-1631, -8, 1.050)]), (-1639, [(-1639, -8, 0.5237)]), (-1640, [(-1640, 8, 1.047)]), (-1652, [(-1652, -4, 0.5216)]), (-1663, [(-1663, -16, 2.079)]), (-1668, [(-1668, 12, 2.336)]), (-1684, [(-1684, 8, 1.033)]), (-1687, [(-1687, -12, 2.323)]), (-1688, [(-1688, -4, 0.2580)]), (-1695, [(-1695, 8, 0.5149)]), (-1703, [(-1703, 4, 0.1284)]), (-1716, [(-1716, 8, 1.024)]), (-1736, [(-1736, 0, 0)]), (-1743, [(-1743, 12, 2.285)]), (-1751, [(-1751, 0, 0)]), (-1752, [(-1752, -8, 1.013)]), (-1759, [(-1759, 0, 0)]), (-1768, [(-1768, -8, 1.008)]), (-1780, [(-1780, -8, 1.005)]), (-1796, [(-1796, -8, 1.000)]), (-1799, [(-1799, 4, 0.2499)]), (-1807, [(-1807, -12, 1.122)]), (-1828, [(-1828, 4, 0.2479)]), (-1831, [(-1831, 4, 0.1239)]), (-1848, [(-1848, 8, 1.973)]), (-1855, [(-1855, 8, 0.9845)]), (-1864, [(-1864, 16, 3.928)]), (-1871, [(-1871, 0, 0)]), (-1876, [(-1876, 4, 0.4895)]), (-1880, [(-1880, -8, 0.9779)]), (-1887, [(-1887, 8, 0.4880)]), (-1892, [(-1892, 0, 0)]), (-1912, [(-1912, 16, 3.879)]), (-1919, [(-1919, -4, 0.1210)]), (-1927, [(-1927, 0, 0)]), (-1940, [(-1940, -8, 0.9626)]), (-1943, [(-1943, 8, 0.4810)]), (-1967, [(-1967, 0, 0)]), (-1976, [(-1976, -4, 0.2385)]), (-1983, [(-1983, 4, 0.1190)]), (-1988, [(-1988, 0, 0)]), (-1992, [(-1992, 4, 0.2375)]), (-1999, [(-1999, -12, 1.067)]), (-2004, [(-2004, -16, 3.789)]), (-2020, [(-2020, -20, 5.896)]), (-2024, [(-2024, 8, 0.9425)]), (-2031, [(-2031, -4, 0.1176)]), (-2039, [(-2039, 0, 0)]), (-2055, [(-2055, 16, 1.871)]), (-2072, [(-2072, 4, 0.4657)]), (-2087, [(-2087, -4, 0.1160)]), (-2095, [(-2095, -20, 2.895)]), (-2104, [(-2104, 12, 2.080)]), (-2111, [(-2111, 4, 0.1154)]), (-2132, [(-2132, 0, 0)]), (-2135, [(-2135, 4, 0.2294)]), (-2136, [(-2136, 16, 3.670)]), (-2143, [(-2143, -20, 2.862)]), (-2164, [(-2164, 8, 0.9115)]), (-2167, [(-2167, 0, 0)]), (-2184, [(-2184, -12, 4.083)]), (-2191, [(-2191, -12, 2.038)]), (-2199, [(-2199, -12, 1.017)]), (-2207, [(-2207, 0, 0)]), (-2212, [(-2212, -16, 7.212)]), (-2216, [(-2216, -4, 0.2252)]), (-2228, [(-2228, 0, 0)]), (-2244, [(-2244, 8, 0.8951)]), (-2247, [(-2247, -8, 0.8945)]), (-2248, [(-2248, -8, 0.8943)]), (-2255, [(-2255, -8, 0.4464)]), (-2263, [(-2263, -8, 0.4456)]), (-2276, [(-2276, 4, 0.2222)]), (-2279, [(-2279, 8, 0.4441)]), (-2296, [(-2296, 4, 0.4424)]), (-2311, [(-2311, 20, 2.756)]), (-2319, [(-2319, 12, 0.9905)]), (-2324, [(-2324, 4, 0.4398)]), (-2328, [(-2328, -16, 3.515)]), (-2335, [(-2335, 20, 2.742)]), (-2356, [(-2356, 8, 0.8735)]), (-2359, [(-2359, 20, 5.456)]), (-2360, [(-2360, 4, 0.2182)]), (-2388, [(-2388, 0, 0)]), (-2391, [(-2391, 4, 0.1084)]), (-2408, [(-2408, 0, 0)]), (-2415, [(-2415, -16, 3.451)]), (-2423, [(-2423, 0, 0)]), (-2424, [(-2424, -12, 1.938)]), (-2431, [(-2431, -8, 0.4300)]), (-2436, [(-2436, -8, 1.718)]), (-2440, [(-2440, -12, 1.931)]), (-2447, [(-2447, -8, 0.4286)]), (-2452, [(-2452, 8, 0.8563)]), (-2468, [(-2468, 12, 1.920)]), (-2471, [(-2471, 4, 0.2132)]), (-2472, [(-2472, 0, 0)]), (-2479, [(-2479, 0, 0)]), (-2487, [(-2487, -4, 0.1063)]), (-2503, [(-2503, 0, 0)]), (-2536, [(-2536, 4, 0.2105)]), (-2543, [(-2543, -4, 0.1051)]), (-2552, [(-2552, -8, 0.8393)]), (-2559, [(-2559, -20, 2.619)]), (-2564, [(-2564, -4, 0.2093)]), (-2580, [(-2580, 8, 0.8347)]), (-2584, [(-2584, -16, 3.336)]), (-2591, [(-2591, 0, 0)]), (-2599, [(-2599, 24, 3.743)]), (-2612, [(-2612, -8, 0.8296)]), (-2615, [(-2615, 4, 0.1036)]), (-2632, [(-2632, 8, 1.653)]), (-2639, [(-2639, 8, 0.8254)]), (-2647, [(-2647, 12, 0.9271)]), (-2648, [(-2648, -4, 0.2060)]), (-2660, [(-2660, 12, 3.699)]), (-2671, [(-2671, -28, 5.025)]), (-2676, [(-2676, 0, 0)]), (-2692, [(-2692, 0, 0)]), (-2696, [(-2696, -12, 1.837)]), (-2703, [(-2703, 16, 1.631)]), (-2711, [(-2711, -16, 1.629)]), (-2724, [(-2724, 4, 0.2031)]), (-2751, [(-2751, -4, 0.2021)]), (-2759, [(-2759, 0, 0)]), (-2760, [(-2760, 8, 0.8071)]), (-2767, [(-2767, -12, 0.9068)]), (-2776, [(-2776, -4, 0.2012)]), (-2788, [(-2788, 16, 3.212)]), (-2804, [(-2804, 8, 0.8007)]), (-2807, [(-2807, -4, 0.2001)]), (-2815, [(-2815, 4, 0.09989)]), (-2823, [(-2823, 20, 2.494)]), (-2836, [(-2836, -16, 3.185)]), (-2839, [(-2839, -16, 1.592)]), (-2856, [(-2856, 0, 0)]), (-2863, [(-2863, -4, 0.1981)]), (-2872, [(-2872, 0, 0)]), (-2879, [(-2879, 12, 0.8890)]), (-2884, [(-2884, -8, 1.579)]), (-2895, [(-2895, 0, 0)]), (-2919, [(-2919, -4, 0.1962)]), (-2920, [(-2920, -24, 7.062)]), (-2927, [(-2927, 4, 0.09796)]), (-2935, [(-2935, 4, 0.09783)]), (-2948, [(-2948, -8, 0.7809)]), (-2951, [(-2951, 12, 0.8781)]), (-2968, [(-2968, -4, 0.3891)]), (-2983, [(-2983, 20, 2.426)]), (-2984, [(-2984, 4, 0.1940)]), (-2991, [(-2991, 12, 0.8722)]), (-2996, [(-2996, -4, 0.3873)]), (-3007, [(-3007, 8, 0.3866)]), (-3012, [(-3012, -12, 1.738)]), (-3028, [(-3028, 8, 0.7705)]), (-3031, [(-3031, -4, 0.1925)]), (-3032, [(-3032, -4, 0.1925)]), (-3039, [(-3039, 12, 0.8653)]), (-3047, [(-3047, 8, 0.3841)]), (-3063, [(-3063, -20, 2.394)]), (-3080, [(-3080, 8, 1.528)]), (-3095, [(-3095, -12, 0.8574)]), (-3103, [(-3103, -16, 1.522)]), (-3108, [(-3108, -8, 1.521)]), (-3112, [(-3112, 4, 0.1900)]), (-3119, [(-3119, -12, 0.8541)]), (-3124, [(-3124, -8, 0.7586)]), (-3140, [(-3140, -4, 0.1892)]), (-3143, [(-3143, -8, 0.7563)]), (-3144, [(-3144, 20, 4.726)]), (-3151, [(-3151, 16, 1.511)]), (-3172, [(-3172, 4, 0.1882)]), (-3192, [(-3192, 4, 0.3752)]), (-3199, [(-3199, 4, 0.1874)]), (-3207, [(-3207, -4, 0.09359)]), (-3208, [(-3208, 12, 1.684)]), (-3215, [(-3215, -4, 0.09347)]), (-3220, [(-3220, -8, 1.494)]), (-3224, [(-3224, 8, 0.7467)]), (-3236, [(-3236, 4, 0.1863)]), (-3252, [(-3252, 0, 0)]), (-3255, [(-3255, -16, 2.973)]), (-3256, [(-3256, 0, 0)]), (-3263, [(-3263, -12, 0.8350)]), (-3271, [(-3271, -24, 3.336)]), (-3284, [(-3284, 0, 0)]), (-3287, [(-3287, 4, 0.09244)]), (-3304, [(-3304, -12, 3.319)]), (-3311, [(-3311, 0, 0)]), (-3319, [(-3319, -16, 1.472)]), (-3320, [(-3320, 4, 0.1840)]), (-3327, [(-3327, -4, 0.09189)]), (-3336, [(-3336, -4, 0.1835)]), (-3343, [(-3343, 16, 1.467)]), (-3367, [(-3367, 16, 2.923)]), (-3368, [(-3368, 4, 0.1827)]), (-3383, [(-3383, -8, 0.3645)]), (-3396, [(-3396, -4, 0.1819)]), (-3399, [(-3399, -8, 0.3636)]), (-3416, [(-3416, 8, 1.451)]), (-3423, [(-3423, 8, 0.7247)]), (-3431, [(-3431, 0, 0)]), (-3432, [(-3432, -16, 2.895)]), (-3439, [(-3439, -12, 0.8134)]), (-3444, [(-3444, 0, 0)]), (-3448, [(-3448, 16, 2.888)]), (-3455, [(-3455, 4, 0.09017)]), (-3460, [(-3460, 20, 4.505)]), (-3476, [(-3476, -8, 0.7192)]), (-3480, [(-3480, 8, 0.7187)]), (-3487, [(-3487, 16, 1.436)]), (-3495, [(-3495, 0, 0)]), (-3508, [(-3508, 8, 0.7159)]), (-3511, [(-3511, 8, 0.3578)]), (-3535, [(-3535, -4, 0.1783)]), (-3543, [(-3543, -12, 0.8014)]), (-3544, [(-3544, -12, 1.603)]), (-3551, [(-3551, 16, 1.423)]), (-3556, [(-3556, 4, 0.3555)]), (-3560, [(-3560, 0, 0)]), (-3567, [(-3567, 8, 0.3550)]), (-3572, [(-3572, 8, 0.7094)]), (-3588, [(-3588, -16, 2.831)]), (-3592, [(-3592, 0, 0)]), (-3599, [(-3599, -12, 0.7951)]), (-3607, [(-3607, -8, 0.3530)]), (-3620, [(-3620, 12, 1.586)]), (-3623, [(-3623, 12, 0.7925)]), (-3640, [(-3640, -20, 8.785)]), (-3647, [(-3647, 12, 1.580)]), (-3655, [(-3655, -16, 1.403)]), (-3656, [(-3656, -12, 1.578)]), (-3668, [(-3668, -4, 0.3500)]), (-3679, [(-3679, -4, 0.08738)]), (-3684, [(-3684, 4, 0.1746)]), (-3704, [(-3704, -4, 0.1742)]), (-3711, [(-3711, -12, 0.7830)]), (-3719, [(-3719, -8, 0.3476)]), (-3732, [(-3732, 8, 0.6941)]), (-3752, [(-3752, -8, 1.384)]), (-3759, [(-3759, 8, 0.6916)]), (-3767, [(-3767, 12, 0.7772)]), (-3768, [(-3768, 12, 1.554)]), (-3784, [(-3784, -16, 2.757)]), (-3791, [(-3791, 8, 0.3443)]), (-3796, [(-3796, 24, 6.194)]), (-3812, [(-3812, -8, 0.6867)]), (-3815, [(-3815, -8, 0.6865)]), (-3823, [(-3823, -28, 4.200)]), (-3831, [(-3831, -12, 0.7707)]), (-3847, [(-3847, -16, 1.367)]), (-3864, [(-3864, 0, 0)]), (-3880, [(-3880, 0, 0)]), (-3892, [(-3892, 12, 3.058)]), (-3896, [(-3896, 0, 0)]), (-3903, [(-3903, -4, 0.08484)]), (-3908, [(-3908, -8, 0.6782)]), (-3927, [(-3927, 8, 0.6766)]), (-3928, [(-3928, -4, 0.1691)]), (-3935, [(-3935, 12, 0.7604)]), (-3943, [(-3943, 0, 0)]), (-3956, [(-3956, 0, 0)]), (-3959, [(-3959, -16, 1.348)]), (-3976, [(-3976, 16, 5.379)]), (-3983, [(-3983, 4, 0.1680)]), (-3991, [(-3991, -12, 0.7551)]), (-3992, [(-3992, 4, 0.1678)]), (-3999, [(-3999, 24, 3.017)]), (-4004, [(-4004, -8, 1.340)]), (-4008, [(-4008, 8, 0.6697)]), (-4015, [(-4015, 8, 0.3346)]), (-4020, [(-4020, 8, 0.6687)]), (-4036, [(-4036, 4, 0.1669)]), (-4039, [(-4039, 12, 1.501)]), (-4040, [(-4040, -4, 0.1668)]), (-4047, [(-4047, -8, 0.3332)]), (-4055, [(-4055, -4, 0.08323)]), (-4071, [(-4071, 16, 1.329)]), (-4088, [(-4088, -4, 0.3316)]), (-4103, [(-4103, 0, 0)]), (-4111, [(-4111, 0, 0)]), (-4120, [(-4120, 0, 0)]), (-4127, [(-4127, -8, 0.3300)]), (-4132, [(-4132, -24, 5.937)]), (-4148, [(-4148, -8, 0.6583)]), (-4151, [(-4151, 4, 0.1645)]), (-4152, [(-4152, -12, 1.481)]), (-4159, [(-4159, 16, 1.315)]), (-4180, [(-4180, 8, 0.6558)]), (-4183, [(-4183, -8, 0.3278)]), (-4207, [(-4207, 4, 0.1634)]), (-4215, [(-4215, 8, 0.3265)]), (-4216, [(-4216, -16, 2.612)]), (-4223, [(-4223, -16, 1.305)]), (-4228, [(-4228, 4, 0.3260)]), (-4244, [(-4244, -8, 0.6508)]), (-4260, [(-4260, 8, 0.6496)]), (-4264, [(-4264, 16, 2.597)]), (-4271, [(-4271, 8, 0.3244)]), (-4279, [(-4279, 16, 1.296)]), (-4292, [(-4292, 0, 0)]), (-4295, [(-4295, -12, 0.7278)]), (-4319, [(-4319, -12, 1.452)]), (-4327, [(-4327, 28, 3.948)]), (-4328, [(-4328, -4, 0.1611)]), (-4340, [(-4340, 8, 1.287)]), (-4344, [(-4344, 20, 4.021)]), (-4351, [(-4351, -4, 0.08035)]), (-4372, [(-4372, -16, 2.565)]), (-4376, [(-4376, 4, 0.1602)]), (-4391, [(-4391, 16, 1.280)]), (-4404, [(-4404, -16, 2.556)]), (-4407, [(-4407, 16, 1.277)]), (-4424, [(-4424, 0, 0)]), (-4431, [(-4431, 0, 0)]), (-4439, [(-4439, 16, 1.273)]), (-4440, [(-4440, 8, 0.6363)]), (-4447, [(-4447, -4, 0.07948)]), (-4452, [(-4452, 16, 5.084)]), (-4456, [(-4456, 20, 3.970)]), (-4463, [(-4463, 4, 0.07933)]), (-4468, [(-4468, -8, 0.6343)]), (-4484, [(-4484, 4, 0.1583)]), (-4487, [(-4487, -12, 1.424)]), (-4488, [(-4488, 8, 0.6329)]), (-4495, [(-4495, 8, 0.3162)]), (-4503, [(-4503, 0, 0)]), (-4516, [(-4516, -16, 2.524)]), (-4519, [(-4519, 8, 0.3154)]), (-4543, [(-4543, -16, 2.516)]), (-4551, [(-4551, -16, 1.257)]), (-4552, [(-4552, -12, 1.414)]), (-4559, [(-4559, 0, 0)]), (-4564, [(-4564, -12, 2.824)]), (-4568, [(-4568, 12, 1.412)]), (-4580, [(-4580, 12, 1.410)]), (-4596, [(-4596, 8, 0.6254)]), (-4607, [(-4607, -8, 0.3123)]), (-4615, [(-4615, 0, 0)]), (-4628, [(-4628, 8, 0.6233)]), (-4631, [(-4631, -8, 0.3115)]), (-4648, [(-4648, 12, 2.799)]), (-4663, [(-4663, 12, 0.6985)]), (-4664, [(-4664, 0, 0)]), (-4676, [(-4676, 0, 0)]), (-4687, [(-4687, -8, 0.3097)]), (-4692, [(-4692, 0, 0)]), (-4708, [(-4708, -24, 5.562)]), (-4711, [(-4711, -8, 0.6177)]), (-4712, [(-4712, 8, 0.6177)]), (-4727, [(-4727, 0, 0)]), (-4740, [(-4740, -16, 2.463)]), (-4760, [(-4760, -8, 1.229)]), (-4767, [(-4767, 4, 0.1535)]), (-4776, [(-4776, -16, 2.454)]), (-4783, [(-4783, 20, 1.916)]), (-4792, [(-4792, 12, 1.378)]), (-4799, [(-4799, -12, 0.6886)]), (-4804, [(-4804, -4, 0.1529)]), (-4820, [(-4820, 8, 0.6107)]), (-4823, [(-4823, 0, 0)]), (-4831, [(-4831, 0, 0)]), (-4839, [(-4839, 4, 0.07619)]), (-4852, [(-4852, 8, 0.6087)]), (-4855, [(-4855, 20, 1.902)]), (-4872, [(-4872, 0, 0)]), (-4879, [(-4879, 8, 0.6070)]), (-4888, [(-4888, 24, 5.458)]), (-4895, [(-4895, 16, 1.212)]), (-4904, [(-4904, -12, 1.362)]), (-4911, [(-4911, -4, 0.07563)]), (-4916, [(-4916, -8, 0.6047)]), (-4935, [(-4935, 0, 0)]), (-4936, [(-4936, -12, 1.358)]), (-4943, [(-4943, 16, 1.206)]), (-4951, [(-4951, 28, 3.691)]), (-4964, [(-4964, -8, 0.6018)]), (-4967, [(-4967, 8, 0.3008)]), (-4984, [(-4984, 4, 0.3003)]), (-4991, [(-4991, -8, 0.6002)]), (-4999, [(-4999, -24, 2.699)])]]

# map: (1 |-> 1.0) -> 1, Fractional ideal (2) -> -1, Fractional ideal (7) -> -1
[-71, -9/2 + (-13/2)*i + (-3/2)*j + k, [(5, [(5, 4, 2.658)]), (13, [(13, -4, 1.648)]), (21, [(21, -4, 2.594)]), (61, [(61, -4, 0.7610)]), (69, [(69, 8, 2.862)]), (77, [(77, 8, 5.419)]), (101, [(101, -12, 5.323)]), (133, [(133, 4, 1.031)]), (157, [(157, 4, 0.4743)]), (173, [(173, 4, 0.4519)]), (181, [(181, 4, 0.4418)]), (213, [(213, 16, 6.516)]), (229, [(229, 12, 3.535)]), (237, [(237, -8, 1.544)]), (269, [(269, -12, 3.261)]), (285, [(285, 8, 1.408)]), (293, [(293, -20, 8.681)]), (301, [(301, -8, 2.741)]), (341, [(341, 8, 1.287)]), (349, [(349, 12, 2.863)]), (357, [(357, 8, 2.516)]), (381, [(381, 0, 0)]), (397, [(397, -4, 0.2983)]), (413, [(413, 4, 0.5849)]), (437, [(437, 16, 4.549)]), (453, [(453, -16, 4.468)]), (461, [(461, 28, 13.56)]), (469, [(469, 0, 0)]), (493, [(493, -8, 1.071)]), (509, [(509, -20, 6.586)]), (517, [(517, -8, 1.046)]), (565, [(565, -16, 4.001)]), (573, [(573, 0, 0)]), (581, [(581, 4, 0.4932)]), (629, [(629, 8, 0.9479)]), (661, [(661, -4, 0.2312)]), (677, [(677, 12, 2.056)]), (685, [(685, -8, 0.9083)]), (717, [(717, -8, 0.8878)]), (733, [(733, 12, 1.976)]), (741, [(741, 8, 0.8734)]), (749, [(749, -16, 6.949)]), (773, [(773, 20, 5.344)]), (789, [(789, 16, 3.385)]), (797, [(797, -28, 10.32)]), (805, [(805, -8, 1.676)]), (829, [(829, 12, 1.858)]), (853, [(853, -4, 0.2035)]), (861, [(861, -8, 1.620)]), (885, [(885, -24, 7.192)]), (901, [(901, 0, 0)]), (917, [(917, -20, 9.813)]), (941, [(941, 20, 4.844)]), (957, [(957, 16, 3.074)]), (965, [(965, 16, 3.061)]), (973, [(973, 12, 3.430)]), (997, [(997, 12, 1.694)]), (1013, [(1013, -4, 0.1867)]), (1021, [(1021, -4, 0.1860)]), (1069, [(1069, 4, 0.1818)]), (1077, [(1077, 8, 0.7244)]), (1085, [(1085, 16, 5.774)]), (1109, [(1109, -20, 4.462)]), (1133, [(1133, 8, 0.7063)]), (1141, [(1141, 8, 1.408)]), (1165, [(1165, 8, 0.6965)]), (1181, [(1181, -28, 8.474)]), (1189, [(1189, 8, 0.6895)]), (1221, [(1221, -16, 2.721)]), (1237, [(1237, -4, 0.1690)]), (1245, [(1245, 8, 0.6738)]), (1253, [(1253, -16, 5.373)]), (1277, [(1277, -4, 0.1663)]), (1293, [(1293, -24, 5.950)]), (1301, [(1301, -12, 1.483)]), (1309, [(1309, 8, 1.314)]), (1333, [(1333, -8, 0.6512)]), (1349, [(1349, -16, 2.589)]), (1357, [(1357, 8, 0.6454)]), (1365, [(1365, 8, 1.287)]), (1389, [(1389, 24, 5.741)]), (1405, [(1405, 0, 0)]), (1461, [(1461, 16, 2.488)]), (1469, [(1469, 8, 0.6203)]), (1477, [(1477, -16, 4.949)]), (1501, [(1501, -16, 2.455)]), (1517, [(1517, 16, 2.442)]), (1533, [(1533, -8, 1.214)]), (1581, [(1581, -32, 9.567)]), (1589, [(1589, 20, 7.455)]), (1613, [(1613, -12, 1.332)]), (1637, [(1637, -4, 0.1469)]), (1645, [(1645, -16, 4.689)]), (1669, [(1669, 4, 0.1455)]), (1685, [(1685, 32, 9.267)]), (1693, [(1693, -4, 0.1444)]), (1741, [(1741, -4, 0.1424)]), (1749, [(1749, -32, 9.095)]), (1757, [(1757, -12, 2.552)]), (1781, [(1781, -8, 0.5633)]), (1797, [(1797, -16, 2.243)]), (1837, [(1837, -16, 2.219)]), (1853, [(1853, 40, 13.81)]), (1861, [(1861, -12, 1.240)]), (1869, [(1869, -8, 1.100)]), (1893, [(1893, 24, 4.918)]), (1909, [(1909, 0, 0)]), (1949, [(1949, 12, 1.212)]), (1965, [(1965, -8, 0.5363)]), (1973, [(1973, 12, 1.204)]), (1981, [(1981, -4, 0.2671)]), (2005, [(2005, 8, 0.5309)]), (2021, [(2021, -24, 4.759)]), (2029, [(2029, 4, 0.1319)]), (2037, [(2037, 8, 1.053)]), (2077, [(2077, 0, 0)]), (2085, [(2085, -8, 0.5207)]), (2093, [(2093, 0, 0)]), (2117, [(2117, -24, 4.650)]), (2141, [(2141, 4, 0.1284)]), (2149, [(2149, 4, 0.2564)]), (2173, [(2173, -24, 4.590)]), (2189, [(2189, -8, 0.5081)]), (2229, [(2229, 8, 0.5035)]), (2245, [(2245, -16, 2.007)]), (2253, [(2253, 32, 8.014)]), (2261, [(2261, 24, 9.000)]), (2285, [(2285, -32, 7.957)]), (2301, [(2301, -24, 4.461)]), (2309, [(2309, -28, 6.061)]), (2317, [(2317, 8, 0.9878)]), (2341, [(2341, 12, 1.106)]), (2357, [(2357, -12, 1.102)]), (2365, [(2365, 0, 0)]), (2373, [(2373, -16, 3.904)]), (2397, [(2397, -16, 1.942)]), (2413, [(2413, 8, 0.4840)]), (2429, [(2429, 24, 8.683)]), (2453, [(2453, -24, 4.320)]), (2469, [(2469, 8, 0.4785)]), (2477, [(2477, 20, 2.986)]), (2485, [(2485, 8, 0.9538)]), (2509, [(2509, 16, 1.898)]), (2533, [(2533, 16, 1.889)]), (2581, [(2581, 24, 4.212)]), (2589, [(2589, 0, 0)]), (2621, [(2621, 12, 1.045)]), (2653, [(2653, -8, 0.9231)]), (2677, [(2677, 12, 1.034)]), (2693, [(2693, 20, 2.863)]), (2701, [(2701, -16, 1.830)]), (2733, [(2733, -8, 0.4548)]), (2749, [(2749, -20, 2.834)]), (2757, [(2757, 24, 4.075)]), (2765, [(2765, -24, 8.138)]), (2789, [(2789, -4, 0.1125)]), (2805, [(2805, 16, 1.796)]), (2813, [(2813, -40, 11.21)]), (2821, [(2821, 16, 3.581)]), (2845, [(2845, 24, 4.011)]), (2861, [(2861, 20, 2.778)]), (2869, [(2869, -24, 3.995)]), (2877, [(2877, -8, 0.8865)]), (2901, [(2901, 16, 1.766)]), (2917, [(2917, 12, 0.9904)]), (2933, [(2933, -28, 10.76)]), (2957, [(2957, -20, 2.732)]), (2973, [(2973, -8, 0.4360)]), (2981, [(2981, 0, 0)]), (3013, [(3013, -8, 0.4331)]), (3029, [(3029, -16, 1.728)]), (3037, [(3037, -4, 0.1078)]), (3045, [(3045, -16, 3.447)]), (3085, [(3085, 16, 1.712)]), (3093, [(3093, 16, 1.710)]), (3101, [(3101, 16, 3.415)]), (3149, [(3149, -8, 0.4237)]), (3157, [(3157, -8, 0.8462)]), (3181, [(3181, 12, 0.9484)]), (3197, [(3197, 24, 3.784)]), (3205, [(3205, -8, 0.4199)]), (3237, [(3237, -8, 0.4179)]), (3253, [(3253, -4, 0.1042)]), (3261, [(3261, 0, 0)]), (3269, [(3269, 28, 10.19)]), (3293, [(3293, 24, 3.729)]), (3309, [(3309, 8, 0.4133)]), (3317, [(3317, 32, 6.605)]), (3349, [(3349, -24, 3.697)]), (3365, [(3365, -24, 3.689)]), (3373, [(3373, 4, 0.1023)]), (3405, [(3405, -8, 0.4074)]), (3421, [(3421, -24, 3.658)]), (3437, [(3437, 0, 0)]), (3461, [(3461, 4, 0.1010)]), (3477, [(3477, -40, 10.08)]), (3485, [(3485, -16, 1.611)]), (3493, [(3493, 0, 0)]), (3517, [(3517, -4, 0.1002)]), (3533, [(3533, 4, 0.09999)]), (3541, [(3541, 20, 2.497)]), (3589, [(3589, -8, 0.3968)]), (3597, [(3597, 0, 0)]), (3605, [(3605, 0, 0)]), (3629, [(3629, 24, 3.552)]), (3653, [(3653, 40, 9.834)]), (3661, [(3661, -4, 0.1965)]), (3685, [(3685, -32, 6.266)]), (3701, [(3701, -28, 4.787)]), (3709, [(3709, -12, 0.8783)]), (3741, [(3741, 0, 0)]), (3765, [(3765, -8, 0.3874)]), (3797, [(3797, 36, 7.813)]), (3813, [(3813, 0, 0)]), (3821, [(3821, 12, 0.8654)]), (3829, [(3829, -8, 0.7684)]), (3853, [(3853, 12, 0.8618)]), (3869, [(3869, -8, 0.3822)]), (3877, [(3877, -12, 0.8591)]), (3885, [(3885, 32, 12.21)]), (3909, [(3909, -16, 1.521)]), (3941, [(3941, 12, 1.704)]), (3965, [(3965, 8, 0.3776)]), (3981, [(3981, 24, 3.391)]), (3989, [(3989, 20, 2.353)]), (3997, [(3997, -8, 0.7521)]), (4021, [(4021, 12, 0.8436)]), (4037, [(4037, 40, 9.354)]), (4045, [(4045, 24, 3.364)]), (4053, [(4053, 8, 0.7469)]), (4093, [(4093, 12, 0.8361)]), (4101, [(4101, -32, 5.940)]), (4109, [(4109, -20, 4.636)]), (4133, [(4133, -12, 0.8321)]), (4157, [(4157, -28, 4.517)]), (4189, [(4189, -8, 0.3673)]), (4213, [(4213, -8, 0.3663)]), (4245, [(4245, 40, 9.122)]), (4261, [(4261, -4, 0.09105)]), (4269, [(4269, -32, 5.822)]), (4277, [(4277, -16, 2.908)]), (4301, [(4301, -32, 5.800)]), (4317, [(4317, 24, 3.257)]), (4333, [(4333, 4, 0.1806)]), (4357, [(4357, -12, 0.8104)]), (4373, [(4373, -4, 0.08988)]), (4381, [(4381, 8, 0.3592)]), (4389, [(4389, 0, 0)]), (4413, [(4413, -8, 0.3579)]), (4429, [(4429, 24, 3.215)]), (4445, [(4445, -24, 6.419)]), (4469, [(4469, 40, 8.891)]), (4485, [(4485, 32, 5.680)]), (4493, [(4493, -36, 7.182)]), (4501, [(4501, -12, 1.595)]), (4541, [(4541, -16, 1.411)]), (4549, [(4549, -4, 0.08812)]), (4597, [(4597, 12, 0.7889)]), (4605, [(4605, 40, 8.758)]), (4613, [(4613, -8, 0.7001)]), (4637, [(4637, 44, 10.56)]), (4661, [(4661, -24, 3.134)]), (4669, [(4669, -16, 2.783)]), (4709, [(4709, -8, 0.3464)]), (4717, [(4717, 32, 5.538)]), (4749, [(4749, 0, 0)]), (4765, [(4765, 24, 3.100)]), (4773, [(4773, -32, 5.506)]), (4781, [(4781, -16, 2.751)]), (4821, [(4821, 0, 0)]), (4829, [(4829, 64, 21.90)]), (4837, [(4837, 12, 1.538)]), (4861, [(4861, 4, 0.08525)]), (4877, [(4877, 20, 2.128)]), (4885, [(4885, 8, 0.3401)]), (4893, [(4893, 24, 6.118)]), (4917, [(4917, 0, 0)]), (4933, [(4933, -12, 0.7616)]), (4973, [(4973, -4, 0.08428)]), (4989, [(4989, -16, 1.346)]), (4997, [(4997, -40, 8.408)])]]

# map: (1 |-> 1.0) -> 1, Fractional ideal (2) -> 1, Fractional ideal (7) -> 1
[-3, -11/2 + (-3)*i + (-1/2)*j + 1/2*k, [(1, [(1, -2/3, 0.3302)]), (8, [(8, -2, 2.101)]), (44, [(44, 4, 3.584)]), (57, [(57, 4, 1.574)]), (60, [(60, 4, 3.069)]), (65, [(65, 4, 1.474)]), (88, [(88, 0, 0)]), (92, [(92, 4, 2.479)]), (113, [(113, -4, 1.118)]), (120, [(120, -4, 2.170)]), (137, [(137, -8, 4.062)]), (156, [(156, -4, 1.903)]), (172, [(172, -4, 1.813)]), (177, [(177, -4, 0.8935)]), (184, [(184, -4, 1.753)]), (193, [(193, 4, 0.8557)]), (204, [(204, 0, 0)]), (232, [(232, 4, 1.561)]), (233, [(233, 0, 0)]), (249, [(249, -4, 0.7533)]), (268, [(268, 4, 1.452)]), (281, [(281, 8, 2.837)]), (284, [(284, 0, 0)]), (296, [(296, 4, 1.382)]), (305, [(305, 12, 6.126)]), (312, [(312, -4, 1.346)]), (316, [(316, 0, 0)]), (337, [(337, 4, 0.6475)]), (344, [(344, 8, 5.127)]), (345, [(345, 0, 0)]), (380, [(380, -4, 1.220)]), (393, [(393, 4, 0.5996)]), (401, [(401, -4, 0.5936)]), (408, [(408, 8, 4.708)]), (417, [(417, -4, 0.5821)]), (424, [(424, 4, 1.155)]), (428, [(428, -4, 1.149)]), (449, [(449, -8, 2.244)]), (456, [(456, -4, 1.113)]), (457, [(457, -4, 0.5561)]), (473, [(473, 0, 0)]), (492, [(492, -8, 4.287)]), (505, [(505, -4, 0.5290)]), (508, [(508, -4, 1.055)]), (520, [(520, -4, 1.043)]), (536, [(536, 8, 4.108)]), (561, [(561, -8, 2.008)]), (568, [(568, 0, 0)]), (569, [(569, -12, 4.485)]), (604, [(604, 4, 0.9674)]), (617, [(617, 4, 0.4786)]), (620, [(620, 8, 3.819)]), (632, [(632, 0, 0)]), (641, [(641, -4, 0.4695)]), (652, [(652, -4, 0.9311)]), (673, [(673, 0, 0)]), (680, [(680, 8, 3.647)]), (681, [(681, 12, 4.100)]), (697, [(697, 0, 0)]), (716, [(716, -4, 0.8885)]), (732, [(732, 4, 0.8787)]), (737, [(737, 8, 1.751)]), (744, [(744, 8, 3.486)]), (753, [(753, 4, 0.4332)]), (760, [(760, 4, 0.8624)]), (764, [(764, 0, 0)]), (785, [(785, 12, 3.818)]), (793, [(793, -4, 0.4221)]), (809, [(809, 4, 0.4179)]), (844, [(844, 4, 0.8184)]), (849, [(849, -4, 0.4080)]), (856, [(856, 0, 0)]), (865, [(865, -4, 0.4042)]), (872, [(872, 4, 0.8051)]), (876, [(876, 8, 3.213)]), (897, [(897, -8, 1.588)]), (904, [(904, -4, 0.7907)]), (905, [(905, 4, 0.3951)]), (921, [(921, 4, 0.3917)]), (940, [(940, 0, 0)]), (953, [(953, -8, 1.540)]), (956, [(956, -12, 6.920)]), (977, [(977, 8, 1.521)]), (984, [(984, -8, 3.032)]), (988, [(988, -4, 0.7564)]), (1009, [(1009, 4, 0.3742)]), (1016, [(1016, -12, 6.713)]), (1033, [(1033, -8, 1.479)]), (1052, [(1052, 8, 2.932)]), (1065, [(1065, 0, 0)]), (1068, [(1068, 0, 0)]), (1073, [(1073, -16, 5.806)]), (1096, [(1096, 0, 0)]), (1121, [(1121, -4, 0.3550)]), (1128, [(1128, 0, 0)]), (1129, [(1129, 0, 0)]), (1145, [(1145, -4, 0.3513)]), (1164, [(1164, -8, 2.787)]), (1177, [(1177, -8, 1.386)]), (1180, [(1180, -4, 0.6921)]), (1185, [(1185, -8, 1.381)]), (1192, [(1192, -4, 0.6886)]), (1201, [(1201, 4, 0.3430)]), (1208, [(1208, -12, 6.156)]), (1212, [(1212, 4, 0.6829)]), (1240, [(1240, 8, 2.701)]), (1241, [(1241, 8, 1.350)]), (1257, [(1257, 12, 3.018)]), (1276, [(1276, 8, 2.662)]), (1289, [(1289, -4, 0.3311)]), (1292, [(1292, 8, 2.646)]), (1297, [(1297, 4, 0.3301)]), (1304, [(1304, 0, 0)]), (1313, [(1313, -12, 2.952)]), (1320, [(1320, -8, 2.617)]), (1324, [(1324, 4, 0.6534)]), (1345, [(1345, 12, 2.917)]), (1353, [(1353, 8, 1.293)]), (1388, [(1388, 4, 0.6381)]), (1401, [(1401, 4, 0.3176)]), (1409, [(1409, 16, 5.067)]), (1416, [(1416, -4, 0.6318)]), (1432, [(1432, 8, 2.513)]), (1436, [(1436, 12, 5.646)]), (1457, [(1457, 0, 0)]), (1464, [(1464, 4, 0.6214)]), (1465, [(1465, -4, 0.3106)]), (1481, [(1481, 0, 0)]), (1513, [(1513, 0, 0)]), (1516, [(1516, -4, 0.6106)]), (1528, [(1528, 0, 0)]), (1537, [(1537, 0, 0)]), (1544, [(1544, -4, 0.6050)]), (1569, [(1569, -4, 0.3001)]), (1576, [(1576, -4, 0.5989)]), (1577, [(1577, 12, 2.694)]), (1612, [(1612, 0, 0)]), (1628, [(1628, -8, 2.357)]), (1633, [(1633, 8, 1.177)]), (1640, [(1640, -8, 2.348)]), (1649, [(1649, -16, 4.684)]), (1660, [(1660, -4, 0.5835)]), (1688, [(1688, -8, 2.315)]), (1689, [(1689, -4, 0.2892)]), (1705, [(1705, -8, 1.152)]), (1724, [(1724, -4, 0.5726)]), (1740, [(1740, 0, 0)]), (1745, [(1745, -4, 0.2846)]), (1752, [(1752, 0, 0)]), (1761, [(1761, -12, 2.549)]), (1768, [(1768, 0, 0)]), (1772, [(1772, -12, 5.083)]), (1793, [(1793, 0, 0)]), (1801, [(1801, -12, 2.521)]), (1817, [(1817, 16, 4.462)]), (1852, [(1852, 8, 2.210)]), (1857, [(1857, -4, 0.2759)]), (1864, [(1864, 0, 0)]), (1873, [(1873, 0, 0)]), (1880, [(1880, -8, 2.193)]), (1884, [(1884, -4, 0.5477)]), (1905, [(1905, -8, 1.089)]), (1912, [(1912, -4, 0.5437)]), (1913, [(1913, -4, 0.2718)]), (1929, [(1929, 12, 2.436)]), (1948, [(1948, -4, 0.5387)]), (1961, [(1961, -8, 1.074)]), (1964, [(1964, 4, 0.5365)]), (1969, [(1969, 0, 0)]), (1976, [(1976, 4, 0.5348)]), (1985, [(1985, -12, 2.401)]), (1992, [(1992, 4, 0.5327)]), (1996, [(1996, -4, 0.5321)]), (2017, [(2017, 0, 0)]), (2024, [(2024, 0, 0)]), (2041, [(2041, 4, 0.2631)]), (2060, [(2060, 8, 2.095)]), (2073, [(2073, 20, 6.527)]), (2076, [(2076, 4, 0.5218)]), (2081, [(2081, 0, 0)]), (2104, [(2104, -8, 2.073)]), (2108, [(2108, -8, 2.071)]), (2129, [(2129, 16, 4.122)]), (2136, [(2136, 0, 0)]), (2137, [(2137, 8, 1.029)]), (2153, [(2153, 4, 0.2562)]), (2172, [(2172, 4, 0.5101)]), (2185, [(2185, -8, 1.017)]), (2188, [(2188, -4, 0.5083)]), (2193, [(2193, 0, 0)]), (2216, [(2216, 12, 4.545)]), (2220, [(2220, 0, 0)]), (2248, [(2248, 8, 2.006)]), (2249, [(2249, -4, 0.2507)]), (2265, [(2265, 0, 0)]), (2284, [(2284, 4, 0.4975)]), (2297, [(2297, -4, 0.2480)]), (2305, [(2305, 4, 0.2476)]), (2321, [(2321, 8, 0.9870)]), (2328, [(2328, 8, 1.971)]), (2332, [(2332, 8, 1.969)]), (2353, [(2353, 4, 0.2451)]), (2360, [(2360, 12, 4.404)]), (2361, [(2361, 12, 2.202)]), (2377, [(2377, 0, 0)]), (2396, [(2396, -16, 7.771)]), (2409, [(2409, 8, 0.9688)]), (2417, [(2417, -16, 3.869)]), (2424, [(2424, 4, 0.4829)]), (2433, [(2433, -12, 2.169)]), (2440, [(2440, 4, 0.4813)]), (2444, [(2444, -16, 7.695)]), (2465, [(2465, 8, 0.9577)]), (2472, [(2472, 0, 0)]), (2473, [(2473, -4, 0.2390)]), (2489, [(2489, 12, 2.144)]), (2508, [(2508, 8, 1.899)]), (2521, [(2521, -4, 0.2368)]), (2524, [(2524, 0, 0)]), (2536, [(2536, 4, 0.4721)]), (2545, [(2545, -4, 0.2356)]), (2552, [(2552, 8, 1.882)]), (2577, [(2577, -4, 0.2342)]), (2584, [(2584, -8, 1.871)]), (2585, [(2585, 8, 0.9352)]), (2620, [(2620, -12, 4.180)]), (2633, [(2633, -20, 5.792)]), (2636, [(2636, -12, 4.167)]), (2641, [(2641, -4, 0.2313)]), (2648, [(2648, -8, 1.848)]), (2657, [(2657, 0, 0)]), (2668, [(2668, 0, 0)]), (2689, [(2689, -4, 0.2292)]), (2696, [(2696, 4, 0.4579)]), (2697, [(2697, 8, 0.9156)]), (2713, [(2713, 0, 0)]), (2732, [(2732, -12, 4.094)]), (2748, [(2748, 4, 0.4535)]), (2753, [(2753, -8, 0.9062)]), (2760, [(2760, 0, 0)]), (2769, [(2769, -8, 0.9036)]), (2776, [(2776, -8, 1.805)]), (2780, [(2780, -4, 0.4509)]), (2801, [(2801, -4, 0.2246)]), (2857, [(2857, 0, 0)]), (2860, [(2860, 8, 1.778)]), (2865, [(2865, -16, 3.553)]), (2872, [(2872, 4, 0.4436)]), (2881, [(2881, 8, 0.8859)]), (2892, [(2892, -8, 1.768)]), (2913, [(2913, -4, 0.2202)]), (2920, [(2920, 0, 0)]), (2921, [(2921, 0, 0)]), (2937, [(2937, -16, 3.510)]), (2956, [(2956, -4, 0.4373)]), (2969, [(2969, 16, 3.491)]), (2972, [(2972, 4, 0.4361)]), (2977, [(2977, 4, 0.2179)]), (2984, [(2984, -20, 10.88)]), (2993, [(2993, 0, 0)]), (3004, [(3004, 4, 0.4338)]), (3032, [(3032, 8, 1.727)]), (3049, [(3049, -4, 0.2153)]), (3068, [(3068, -12, 3.863)]), (3081, [(3081, -8, 0.8566)]), (3084, [(3084, -8, 1.712)]), (3089, [(3089, 12, 1.925)]), (3112, [(3112, -12, 3.836)]), (3116, [(3116, 8, 1.704)]), (3137, [(3137, 12, 1.910)]), (3144, [(3144, 12, 3.816)]), (3145, [(3145, 8, 0.8479)]), (3161, [(3161, 8, 0.8457)]), (3180, [(3180, 16, 6.745)]), (3193, [(3193, -8, 0.8415)]), (3196, [(3196, -8, 1.682)]), (3201, [(3201, 0, 0)]), (3208, [(3208, 4, 0.4198)]), (3217, [(3217, 4, 0.2096)]), (3224, [(3224, 8, 1.675)]), (3228, [(3228, -4, 0.4184)]), (3256, [(3256, 8, 1.667)]), (3257, [(3257, -12, 1.875)]), (3273, [(3273, 12, 1.870)]), (3292, [(3292, 0, 0)]), (3305, [(3305, 12, 1.861)]), (3308, [(3308, -4, 0.4134)]), (3313, [(3313, 8, 0.8261)]), (3320, [(3320, 12, 3.713)]), (3329, [(3329, -4, 0.2060)]), (3336, [(3336, 12, 3.705)]), (3340, [(3340, 8, 1.645)]), (3361, [(3361, 4, 0.2050)]), (3368, [(3368, -12, 3.687)]), (3369, [(3369, 4, 0.2048)]), (3385, [(3385, 12, 1.839)]), (3404, [(3404, 8, 1.630)]), (3417, [(3417, 16, 3.254)]), (3432, [(3432, -8, 1.623)]), (3441, [(3441, -8, 0.8106)]), (3448, [(3448, 4, 0.4049)]), (3452, [(3452, 16, 6.474)]), (3473, [(3473, 0, 0)]), (3480, [(3480, -8, 1.612)]), (3497, [(3497, -4, 0.2010)]), (3516, [(3516, 4, 0.4009)]), (3529, [(3529, 0, 0)]), (3532, [(3532, -4, 0.4000)]), (3544, [(3544, -8, 1.597)]), (3553, [(3553, 8, 0.7977)]), (3560, [(3560, -8, 1.594)]), (3585, [(3585, -8, 0.7941)]), (3592, [(3592, 0, 0)]), (3593, [(3593, -8, 0.7933)]), (3628, [(3628, -4, 0.3947)]), (3641, [(3641, -8, 0.7880)]), (3644, [(3644, -4, 0.3938)]), (3649, [(3649, 8, 0.7871)]), (3656, [(3656, 12, 3.539)]), (3665, [(3665, 20, 4.909)]), (3676, [(3676, 0, 0)]), (3697, [(3697, 8, 0.7820)]), (3704, [(3704, -8, 1.563)]), (3705, [(3705, -8, 0.7812)]), (3740, [(3740, 8, 1.555)]), (3756, [(3756, 0, 0)]), (3761, [(3761, -4, 0.1938)]), (3768, [(3768, -12, 3.486)]), (3777, [(3777, -12, 1.741)]), (3784, [(3784, 0, 0)]), (3788, [(3788, 4, 0.3863)]), (3809, [(3809, -20, 4.815)]), (3817, [(3817, -16, 3.078)]), (3833, [(3833, -16, 3.072)]), (3865, [(3865, -12, 1.721)]), (3868, [(3868, 12, 3.440)]), (3873, [(3873, -12, 1.719)]), (3880, [(3880, 8, 1.527)]), (3889, [(3889, -12, 1.716)]), (3896, [(3896, -4, 0.3809)]), (3921, [(3921, -4, 0.1898)]), (3928, [(3928, -8, 1.517)]), (3929, [(3929, -4, 0.1896)]), (3945, [(3945, 8, 0.7570)]), (3964, [(3964, 0, 0)]), (3977, [(3977, 8, 0.7540)]), (3980, [(3980, 16, 6.030)]), (3985, [(3985, 4, 0.1883)]), (3992, [(3992, -16, 6.021)]), (4001, [(4001, 0, 0)]), (4008, [(4008, 8, 1.502)]), (4012, [(4012, -8, 1.501)]), (4033, [(4033, 0, 0)]), (4040, [(4040, -4, 0.3740)]), (4057, [(4057, -4, 0.1866)]), (4076, [(4076, 4, 0.3724)]), (4089, [(4089, 8, 0.7436)]), (4092, [(4092, -8, 1.487)]), (4097, [(4097, 8, 0.7429)]), (4120, [(4120, -8, 1.482)]), (4124, [(4124, -8, 1.481)]), (4145, [(4145, -20, 4.616)]), (4152, [(4152, 4, 0.3690)]), (4153, [(4153, -4, 0.1845)]), (4169, [(4169, 16, 2.946)]), (4188, [(4188, 12, 3.306)]), (4201, [(4201, 4, 0.1834)]), (4204, [(4204, 4, 0.3667)]), (4209, [(4209, 0, 0)]), (4216, [(4216, 8, 1.465)]), (4236, [(4236, 8, 1.461)]), (4264, [(4264, 0, 0)]), (4265, [(4265, 20, 4.550)]), (4281, [(4281, -12, 1.635)]), (4313, [(4313, -4, 0.1810)]), (4316, [(4316, 4, 0.3619)]), (4321, [(4321, 8, 0.7234)]), (4328, [(4328, -4, 0.3614)]), (4337, [(4337, -20, 4.513)]), (4344, [(4344, 12, 3.246)]), (4348, [(4348, 4, 0.3605)]), (4369, [(4369, 8, 0.7194)]), (4376, [(4376, -16, 5.750)]), (4377, [(4377, -4, 0.1797)]), (4393, [(4393, 0, 0)]), (4412, [(4412, 20, 8.948)]), (4433, [(4433, 24, 6.427)]), (4440, [(4440, -8, 1.427)]), (4449, [(4449, 12, 1.604)]), (4456, [(4456, 4, 0.3562)]), (4460, [(4460, 8, 1.424)]), (4481, [(4481, 12, 1.598)]), (4488, [(4488, 8, 1.420)]), (4505, [(4505, -16, 2.834)]), (4524, [(4524, 0, 0)]), (4537, [(4537, -4, 0.1765)]), (4540, [(4540, 4, 0.3528)]), (4552, [(4552, 4, 0.3524)]), (4561, [(4561, 8, 0.7041)]), (4568, [(4568, 8, 1.407)]), (4593, [(4593, -4, 0.1754)]), (4601, [(4601, 8, 0.7010)]), (4636, [(4636, -4, 0.3492)]), (4649, [(4649, 24, 6.276)]), (4652, [(4652, -4, 0.3486)]), (4657, [(4657, -8, 0.6968)]), (4664, [(4664, 8, 1.392)]), (4673, [(4673, 16, 2.782)]), (4684, [(4684, 12, 3.126)]), (4705, [(4705, -4, 0.1733)]), (4712, [(4712, 0, 0)]), (4713, [(4713, 12, 1.558)]), (4729, [(4729, 0, 0)]), (4748, [(4748, -4, 0.3450)]), (4764, [(4764, -12, 3.100)]), (4769, [(4769, 4, 0.1721)]), (4776, [(4776, -16, 5.504)]), (4785, [(4785, 16, 2.750)]), (4792, [(4792, 0, 0)]), (4796, [(4796, 0, 0)]), (4817, [(4817, 0, 0)]), (4841, [(4841, -24, 6.151)]), (4873, [(4873, 0, 0)]), (4876, [(4876, 8, 1.362)]), (4881, [(4881, 12, 1.531)]), (4888, [(4888, 8, 1.360)]), (4897, [(4897, -4, 0.1699)]), (4904, [(4904, -12, 3.055)]), (4908, [(4908, 0, 0)]), (4929, [(4929, -8, 0.6773)]), (4936, [(4936, -4, 0.3384)]), (4937, [(4937, -4, 0.1692)]), (4953, [(4953, 0, 0)]), (4972, [(4972, -8, 1.349)]), (4985, [(4985, -12, 1.515)]), (4988, [(4988, 0, 0)]), (4993, [(4993, -8, 0.6729)])]]