# label = 75.2.a.b
# Base field F = Number Field in a with defining polynomial x - 1
# Quaternion algebra given by i^2 = -3, j^2 = -1
# Order with basis over the integers given by [1, 1/2 + 25/2*i, 5*i + j, 6*i + 1/2*j + 1/2*k]

# Nmax = 10000

[(1, [1/2 + 175/2*i, 5*i + j, 1/2 + 237/14*i + 1/14*j + 1/14*k]), (1, [1/2 + 175/2*i, 5*i + j, 1/2 + 237/14*i + 1/14*j + 1/14*k]), (-1, [1/2 + 175/2*i, (-45/7)*i + 1/7*j, 2/7*i + 1/14*j + 1/2*k]), (-1, [1/2 + 175/2*i, (-45/7)*i + 1/7*j, 2/7*i + 1/14*j + 1/2*k])]
[((3,), 3 + 5*i + j), ((5,), -3/2 + 11/2*i + 3/2*j + 3/2*k)]

# map: (1 |-> 1.0) -> -1, Fractional ideal (3) -> -1, Fractional ideal (5) -> -1
[13, 13 + 35*i + 2*j, [(-3, [(-3, -2, 0.8243)]), (-7, [(-7, 4, 1.079)]), (-43, [(-43, 4, 0.4355)]), (-52, [(-52, 0, 0)]), (-67, [(-67, 4, 0.3489)]), (-87, [(-87, 4, 0.6123)]), (-88, [(-88, 8, 1.218)]), (-103, [(-103, -12, 2.532)]), (-123, [(-123, -4, 0.5149)]), (-127, [(-127, -12, 2.280)]), (-132, [(-132, 8, 1.988)]), (-148, [(-148, -16, 3.755)]), (-163, [(-163, 4, 0.2237)]), (-168, [(-168, 8, 1.762)]), (-183, [(-183, 8, 1.689)]), (-187, [(-187, -8, 0.8352)]), (-223, [(-223, 12, 1.721)]), (-228, [(-228, 0, 0)]), (-232, [(-232, 8, 0.7499)]), (-247, [(-247, -8, 0.7268)]), (-267, [(-267, -4, 0.3495)]), (-283, [(-283, -4, 0.1697)]), (-292, [(-292, -8, 0.6684)]), (-303, [(-303, -12, 2.953)]), (-307, [(-307, 12, 1.467)]), (-312, [(-312, -16, 5.173)]), (-327, [(-327, -8, 1.263)]), (-328, [(-328, 0, 0)]), (-367, [(-367, 20, 3.726)]), (-372, [(-372, 0, 0)]), (-388, [(-388, 8, 0.5799)]), (-403, [(-403, -8, 0.5690)]), (-408, [(-408, -16, 4.524)]), (-427, [(-427, -8, 0.5527)]), (-447, [(-447, -4, 0.2701)]), (-463, [(-463, -4, 0.1327)]), (-472, [(-472, 8, 0.5257)]), (-483, [(-483, 8, 1.039)]), (-487, [(-487, 12, 1.165)]), (-523, [(-523, 4, 0.1249)]), (-532, [(-532, -16, 1.981)]), (-543, [(-543, -8, 0.9803)]), (-547, [(-547, -4, 0.1221)]), (-552, [(-552, 0, 0)]), (-568, [(-568, 0, 0)]), (-583, [(-583, 16, 1.892)]), (-607, [(-607, 4, 0.1159)]), (-627, [(-627, 8, 0.9123)]), (-628, [(-628, 16, 1.823)]), (-643, [(-643, -4, 0.1126)]), (-663, [(-663, -8, 0.8872)]), (-667, [(-667, 0, 0)]), (-687, [(-687, 16, 3.486)]), (-703, [(-703, -8, 0.4308)]), (-708, [(-708, 8, 0.8585)]), (-712, [(-712, -16, 1.712)]), (-723, [(-723, 0, 0)]), (-727, [(-727, -12, 0.9531)]), (-763, [(-763, -16, 1.654)]), (-772, [(-772, 8, 0.4111)]), (-787, [(-787, 4, 0.1018)]), (-807, [(-807, -4, 0.2010)]), (-808, [(-808, -24, 3.616)]), (-823, [(-823, 20, 2.488)]), (-843, [(-843, 4, 0.1967)]), (-852, [(-852, 16, 3.130)]), (-868, [(-868, 0, 0)]), (-883, [(-883, -4, 0.09609)]), (-888, [(-888, -16, 3.066)]), (-903, [(-903, 0, 0)]), (-907, [(-907, -20, 2.370)]), (-943, [(-943, -16, 1.488)]), (-948, [(-948, 0, 0)]), (-952, [(-952, 16, 1.481)]), (-967, [(-967, -4, 0.09183)]), (-987, [(-987, 0, 0)]), (-1003, [(-1003, 16, 1.443)]), (-1012, [(-1012, 16, 1.436)]), (-1023, [(-1023, 16, 2.857)]), (-1027, [(-1027, 16, 1.426)]), (-1032, [(-1032, 0, 0)]), (-1047, [(-1047, -8, 0.7060)]), (-1048, [(-1048, 24, 3.175)]), (-1063, [(-1063, -4, 0.08758)]), (-1087, [(-1087, 20, 2.165)]), (-1092, [(-1092, -16, 2.765)]), (-1108, [(-1108, 16, 1.373)]), (-1123, [(-1123, 4, 0.08521)]), (-1128, [(-1128, 16, 2.721)]), (-1147, [(-1147, 8, 0.3373)]), (-1167, [(-1167, -4, 0.1672)]), (-1192, [(-1192, 8, 0.3308)]), (-1203, [(-1203, -4, 0.1647)]), (-1207, [(-1207, -8, 0.3288)]), (-1227, [(-1227, -8, 0.6521)]), (-1243, [(-1243, 0, 0)]), (-1252, [(-1252, 8, 0.3228)]), (-1263, [(-1263, 0, 0)]), (-1267, [(-1267, -8, 0.3209)]), (-1272, [(-1272, 0, 0)]), (-1288, [(-1288, -32, 5.092)]), (-1303, [(-1303, -20, 1.978)]), (-1327, [(-1327, -4, 0.07839)]), (-1347, [(-1347, -4, 0.1556)]), (-1348, [(-1348, -24, 2.800)]), (-1363, [(-1363, 8, 0.3094)]), (-1383, [(-1383, 4, 0.1536)]), (-1387, [(-1387, 16, 1.227)]), (-1407, [(-1407, 0, 0)]), (-1423, [(-1423, 4, 0.07570)]), (-1428, [(-1428, 0, 0)]), (-1432, [(-1432, 8, 0.3018)]), (-1443, [(-1443, -8, 0.6014)]), (-1447, [(-1447, 12, 0.6756)]), (-1483, [(-1483, 12, 0.6673)]), (-1492, [(-1492, -16, 1.183)]), (-1507, [(-1507, 0, 0)]), (-1527, [(-1527, 20, 3.654)]), (-1528, [(-1528, 16, 1.169)]), (-1543, [(-1543, -4, 0.07269)]), (-1563, [(-1563, -20, 3.611)]), (-1567, [(-1567, -4, 0.07213)]), (-1572, [(-1572, 8, 0.5762)]), (-1588, [(-1588, 0, 0)]), (-1603, [(-1603, 8, 0.2853)]), (-1608, [(-1608, 16, 2.279)]), (-1623, [(-1623, 8, 0.5670)]), (-1627, [(-1627, -4, 0.07079)]), (-1663, [(-1663, -12, 0.6302)]), (-1668, [(-1668, -16, 2.237)]), (-1672, [(-1672, -32, 4.469)]), (-1687, [(-1687, 24, 2.503)]), (-1707, [(-1707, 4, 0.1382)]), (-1723, [(-1723, -12, 0.6191)]), (-1732, [(-1732, -24, 2.470)]), (-1743, [(-1743, 32, 8.755)]), (-1747, [(-1747, -12, 0.6149)]), (-1752, [(-1752, -8, 0.5458)]), (-1767, [(-1767, 16, 2.174)]), (-1768, [(-1768, 16, 1.087)]), (-1783, [(-1783, -12, 0.6086)]), (-1803, [(-1803, 8, 0.5380)]), (-1807, [(-1807, -16, 1.075)]), (-1812, [(-1812, 16, 2.147)]), (-1828, [(-1828, -8, 0.2671)]), (-1843, [(-1843, -8, 0.2661)]), (-1848, [(-1848, 0, 0)]), (-1867, [(-1867, 4, 0.06609)]), (-1887, [(-1887, 0, 0)]), (-1903, [(-1903, 8, 0.2618)]), (-1912, [(-1912, -32, 4.179)]), (-1923, [(-1923, 12, 1.172)]), (-1927, [(-1927, -8, 0.2602)]), (-1947, [(-1947, 0, 0)]), (-1963, [(-1963, 8, 0.2578)]), (-1972, [(-1972, 32, 4.115)]), (-1983, [(-1983, -8, 0.5130)]), (-1987, [(-1987, -4, 0.06406)]), (-1992, [(-1992, 16, 2.047)]), (-2008, [(-2008, -8, 0.2549)]), (-2047, [(-2047, -8, 0.2524)]), (-2067, [(-2067, -8, 0.5025)]), (-2068, [(-2068, -16, 1.005)]), (-2083, [(-2083, 12, 0.5631)]), (-2103, [(-2103, -4, 0.1245)]), (-2127, [(-2127, -16, 1.981)]), (-2143, [(-2143, -12, 0.5551)]), (-2148, [(-2148, -24, 4.436)]), (-2152, [(-2152, -8, 0.2462)]), (-2163, [(-2163, 0, 0)]), (-2167, [(-2167, -8, 0.2454)]), (-2203, [(-2203, -12, 0.5475)]), (-2212, [(-2212, 16, 0.9714)]), (-2227, [(-2227, 8, 0.2420)]), (-2247, [(-2247, -24, 4.337)]), (-2248, [(-2248, 16, 0.9636)]), (-2263, [(-2263, 8, 0.2401)]), (-2283, [(-2283, -4, 0.1195)]), (-2287, [(-2287, -12, 0.5374)]), (-2292, [(-2292, -32, 7.634)]), (-2307, [(-2307, 8, 0.4756)]), (-2308, [(-2308, 8, 0.2377)]), (-2323, [(-2323, 0, 0)]), (-2328, [(-2328, -8, 0.4734)]), (-2343, [(-2343, -16, 1.888)]), (-2347, [(-2347, 20, 1.474)]), (-2383, [(-2383, 20, 1.462)]), (-2388, [(-2388, 16, 1.870)]), (-2392, [(-2392, 16, 0.9342)]), (-2407, [(-2407, 0, 0)]), (-2427, [(-2427, 4, 0.1159)]), (-2443, [(-2443, 8, 0.2311)]), (-2452, [(-2452, 0, 0)]), (-2463, [(-2463, -4, 0.1151)]), (-2467, [(-2467, -20, 1.437)]), (-2472, [(-2472, 8, 0.4595)]), (-2487, [(-2487, -24, 4.123)]), (-2488, [(-2488, 0, 0)]), (-2503, [(-2503, 20, 1.427)]), (-2532, [(-2532, -16, 1.816)]), (-2563, [(-2563, 8, 0.2256)]), (-2568, [(-2568, 16, 1.803)]), (-2587, [(-2587, 0, 0)]), (-2607, [(-2607, -8, 0.4474)]), (-2623, [(-2623, -24, 2.007)]), (-2632, [(-2632, 32, 3.562)]), (-2643, [(-2643, 12, 0.9998)]), (-2647, [(-2647, 12, 0.4995)]), (-2667, [(-2667, 16, 1.769)]), (-2683, [(-2683, -12, 0.4961)]), (-2692, [(-2692, 8, 0.2201)]), (-2703, [(-2703, 0, 0)]), (-2707, [(-2707, -4, 0.05488)]), (-2712, [(-2712, 0, 0)]), (-2728, [(-2728, -16, 0.8747)]), (-2743, [(-2743, 32, 3.489)]), (-2767, [(-2767, 4, 0.05428)]), (-2787, [(-2787, -20, 2.704)]), (-2788, [(-2788, 16, 0.8653)]), (-2803, [(-2803, -28, 2.643)]), (-2823, [(-2823, 4, 0.1075)]), (-2827, [(-2827, -16, 0.8593)]), (-2847, [(-2847, 24, 3.853)]), (-2863, [(-2863, 24, 1.921)]), (-2868, [(-2868, -16, 1.706)]), (-2872, [(-2872, -16, 0.8525)]), (-2887, [(-2887, -28, 2.604)]), (-2923, [(-2923, -8, 0.2113)]), (-2932, [(-2932, 16, 0.8438)]), (-2947, [(-2947, -16, 0.8416)]), (-2967, [(-2967, 8, 0.4194)]), (-2968, [(-2968, 16, 0.8386)]), (-2983, [(-2983, -16, 0.8365)]), (-3003, [(-3003, 0, 0)]), (-3007, [(-3007, 32, 3.333)]), (-3012, [(-3012, 8, 0.4162)]), (-3027, [(-3027, 0, 0)]), (-3028, [(-3028, -16, 0.8303)]), (-3043, [(-3043, -16, 0.8282)]), (-3048, [(-3048, 8, 0.4138)]), (-3063, [(-3063, 0, 0)]), (-3067, [(-3067, 28, 2.526)]), (-3103, [(-3103, 0, 0)]), (-3108, [(-3108, 16, 1.639)]), (-3112, [(-3112, -24, 1.843)]), (-3127, [(-3127, 0, 0)]), (-3147, [(-3147, 12, 0.9162)]), (-3163, [(-3163, -12, 0.4570)]), (-3172, [(-3172, 0, 0)]), (-3183, [(-3183, -28, 4.960)]), (-3187, [(-3187, -4, 0.05058)]), (-3192, [(-3192, 16, 1.617)]), (-3207, [(-3207, 16, 1.614)]), (-3208, [(-3208, -16, 0.8066)]), (-3223, [(-3223, -24, 1.811)]), (-3243, [(-3243, 16, 1.605)]), (-3247, [(-3247, 16, 0.8018)]), (-3252, [(-3252, -16, 1.602)]), (-3268, [(-3268, 16, 0.7992)]), (-3288, [(-3288, 0, 0)]), (-3307, [(-3307, 4, 0.04965)]), (-3327, [(-3327, 28, 4.852)]), (-3343, [(-3343, -4, 0.04939)]), (-3352, [(-3352, -24, 1.776)]), (-3363, [(-3363, 16, 1.576)]), (-3367, [(-3367, 0, 0)]), (-3387, [(-3387, 8, 0.3925)]), (-3403, [(-3403, 16, 0.7832)]), (-3412, [(-3412, 0, 0)]), (-3423, [(-3423, -16, 1.562)]), (-3427, [(-3427, -8, 0.1951)]), (-3432, [(-3432, 16, 1.560)]), (-3448, [(-3448, 16, 0.7781)]), (-3463, [(-3463, 12, 0.4367)]), (-3487, [(-3487, -32, 3.095)]), (-3507, [(-3507, 16, 1.543)]), (-3508, [(-3508, 16, 0.7714)]), (-3523, [(-3523, 8, 0.1924)]), (-3543, [(-3543, 12, 0.8635)]), (-3547, [(-3547, 4, 0.04795)]), (-3567, [(-3567, -24, 3.442)]), (-3583, [(-3583, 4, 0.04770)]), (-3588, [(-3588, 16, 1.525)]), (-3592, [(-3592, 16, 0.7623)]), (-3603, [(-3603, -8, 0.3806)]), (-3607, [(-3607, -4, 0.04754)]), (-3643, [(-3643, 20, 1.183)]), (-3652, [(-3652, 0, 0)]), (-3667, [(-3667, -24, 1.698)]), (-3687, [(-3687, -4, 0.09405)]), (-3688, [(-3688, -8, 0.1881)]), (-3723, [(-3723, -16, 1.498)]), (-3727, [(-3727, 28, 2.292)]), (-3732, [(-3732, 16, 1.496)]), (-3747, [(-3747, -16, 1.493)]), (-3748, [(-3748, -8, 0.1866)]), (-3763, [(-3763, 8, 0.1862)]), (-3768, [(-3768, 0, 0)]), (-3783, [(-3783, 8, 0.3714)]), (-3787, [(-3787, 0, 0)]), (-3823, [(-3823, 4, 0.04618)]), (-3828, [(-3828, -16, 1.477)]), (-3832, [(-3832, 32, 2.952)]), (-3847, [(-3847, 12, 0.4143)]), (-3867, [(-3867, 4, 0.09184)]), (-3883, [(-3883, -16, 0.7332)]), (-3892, [(-3892, -16, 0.7323)]), (-3903, [(-3903, -20, 2.285)]), (-3907, [(-3907, 12, 0.4111)]), (-3912, [(-3912, -16, 1.461)]), (-3927, [(-3927, 0, 0)]), (-3928, [(-3928, -24, 1.640)]), (-3943, [(-3943, 12, 0.4093)]), (-3963, [(-3963, -8, 0.3629)]), (-3967, [(-3967, -12, 0.4080)]), (-3972, [(-3972, 0, 0)]), (-3988, [(-3988, 32, 2.894)]), (-4003, [(-4003, 4, 0.04513)]), (-4008, [(-4008, -32, 5.773)]), (-4027, [(-4027, 4, 0.04500)]), (-4047, [(-4047, 0, 0)]), (-4063, [(-4063, 0, 0)]), (-4072, [(-4072, 8, 0.1790)]), (-4083, [(-4083, 4, 0.08938)]), (-4087, [(-4087, 8, 0.1787)]), (-4123, [(-4123, -32, 2.846)]), (-4132, [(-4132, -8, 0.1777)]), (-4143, [(-4143, 16, 1.420)]), (-4147, [(-4147, 16, 0.7095)]), (-4152, [(-4152, 0, 0)]), (-4168, [(-4168, -16, 0.7077)]), (-4183, [(-4183, -32, 2.826)]), (-4207, [(-4207, -8, 0.1761)]), (-4227, [(-4227, -4, 0.08784)]), (-4228, [(-4228, 16, 0.7026)]), (-4243, [(-4243, 4, 0.04384)]), (-4267, [(-4267, 16, 0.6994)]), (-4287, [(-4287, -16, 1.396)]), (-4303, [(-4303, 24, 1.567)]), (-4308, [(-4308, 16, 1.392)]), (-4323, [(-4323, 0, 0)]), (-4327, [(-4327, -4, 0.04341)]), (-4363, [(-4363, 4, 0.04323)]), (-4372, [(-4372, -32, 2.764)]), (-4387, [(-4387, -16, 0.6898)]), (-4407, [(-4407, -24, 3.097)]), (-4408, [(-4408, -16, 0.6881)]), (-4423, [(-4423, -12, 0.3864)]), (-4443, [(-4443, -12, 0.7711)]), (-4447, [(-4447, -12, 0.3854)]), (-4452, [(-4452, -16, 1.369)]), (-4467, [(-4467, -24, 3.076)]), (-4468, [(-4468, -16, 0.6835)]), (-4483, [(-4483, 4, 0.04265)]), (-4488, [(-4488, -16, 1.364)]), (-4503, [(-4503, 32, 5.447)]), (-4507, [(-4507, 4, 0.04253)]), (-4543, [(-4543, 16, 0.6778)]), (-4548, [(-4548, 16, 1.355)]), (-4552, [(-4552, -16, 0.6772)]), (-4567, [(-4567, -12, 0.3803)]), (-4587, [(-4587, 8, 0.3373)]), (-4603, [(-4603, 12, 0.3788)]), (-4612, [(-4612, 40, 4.205)]), (-4623, [(-4623, -8, 0.3360)]), (-4627, [(-4627, -8, 0.1679)]), (-4632, [(-4632, 8, 0.3356)]), (-4647, [(-4647, 24, 3.016)]), (-4648, [(-4648, 16, 0.6701)]), (-4663, [(-4663, 4, 0.04182)]), (-4683, [(-4683, 0, 0)]), (-4687, [(-4687, -32, 2.669)]), (-4692, [(-4692, 32, 5.336)]), (-4708, [(-4708, 32, 2.663)]), (-4723, [(-4723, 36, 3.366)]), (-4728, [(-4728, 0, 0)]), (-4747, [(-4747, 0, 0)]), (-4767, [(-4767, -16, 1.323)]), (-4783, [(-4783, -36, 3.344)]), (-4792, [(-4792, 16, 0.6600)]), (-4803, [(-4803, -4, 0.08241)]), (-4807, [(-4807, 0, 0)]), (-4827, [(-4827, 8, 0.3288)]), (-4843, [(-4843, 16, 0.6565)]), (-4852, [(-4852, 0, 0)]), (-4863, [(-4863, 40, 8.189)]), (-4867, [(-4867, 16, 0.6549)]), (-4872, [(-4872, -16, 1.309)]), (-4888, [(-4888, -32, 2.614)]), (-4903, [(-4903, -4, 0.04078)]), (-4927, [(-4927, 8, 0.1627)]), (-4947, [(-4947, 0, 0)]), (-4948, [(-4948, -32, 2.598)]), (-4963, [(-4963, 0, 0)]), (-4983, [(-4983, -24, 2.912)]), (-4987, [(-4987, -12, 0.3639)]), (-5007, [(-5007, 16, 1.291)]), (-5023, [(-5023, -12, 0.3626)]), (-5028, [(-5028, 24, 2.899)]), (-5032, [(-5032, -32, 2.576)]), (-5083, [(-5083, 16, 0.6408)]), (-5092, [(-5092, -32, 2.561)]), (-5107, [(-5107, 12, 0.3596)]), (-5127, [(-5127, 36, 6.460)]), (-5128, [(-5128, 0, 0)]), (-5143, [(-5143, 0, 0)]), (-5163, [(-5163, -12, 0.7153)]), (-5167, [(-5167, -12, 0.3575)]), (-5172, [(-5172, -16, 1.271)]), (-5187, [(-5187, 16, 1.269)]), (-5188, [(-5188, -24, 1.427)]), (-5208, [(-5208, 16, 1.266)]), (-5223, [(-5223, -32, 5.057)]), (-5227, [(-5227, 12, 0.3555)]), (-5263, [(-5263, -48, 5.668)]), (-5268, [(-5268, 16, 1.259)]), (-5272, [(-5272, -8, 0.1573)]), (-5287, [(-5287, -8, 0.1571)]), (-5307, [(-5307, -24, 2.822)]), (-5323, [(-5323, 12, 0.3522)]), (-5332, [(-5332, -32, 2.503)]), (-5343, [(-5343, 16, 1.250)]), (-5347, [(-5347, -28, 1.913)]), (-5352, [(-5352, -8, 0.3123)]), (-5367, [(-5367, 8, 0.3118)]), (-5368, [(-5368, 16, 0.6236)]), (-5383, [(-5383, -24, 1.401)]), (-5403, [(-5403, 8, 0.3108)]), (-5407, [(-5407, -20, 0.9708)]), (-5412, [(-5412, 16, 1.242)]), (-5428, [(-5428, -16, 0.6201)]), (-5443, [(-5443, -28, 1.896)]), (-5448, [(-5448, 32, 4.952)]), (-5467, [(-5467, 0, 0)]), (-5487, [(-5487, 24, 2.776)]), (-5503, [(-5503, 68, 11.12)]), (-5512, [(-5512, 32, 2.462)]), (-5523, [(-5523, 8, 0.3074)]), (-5527, [(-5527, 44, 4.647)]), (-5563, [(-5563, -4, 0.03828)]), (-5572, [(-5572, 0, 0)]), (-5583, [(-5583, 16, 1.223)]), (-5587, [(-5587, 16, 0.6112)]), (-5592, [(-5592, -16, 1.222)]), (-5608, [(-5608, 24, 1.373)]), (-5623, [(-5623, -12, 0.3427)]), (-5647, [(-5647, 36, 3.078)]), (-5667, [(-5667, -12, 0.6828)]), (-5668, [(-5668, -48, 5.462)]), (-5683, [(-5683, -4, 0.03788)]), (-5703, [(-5703, 20, 1.891)]), (-5707, [(-5707, -32, 2.419)]), (-5727, [(-5727, 0, 0)]), (-5743, [(-5743, 4, 0.03768)]), (-5748, [(-5748, -16, 1.205)]), (-5752, [(-5752, 0, 0)]), (-5763, [(-5763, 0, 0)]), (-5767, [(-5767, -16, 0.6016)]), (-5803, [(-5803, 8, 0.1499)]), (-5812, [(-5812, 32, 2.397)]), (-5827, [(-5827, 28, 1.833)]), (-5847, [(-5847, -12, 0.6722)]), (-5848, [(-5848, 16, 0.5974)]), (-5863, [(-5863, 16, 0.5967)]), (-5883, [(-5883, 8, 0.2978)]), (-5892, [(-5892, -8, 0.2976)]), (-5907, [(-5907, 0, 0)]), (-5908, [(-5908, 16, 0.5944)]), (-5923, [(-5923, 28, 1.818)]), (-5928, [(-5928, -16, 1.187)]), (-5943, [(-5943, -32, 4.741)]), (-5947, [(-5947, 0, 0)]), (-5983, [(-5983, 0, 0)]), (-5988, [(-5988, -32, 4.723)]), (-5992, [(-5992, 0, 0)]), (-6007, [(-6007, 12, 0.3316)]), (-6043, [(-6043, 4, 0.03673)]), (-6052, [(-6052, 0, 0)]), (-6063, [(-6063, -8, 0.2934)]), (-6067, [(-6067, -20, 0.9165)]), (-6072, [(-6072, 16, 1.173)]), (-6087, [(-6087, 0, 0)]), (-6088, [(-6088, 48, 5.270)]), (-6103, [(-6103, 16, 0.5848)]), (-6123, [(-6123, -8, 0.2919)]), (-6127, [(-6127, 8, 0.1459)]), (-6132, [(-6132, -16, 1.167)]), (-6148, [(-6148, 0, 0)]), (-6163, [(-6163, -20, 0.9093)]), (-6168, [(-6168, 0, 0)]), (-6187, [(-6187, 16, 0.5808)]), (-6207, [(-6207, -36, 5.872)]), (-6232, [(-6232, -16, 0.5787)]), (-6243, [(-6243, -4, 0.07228)]), (-6247, [(-6247, 12, 0.3251)]), (-6267, [(-6267, 0, 0)]), (-6283, [(-6283, -32, 2.306)]), (-6303, [(-6303, 0, 0)]), (-6307, [(-6307, 16, 0.5753)]), (-6312, [(-6312, -32, 4.600)]), (-6328, [(-6328, 16, 0.5743)]), (-6343, [(-6343, -12, 0.3227)]), (-6367, [(-6367, 36, 2.899)]), (-6387, [(-6387, 20, 1.786)]), (-6388, [(-6388, 0, 0)]), (-6403, [(-6403, 8, 0.1427)]), (-6423, [(-6423, 4, 0.07126)]), (-6427, [(-6427, -12, 0.3206)]), (-6447, [(-6447, -16, 1.138)]), (-6463, [(-6463, -24, 1.279)]), (-6472, [(-6472, 32, 2.272)]), (-6483, [(-6483, 0, 0)]), (-6487, [(-6487, -24, 1.276)]), (-6523, [(-6523, -24, 1.273)]), (-6532, [(-6532, -16, 0.5653)]), (-6547, [(-6547, -4, 0.03529)]), (-6567, [(-6567, 0, 0)]), (-6568, [(-6568, -8, 0.1409)]), (-6583, [(-6583, 32, 2.252)]), (-6603, [(-6603, 8, 0.2811)]), (-6607, [(-6607, 20, 0.8782)]), (-6612, [(-6612, 16, 1.124)]), (-6628, [(-6628, -8, 0.1403)]), (-6643, [(-6643, 0, 0)]), (-6648, [(-6648, 16, 1.121)]), (-6663, [(-6663, -32, 4.478)]), (-6667, [(-6667, 8, 0.1399)]), (-6703, [(-6703, 12, 0.3139)]), (-6708, [(-6708, 0, 0)]), (-6712, [(-6712, 16, 0.5577)]), (-6747, [(-6747, -8, 0.2781)]), (-6763, [(-6763, -12, 0.3125)]), (-6772, [(-6772, 16, 0.5552)]), (-6783, [(-6783, -32, 4.438)]), (-6787, [(-6787, 0, 0)]), (-6792, [(-6792, 16, 1.109)]), (-6807, [(-6807, -16, 1.108)]), (-6808, [(-6808, 0, 0)]), (-6823, [(-6823, 36, 2.800)]), (-6843, [(-6843, 16, 1.105)]), (-6847, [(-6847, -40, 3.451)]), (-6852, [(-6852, 32, 4.415)]), (-6868, [(-6868, 0, 0)]), (-6883, [(-6883, 4, 0.03442)]), (-6888, [(-6888, -16, 1.101)]), (-6907, [(-6907, -28, 1.684)]), (-6927, [(-6927, 12, 0.6176)]), (-6943, [(-6943, 16, 0.5483)]), (-6952, [(-6952, 32, 2.192)]), (-6963, [(-6963, 24, 2.464)]), (-6967, [(-6967, -28, 1.676)]), (-6987, [(-6987, -16, 1.093)]), (-7003, [(-7003, 32, 2.184)]), (-7012, [(-7012, 8, 0.1364)]), (-7023, [(-7023, 0, 0)]), (-7027, [(-7027, 12, 0.3066)]), (-7032, [(-7032, 0, 0)]), (-7048, [(-7048, 16, 0.5442)]), (-7063, [(-7063, 16, 0.5436)]), (-7087, [(-7087, -8, 0.1357)]), (-7107, [(-7107, 8, 0.2710)]), (-7108, [(-7108, 8, 0.1355)]), (-7123, [(-7123, 8, 0.1353)]), (-7143, [(-7143, 4, 0.06757)]), (-7147, [(-7147, -8, 0.1351)]), (-7167, [(-7167, -24, 2.429)]), (-7183, [(-7183, -16, 0.5391)]), (-7188, [(-7188, 16, 1.078)]), (-7192, [(-7192, 16, 0.5387)]), (-7207, [(-7207, -28, 1.648)]), (-7243, [(-7243, 4, 0.03355)]), (-7287, [(-7287, -8, 0.2676)]), (-7288, [(-7288, -16, 0.5352)]), (-7303, [(-7303, -8, 0.1337)]), (-7323, [(-7323, -12, 0.6006)]), (-7327, [(-7327, -8, 0.1334)]), (-7332, [(-7332, 0, 0)]), (-7347, [(-7347, 16, 1.066)]), (-7348, [(-7348, 16, 0.5330)]), (-7363, [(-7363, -24, 1.198)]), (-7368, [(-7368, -32, 4.258)]), (-7383, [(-7383, 16, 1.063)]), (-7387, [(-7387, -8, 0.1329)]), (-7423, [(-7423, -16, 0.5303)]), (-7428, [(-7428, -16, 1.060)]), (-7432, [(-7432, -16, 0.5300)]), (-7447, [(-7447, -8, 0.1324)]), (-7467, [(-7467, 24, 2.379)]), (-7483, [(-7483, 8, 0.1320)]), (-7492, [(-7492, -24, 1.188)]), (-7503, [(-7503, 0, 0)]), (-7507, [(-7507, 12, 0.2966)]), (-7512, [(-7512, 8, 0.2636)]), (-7527, [(-7527, 8, 0.2633)]), (-7528, [(-7528, 24, 1.185)]), (-7543, [(-7543, 16, 0.5260)]), (-7563, [(-7563, 8, 0.2627)]), (-7567, [(-7567, 16, 0.5252)]), (-7572, [(-7572, 32, 4.200)]), (-7588, [(-7588, 0, 0)]), (-7603, [(-7603, -20, 0.8187)]), (-7608, [(-7608, 32, 4.190)]), (-7627, [(-7627, -40, 3.270)]), (-7647, [(-7647, 20, 1.633)]), (-7663, [(-7663, 16, 0.5219)]), (-7672, [(-7672, -16, 0.5216)]), (-7683, [(-7683, 0, 0)]), (-7687, [(-7687, 20, 0.8142)]), (-7707, [(-7707, 0, 0)]), (-7723, [(-7723, -28, 1.592)]), (-7732, [(-7732, 16, 0.5196)]), (-7743, [(-7743, 8, 0.2596)]), (-7747, [(-7747, 16, 0.5191)]), (-7752, [(-7752, 0, 0)]), (-7768, [(-7768, -8, 0.1296)]), (-7783, [(-7783, -16, 0.5179)]), (-7807, [(-7807, 0, 0)]), (-7827, [(-7827, 4, 0.06455)]), (-7828, [(-7828, -16, 0.5164)]), (-7843, [(-7843, -32, 2.064)]), (-7863, [(-7863, 20, 1.610)]), (-7867, [(-7867, 12, 0.2897)]), (-7887, [(-7887, 0, 0)]), (-7903, [(-7903, -16, 0.5139)]), (-7908, [(-7908, -24, 2.312)]), (-7912, [(-7912, -16, 0.5136)]), (-7923, [(-7923, 16, 1.027)]), (-7927, [(-7927, 12, 0.2886)]), (-7963, [(-7963, 4, 0.03200)]), (-7972, [(-7972, -8, 0.1279)]), (-8007, [(-8007, 8, 0.2553)]), (-8008, [(-8008, 0, 0)]), (-8023, [(-8023, 8, 0.1275)]), (-8043, [(-8043, 0, 0)]), (-8047, [(-8047, 8, 0.1273)]), (-8052, [(-8052, -32, 4.073)]), (-8067, [(-8067, 8, 0.2543)]), (-8068, [(-8068, -24, 1.144)]), (-8083, [(-8083, 0, 0)]), (-8088, [(-8088, 8, 0.2540)]), (-8103, [(-8103, -8, 0.2538)]), (-8143, [(-8143, -40, 3.164)]), (-8148, [(-8148, -16, 1.012)]), (-8152, [(-8152, -8, 0.1265)]), (-8167, [(-8167, -28, 1.548)]), (-8187, [(-8187, 4, 0.06312)]), (-8203, [(-8203, -8, 0.1261)]), (-8212, [(-8212, -16, 0.5042)]), (-8223, [(-8223, 28, 3.086)]), (-8227, [(-8227, 8, 0.1259)]), (-8247, [(-8247, 0, 0)]), (-8248, [(-8248, -32, 2.012)]), (-8263, [(-8263, 12, 0.2827)]), (-8283, [(-8283, 16, 1.004)]), (-8287, [(-8287, 20, 0.7842)]), (-8292, [(-8292, 0, 0)]), (-8308, [(-8308, 0, 0)]), (-8323, [(-8323, 16, 0.5008)]), (-8328, [(-8328, -32, 4.005)]), (-8347, [(-8347, 0, 0)]), (-8367, [(-8367, 12, 0.5619)]), (-8383, [(-8383, 8, 0.1247)]), (-8392, [(-8392, 16, 0.4987)]), (-8403, [(-8403, -12, 0.5607)]), (-8407, [(-8407, 0, 0)]), (-8443, [(-8443, 12, 0.2797)]), (-8452, [(-8452, -24, 1.118)]), (-8463, [(-8463, -16, 0.9933)]), (-8467, [(-8467, -36, 2.514)]), (-8472, [(-8472, -16, 0.9927)]), (-8488, [(-8488, -8, 0.1240)]), (-8503, [(-8503, 16, 0.4955)]), (-8527, [(-8527, 28, 1.515)]), (-8547, [(-8547, -16, 0.9884)]), (-8548, [(-8548, 40, 3.088)]), (-8563, [(-8563, 36, 2.499)]), (-8583, [(-8583, -12, 0.5548)]), (-8587, [(-8587, -8, 0.1233)]), (-8607, [(-8607, 16, 0.9849)]), (-8623, [(-8623, 12, 0.2767)]), (-8628, [(-8628, 32, 3.935)]), (-8632, [(-8632, 0, 0)]), (-8643, [(-8643, -16, 0.9829)]), (-8647, [(-8647, 28, 1.505)]), (-8683, [(-8683, 0, 0)]), (-8692, [(-8692, 32, 1.960)]), (-8707, [(-8707, 28, 1.499)]), (-8727, [(-8727, -12, 0.5502)]), (-8728, [(-8728, -8, 0.1223)]), (-8743, [(-8743, 24, 1.099)]), (-8763, [(-8763, 0, 0)]), (-8767, [(-8767, 32, 1.952)]), (-8772, [(-8772, -16, 0.9756)]), (-8787, [(-8787, -8, 0.2437)]), (-8803, [(-8803, -12, 0.2739)]), (-8808, [(-8808, 8, 0.2434)]), (-8823, [(-8823, 0, 0)]), (-8827, [(-8827, 0, 0)]), (-8863, [(-8863, 20, 0.7583)]), (-8868, [(-8868, 32, 3.881)]), (-8872, [(-8872, 8, 0.1213)]), (-8887, [(-8887, 12, 0.2726)]), (-8907, [(-8907, -20, 1.513)]), (-8923, [(-8923, -4, 0.03023)]), (-8932, [(-8932, 32, 1.934)]), (-8943, [(-8943, 24, 2.174)]), (-8947, [(-8947, 40, 3.019)]), (-8952, [(-8952, 0, 0)]), (-8968, [(-8968, 32, 1.930)]), (-8983, [(-8983, 8, 0.1205)]), (-9003, [(-9003, -24, 2.167)]), (-9007, [(-9007, 12, 0.2708)]), (-9012, [(-9012, -32, 3.850)]), (-9028, [(-9028, -16, 0.4808)]), (-9043, [(-9043, 28, 1.471)]), (-9048, [(-9048, -16, 0.9606)]), (-9067, [(-9067, 20, 0.7497)]), (-9087, [(-9087, 8, 0.2396)]), (-9103, [(-9103, -44, 3.621)]), (-9112, [(-9112, -48, 4.308)]), (-9123, [(-9123, 12, 0.5381)]), (-9127, [(-9127, -28, 1.465)]), (-9147, [(-9147, 0, 0)]), (-9172, [(-9172, -16, 0.4771)]), (-9183, [(-9183, -24, 2.145)]), (-9187, [(-9187, -12, 0.2681)]), (-9192, [(-9192, -16, 0.9531)]), (-9208, [(-9208, -48, 4.285)]), (-9223, [(-9223, -24, 1.070)]), (-9247, [(-9247, -24, 1.069)]), (-9267, [(-9267, 4, 0.05933)]), (-9268, [(-9268, 48, 4.271)]), (-9283, [(-9283, -4, 0.02964)]), (-9303, [(-9303, -8, 0.2368)]), (-9307, [(-9307, -8, 0.1184)]), (-9327, [(-9327, -32, 3.785)]), (-9343, [(-9343, -20, 0.7385)]), (-9348, [(-9348, -16, 0.9451)]), (-9352, [(-9352, 0, 0)]), (-9363, [(-9363, -8, 0.2361)]), (-9367, [(-9367, 16, 0.4721)]), (-9403, [(-9403, 12, 0.2650)]), (-9412, [(-9412, -32, 1.884)]), (-9427, [(-9427, 8, 0.1176)]), (-9447, [(-9447, -40, 5.876)]), (-9448, [(-9448, -24, 1.058)]), (-9463, [(-9463, -60, 6.605)]), (-9483, [(-9483, -32, 3.753)]), (-9487, [(-9487, -8, 0.1173)]), (-9492, [(-9492, 0, 0)]), (-9507, [(-9507, 24, 2.109)]), (-9508, [(-9508, -24, 1.054)]), (-9523, [(-9523, 0, 0)]), (-9528, [(-9528, 0, 0)]), (-9543, [(-9543, 16, 0.9354)]), (-9547, [(-9547, -12, 0.2630)]), (-9588, [(-9588, 0, 0)]), (-9592, [(-9592, 16, 0.4665)]), (-9607, [(-9607, 8, 0.1165)]), (-9627, [(-9627, -12, 0.5238)]), (-9643, [(-9643, 12, 0.2617)]), (-9652, [(-9652, 16, 0.4650)]), (-9663, [(-9663, 36, 4.706)]), (-9667, [(-9667, 0, 0)]), (-9672, [(-9672, 32, 3.716)]), (-9687, [(-9687, 8, 0.2321)]), (-9688, [(-9688, -32, 1.857)]), (-9703, [(-9703, -40, 2.899)]), (-9723, [(-9723, -16, 0.9267)]), (-9727, [(-9727, -56, 5.675)]), (-9732, [(-9732, -16, 0.9262)]), (-9748, [(-9748, 0, 0)]), (-9763, [(-9763, 16, 0.4624)]), (-9768, [(-9768, -16, 0.9245)]), (-9787, [(-9787, -4, 0.02886)]), (-9807, [(-9807, -16, 0.9227)]), (-9823, [(-9823, 0, 0)]), (-9832, [(-9832, 40, 2.880)]), (-9843, [(-9843, 0, 0)]), (-9847, [(-9847, 0, 0)]), (-9867, [(-9867, 0, 0)]), (-9883, [(-9883, 36, 2.327)]), (-9892, [(-9892, 8, 0.1148)]), (-9903, [(-9903, 0, 0)]), (-9907, [(-9907, 28, 1.406)]), (-9912, [(-9912, 32, 3.671)]), (-9928, [(-9928, 16, 0.4585)]), (-9943, [(-9943, 16, 0.4582)]), (-9967, [(-9967, -36, 2.317)]), (-9987, [(-9987, -20, 1.429)]), (-9988, [(-9988, 32, 1.829)])]]

# map: (1 |-> 1.0) -> -1, Fractional ideal (3) -> -1, Fractional ideal (5) -> 1
[1, None, [(-4, [(-4, -2, 1.428)]), (-19, [(-19, 0, 0)]), (-24, [(-24, 2, 1.166)]), (-31, [(-31, 4, 2.052)]), (-39, [(-39, 2, 0.9146)]), (-51, [(-51, 2, 0.7998)]), (-79, [(-79, 0, 0)]), (-84, [(-84, -4, 2.493)]), (-91, [(-91, -4, 1.198)]), (-111, [(-111, -2, 0.5422)]), (-136, [(-136, 4, 0.9796)]), (-139, [(-139, 0, 0)]), (-151, [(-151, -4, 0.9297)]), (-159, [(-159, -6, 4.077)]), (-184, [(-184, 4, 0.8422)]), (-199, [(-199, 0, 0)]), (-211, [(-211, 4, 0.7865)]), (-219, [(-219, -2, 0.3860)]), (-231, [(-231, -4, 1.503)]), (-244, [(-244, 0, 0)]), (-259, [(-259, 4, 0.7099)]), (-264, [(-264, 4, 1.406)]), (-271, [(-271, -4, 0.6940)]), (-276, [(-276, 4, 1.375)]), (-291, [(-291, 2, 0.3348)]), (-319, [(-319, 0, 0)]), (-331, [(-331, -4, 0.6279)]), (-339, [(-339, 2, 0.3102)]), (-376, [(-376, -4, 0.5891)]), (-379, [(-379, -8, 2.347)]), (-391, [(-391, 4, 0.5777)]), (-399, [(-399, 4, 1.144)]), (-411, [(-411, -6, 2.536)]), (-424, [(-424, -4, 0.5548)]), (-436, [(-436, 0, 0)]), (-439, [(-439, -8, 2.181)]), (-451, [(-451, 8, 2.152)]), (-456, [(-456, -8, 4.280)]), (-471, [(-471, 10, 6.580)]), (-499, [(-499, 0, 0)]), (-511, [(-511, 4, 0.5054)]), (-516, [(-516, 0, 0)]), (-519, [(-519, -2, 0.2507)]), (-559, [(-559, 12, 4.349)]), (-564, [(-564, 4, 0.9621)]), (-571, [(-571, -4, 0.4781)]), (-579, [(-579, 2, 0.2374)]), (-591, [(-591, 2, 0.2350)]), (-616, [(-616, 0, 0)]), (-619, [(-619, 8, 1.837)]), (-631, [(-631, 4, 0.4548)]), (-651, [(-651, -4, 0.8955)]), (-664, [(-664, -12, 3.990)]), (-679, [(-679, 4, 0.4384)]), (-691, [(-691, 4, 0.4346)]), (-696, [(-696, 8, 3.464)]), (-699, [(-699, -6, 1.944)]), (-724, [(-724, 8, 1.698)]), (-739, [(-739, 0, 0)]), (-744, [(-744, -4, 0.8376)]), (-751, [(-751, -12, 3.752)]), (-759, [(-759, -8, 3.317)]), (-771, [(-771, 2, 0.2057)]), (-799, [(-799, -4, 0.4042)]), (-804, [(-804, 0, 0)]), (-811, [(-811, 4, 0.4011)]), (-831, [(-831, -6, 1.783)]), (-856, [(-856, -4, 0.3905)]), (-859, [(-859, -8, 1.559)]), (-871, [(-871, -4, 0.3871)]), (-879, [(-879, 2, 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0.1545)]), (-5479, [(-5479, 16, 2.469)]), (-5496, [(-5496, 4, 0.3082)]), (-5511, [(-5511, -4, 0.3078)]), (-5524, [(-5524, 16, 2.459)]), (-5539, [(-5539, 0, 0)]), (-5551, [(-5551, 8, 0.6133)]), (-5556, [(-5556, -4, 0.3065)]), (-5559, [(-5559, -12, 2.758)]), (-5599, [(-5599, -16, 2.443)]), (-5604, [(-5604, -8, 1.221)]), (-5611, [(-5611, 8, 0.6100)]), (-5619, [(-5619, 2, 0.07620)]), (-5631, [(-5631, 10, 1.903)]), (-5656, [(-5656, 0, 0)]), (-5659, [(-5659, 0, 0)]), (-5671, [(-5671, -4, 0.1517)]), (-5691, [(-5691, 4, 0.3029)]), (-5704, [(-5704, 8, 0.6050)]), (-5716, [(-5716, 0, 0)]), (-5719, [(-5719, 0, 0)]), (-5731, [(-5731, 0, 0)]), (-5736, [(-5736, 8, 1.207)]), (-5739, [(-5739, -2, 0.07540)]), (-5764, [(-5764, 0, 0)]), (-5779, [(-5779, 0, 0)]), (-5784, [(-5784, 8, 1.202)]), (-5791, [(-5791, 12, 1.351)]), (-5799, [(-5799, 14, 3.675)]), (-5811, [(-5811, 8, 1.199)]), (-5839, [(-5839, 8, 0.5980)]), (-5844, [(-5844, -4, 0.2989)]), (-5851, [(-5851, 4, 0.1493)]), (-5871, [(-5871, 8, 1.193)]), (-5896, [(-5896, 8, 0.5951)]), (-5899, [(-5899, -12, 1.339)]), (-5911, [(-5911, 20, 3.715)]), (-5919, [(-5919, 10, 1.856)]), (-5944, [(-5944, 12, 1.334)]), (-5956, [(-5956, 16, 2.368)]), (-5959, [(-5959, 0, 0)]), (-5971, [(-5971, -4, 0.1478)]), (-5979, [(-5979, 10, 1.847)]), (-5991, [(-5991, 6, 0.6642)]), (-6004, [(-6004, -16, 2.359)]), (-6019, [(-6019, -4, 0.1472)]), (-6024, [(-6024, 4, 0.2944)]), (-6031, [(-6031, -12, 1.324)]), (-6036, [(-6036, -12, 2.647)]), (-6051, [(-6051, 2, 0.07343)]), (-6079, [(-6079, -8, 0.5861)]), (-6091, [(-6091, -4, 0.1464)]), (-6099, [(-6099, 8, 1.170)]), (-6136, [(-6136, 0, 0)]), (-6139, [(-6139, 4, 0.1458)]), (-6151, [(-6151, -20, 3.642)]), (-6159, [(-6159, 6, 0.6551)]), (-6184, [(-6184, 4, 0.1453)]), (-6196, [(-6196, -8, 0.5805)]), (-6199, [(-6199, 0, 0)]), (-6211, [(-6211, 12, 1.305)]), (-6216, [(-6216, 16, 4.637)]), (-6231, [(-6231, -4, 0.2894)]), (-6244, [(-6244, -16, 2.313)]), (-6259, [(-6259, 0, 0)]), (-6271, [(-6271, -4, 0.1443)]), (-6276, [(-6276, 8, 1.154)]), (-6279, [(-6279, 0, 0)]), (-6319, [(-6319, 16, 2.299)]), (-6324, [(-6324, -8, 1.149)]), (-6331, [(-6331, 4, 0.1436)]), (-6339, [(-6339, -2, 0.07174)]), (-6351, [(-6351, -8, 1.147)]), (-6376, [(-6376, -12, 1.288)]), (-6379, [(-6379, -8, 0.5721)]), (-6391, [(-6391, -16, 2.286)]), (-6411, [(-6411, -10, 1.783)]), (-6424, [(-6424, -16, 2.281)]), (-6436, [(-6436, 16, 2.278)]), (-6439, [(-6439, -12, 1.281)]), (-6451, [(-6451, 4, 0.1422)]), (-6456, [(-6456, -8, 1.137)]), (-6459, [(-6459, -2, 0.07107)]), (-6484, [(-6484, -8, 0.5675)]), (-6499, [(-6499, -12, 1.275)]), (-6504, [(-6504, 12, 2.550)]), (-6511, [(-6511, -20, 3.539)]), (-6519, [(-6519, -8, 1.132)]), (-6531, [(-6531, 0, 0)]), (-6559, [(-6559, -20, 3.526)]), (-6564, [(-6564, 0, 0)]), (-6571, [(-6571, -4, 0.1409)]), (-6616, [(-6616, 12, 1.264)]), (-6619, [(-6619, 8, 0.5617)]), (-6631, [(-6631, 16, 2.245)]), (-6639, [(-6639, 6, 0.6309)]), (-6676, [(-6676, -8, 0.5593)]), (-6679, [(-6679, -16, 2.237)]), (-6691, [(-6691, 4, 0.1397)]), (-6699, [(-6699, -8, 1.117)]), (-6711, [(-6711, -6, 0.6275)]), (-6739, [(-6739, 4, 0.1392)]), (-6744, [(-6744, 12, 2.504)]), (-6751, [(-6751, -4, 0.1390)]), (-6756, [(-6756, 0, 0)]), (-6771, [(-6771, -4, 0.2777)]), (-6799, [(-6799, 12, 1.247)]), (-6819, [(-6819, 6, 0.6225)]), (-6856, [(-6856, 12, 1.242)]), (-6871, [(-6871, 4, 0.1378)]), (-6879, [(-6879, 2, 0.06887)]), (-6891, [(-6891, 2, 0.06881)]), (-6904, [(-6904, -4, 0.1375)]), (-6916, [(-6916, -16, 2.198)]), (-6919, [(-6919, 8, 0.5494)]), (-6931, [(-6931, 0, 0)]), (-6951, [(-6951, 0, 0)]), (-6964, [(-6964, 8, 0.5476)]), (-6979, [(-6979, 12, 1.231)]), (-6991, [(-6991, -12, 1.230)]), (-6996, [(-6996, 8, 1.093)]), (-6999, [(-6999, -6, 0.6145)]), (-7039, [(-7039, -16, 2.179)]), (-7044, [(-7044, 0, 0)]), (-7051, [(-7051, -16, 2.177)]), (-7059, [(-7059, -8, 1.088)]), (-7071, [(-7071, 18, 5.502)]), (-7096, [(-7096, -4, 0.1356)]), (-7099, [(-7099, 0, 0)]), (-7111, [(-7111, 4, 0.1355)]), (-7131, [(-7131, -10, 1.691)]), (-7144, [(-7144, 24, 4.866)]), (-7156, [(-7156, -8, 0.5402)]), (-7159, [(-7159, 16, 2.160)]), (-7171, [(-7171, 16, 2.158)]), (-7176, [(-7176, 8, 1.079)]), (-7179, [(-7179, -10, 1.685)]), (-7204, [(-7204, -8, 0.5384)]), (-7219, [(-7219, 8, 0.5378)]), (-7224, [(-7224, 8, 1.075)]), (-7231, [(-7231, -12, 1.209)]), (-7239, [(-7239, -8, 1.074)]), (-7251, [(-7251, 6, 0.6037)]), (-7279, [(-7279, 0, 0)]), (-7284, [(-7284, -4, 0.2677)]), (-7291, [(-7291, 4, 0.1338)]), (-7311, [(-7311, -6, 0.6012)]), (-7336, [(-7336, 8, 0.5335)]), (-7339, [(-7339, 0, 0)]), (-7351, [(-7351, -4, 0.1332)]), (-7359, [(-7359, 8, 1.065)]), (-7384, [(-7384, 24, 4.786)]), (-7411, [(-7411, 12, 1.194)]), (-7419, [(-7419, 2, 0.06631)]), (-7431, [(-7431, 6, 0.5964)]), (-7444, [(-7444, 8, 0.5296)]), (-7459, [(-7459, 8, 0.5291)]), (-7464, [(-7464, -8, 1.058)]), (-7471, [(-7471, -8, 0.5287)]), (-7476, [(-7476, 0, 0)]), (-7491, [(-7491, 4, 0.2640)]), (-7519, [(-7519, 12, 1.186)]), (-7531, [(-7531, -4, 0.1316)]), (-7539, [(-7539, 12, 2.368)]), (-7576, [(-7576, 20, 3.281)]), (-7579, [(-7579, -8, 0.5249)]), (-7591, [(-7591, -4, 0.1311)]), (-7599, [(-7599, -4, 0.2621)]), (-7611, [(-7611, -4, 0.2619)]), (-7624, [(-7624, -12, 1.178)]), (-7636, [(-7636, 8, 0.5229)]), (-7639, [(-7639, -8, 0.5228)]), (-7651, [(-7651, -4, 0.1306)]), (-7656, [(-7656, 8, 1.044)]), (-7671, [(-7671, 2, 0.06522)]), (-7684, [(-7684, 8, 0.5213)]), (-7699, [(-7699, -8, 0.5208)]), (-7711, [(-7711, -8, 0.5204)]), (-7716, [(-7716, -8, 1.040)]), (-7719, [(-7719, 0, 0)]), (-7759, [(-7759, 24, 4.669)]), (-7764, [(-7764, -20, 6.483)]), (-7771, [(-7771, -8, 0.5184)]), (-7779, [(-7779, -2, 0.06476)]), (-7816, [(-7816, -4, 0.1292)]), (-7819, [(-7819, -20, 3.230)]), (-7831, [(-7831, 8, 0.5164)]), (-7851, [(-7851, 2, 0.06446)]), (-7864, [(-7864, -12, 1.159)]), (-7876, [(-7876, 0, 0)]), (-7879, [(-7879, 0, 0)]), (-7891, [(-7891, 12, 1.157)]), (-7896, [(-7896, -8, 1.028)]), (-7899, [(-7899, 2, 0.06427)]), (-7924, [(-7924, 8, 0.5133)]), (-7939, [(-7939, 4, 0.1282)]), (-7944, [(-7944, -16, 4.102)]), (-7951, [(-7951, -12, 1.153)]), (-7959, [(-7959, -8, 1.024)]), (-7971, [(-7971, -2, 0.06398)]), (-7999, [(-7999, 16, 2.044)]), (-8004, [(-8004, 16, 4.086)]), (-8011, [(-8011, -4, 0.1276)]), (-8031, [(-8031, -6, 0.5736)]), (-8056, [(-8056, -16, 2.036)]), (-8059, [(-8059, 0, 0)]), (-8071, [(-8071, 4, 0.1272)]), (-8079, [(-8079, 18, 5.148)]), (-8104, [(-8104, -12, 1.142)]), (-8116, [(-8116, -24, 4.565)]), (-8119, [(-8119, -12, 1.141)]), (-8131, [(-8131, 12, 1.140)]), (-8139, [(-8139, -2, 0.06331)]), (-8151, [(-8151, 16, 4.049)]), (-8164, [(-8164, 8, 0.5057)]), (-8179, [(-8179, 0, 0)]), (-8184, [(-8184, -16, 4.041)]), (-8191, [(-8191, 12, 1.136)]), (-8196, [(-8196, 8, 1.009)]), (-8211, [(-8211, 8, 1.009)]), (-8239, [(-8239, -32, 8.055)]), (-8251, [(-8251, -4, 0.1258)]), (-8259, [(-8259, -6, 0.5657)]), (-8296, [(-8296, -16, 2.007)]), (-8299, [(-8299, -4, 0.1254)]), (-8311, [(-8311, 12, 1.128)]), (-8319, [(-8319, -12, 2.255)]), (-8331, [(-8331, -10, 1.565)]), (-8344, [(-8344, 8, 0.5003)]), (-8356, [(-8356, 8, 0.4999)]), (-8359, [(-8359, 12, 1.125)]), (-8371, [(-8371, 8, 0.4994)]), (-8376, [(-8376, -4, 0.2496)]), (-8391, [(-8391, 10, 1.559)]), (-8404, [(-8404, 16, 1.994)]), (-8419, [(-8419, 0, 0)]), (-8431, [(-8431, 12, 1.120)]), (-8436, [(-8436, 0, 0)]), (-8439, [(-8439, 16, 3.979)]), (-8479, [(-8479, 0, 0)]), (-8484, [(-8484, 0, 0)]), (-8491, [(-8491, -4, 0.1240)]), (-8499, [(-8499, 2, 0.06196)]), (-8511, [(-8511, -14, 3.034)]), (-8536, [(-8536, 8, 0.4946)]), (-8539, [(-8539, 8, 0.4945)]), (-8551, [(-8551, 12, 1.112)]), (-8571, [(-8571, 6, 0.5553)]), (-8584, [(-8584, -16, 1.973)]), (-8596, [(-8596, -24, 4.436)]), (-8599, [(-8599, 8, 0.4928)]), (-8611, [(-8611, -8, 0.4924)]), (-8616, [(-8616, 8, 0.9846)]), (-8644, [(-8644, 8, 0.4915)]), (-8659, [(-8659, 12, 1.105)]), (-8671, [(-8671, 16, 1.963)]), (-8679, [(-8679, 4, 0.2453)]), (-8691, [(-8691, 14, 3.002)]), (-8719, [(-8719, 0, 0)]), (-8724, [(-8724, 4, 0.2446)]), (-8731, [(-8731, -4, 0.1223)]), (-8751, [(-8751, 6, 0.5495)]), (-8776, [(-8776, -20, 3.049)]), (-8779, [(-8779, 0, 0)]), (-8791, [(-8791, -8, 0.4874)]), (-8799, [(-8799, 0, 0)]), (-8824, [(-8824, 4, 0.1216)]), (-8839, [(-8839, 8, 0.4860)]), (-8851, [(-8851, -4, 0.1214)]), (-8859, [(-8859, -6, 0.5462)]), (-8871, [(-8871, 2, 0.06065)]), (-8884, [(-8884, 0, 0)]), (-8899, [(-8899, 0, 0)]), (-8904, [(-8904, 16, 3.874)]), (-8911, [(-8911, 24, 4.357)]), (-8916, [(-8916, -4, 0.2420)]), (-8931, [(-8931, -4, 0.2418)]), (-8971, [(-8971, -12, 1.086)]), (-8979, [(-8979, 4, 0.2411)]), (-9019, [(-9019, 16, 1.925)]), (-9031, [(-9031, -8, 0.4809)]), (-9039, [(-9039, 12, 2.163)]), (-9051, [(-9051, -4, 0.2402)]), (-9064, [(-9064, -8, 0.4800)]), (-9076, [(-9076, 16, 1.919)]), (-9079, [(-9079, -4, 0.1199)]), (-9091, [(-9091, 12, 1.078)]), (-9096, [(-9096, 0, 0)]), (-9111, [(-9111, -14, 2.932)]), (-9124, [(-9124, -8, 0.4784)]), (-9139, [(-9139, 0, 0)]), (-9151, [(-9151, 4, 0.1194)]), (-9156, [(-9156, 0, 0)]), (-9159, [(-9159, 8, 0.9550)]), (-9199, [(-9199, 0, 0)]), (-9204, [(-9204, 16, 3.810)]), (-9211, [(-9211, -8, 0.4761)]), (-9219, [(-9219, 4, 0.2380)]), (-9231, [(-9231, -4, 0.2378)]), (-9256, [(-9256, 8, 0.4750)]), (-9259, [(-9259, -4, 0.1187)]), (-9271, [(-9271, -12, 1.068)]), (-9291, [(-9291, -12, 2.133)]), (-9304, [(-9304, -12, 1.066)]), (-9316, [(-9316, 8, 0.4734)]), (-9319, [(-9319, -8, 0.4734)]), (-9331, [(-9331, 8, 0.4731)]), (-9336, [(-9336, 0, 0)]), (-9339, [(-9339, 4, 0.2364)]), (-9364, [(-9364, -16, 1.889)]), (-9379, [(-9379, -4, 0.1180)]), (-9384, [(-9384, -8, 0.9434)]), (-9391, [(-9391, 4, 0.1179)]), (-9399, [(-9399, 4, 0.2357)]), (-9411, [(-9411, -2, 0.05888)]), (-9439, [(-9439, 0, 0)]), (-9444, [(-9444, -8, 0.9404)]), (-9451, [(-9451, -4, 0.1175)]), (-9471, [(-9471, 8, 0.9391)]), (-9496, [(-9496, -12, 1.055)]), (-9499, [(-9499, -8, 0.4689)]), (-9511, [(-9511, 12, 1.054)]), (-9519, [(-9519, -16, 3.747)]), (-9544, [(-9544, -4, 0.1169)]), (-9556, [(-9556, 24, 4.207)]), (-9571, [(-9571, -20, 2.919)]), (-9579, [(-9579, 4, 0.2334)]), (-9591, [(-9591, 0, 0)]), (-9619, [(-9619, -8, 0.4659)]), (-9624, [(-9624, -4, 0.2329)]), (-9631, [(-9631, -4, 0.1164)]), (-9636, [(-9636, -24, 8.379)]), (-9651, [(-9651, 6, 0.5233)]), (-9679, [(-9679, 0, 0)]), (-9691, [(-9691, 0, 0)]), (-9699, [(-9699, -4, 0.2320)]), (-9736, [(-9736, -20, 2.894)]), (-9739, [(-9739, -16, 1.852)]), (-9759, [(-9759, -10, 1.446)]), (-9771, [(-9771, 6, 0.5201)]), (-9784, [(-9784, 4, 0.1155)]), (-9796, [(-9796, 0, 0)]), (-9799, [(-9799, -16, 1.846)]), (-9811, [(-9811, -4, 0.1153)]), (-9816, [(-9816, -16, 3.690)]), (-9831, [(-9831, -8, 0.9217)]), (-9844, [(-9844, 8, 0.4606)]), (-9859, [(-9859, -8, 0.4602)]), (-9871, [(-9871, -36, 9.314)]), (-9876, [(-9876, 12, 2.069)]), (-9879, [(-9879, 8, 0.9195)]), (-9919, [(-9919, 8, 0.4588)]), (-9924, [(-9924, -8, 0.9174)]), (-9931, [(-9931, 12, 1.032)]), (-9939, [(-9939, 2, 0.05729)]), (-9951, [(-9951, -4, 0.2290)]), (-9976, [(-9976, 16, 1.830)]), (-9979, [(-9979, 4, 0.1144)]), (-9991, [(-9991, -20, 2.857)])]]

# map: (1 |-> 1.0) -> 1, Fractional ideal (3) -> 1, Fractional ideal (5) -> -1
[-43, -1/2 + 23/2*i + 1/2*j + (-1/2)*k, [(13, [(13, 4, 1.390)]), (28, [(28, -8, 3.789)]), (37, [(37, 4, 0.8239)]), (73, [(73, 12, 5.279)]), (88, [(88, -8, 2.137)]), (97, [(97, 4, 0.5089)]), (133, [(133, 8, 1.738)]), (157, [(157, -4, 0.4000)]), (172, [(172, -16, 6.114)]), (193, [(193, -4, 0.3608)]), (217, [(217, 8, 1.361)]), (232, [(232, 8, 1.316)]), (253, [(253, 0, 0)]), (268, [(268, 0, 0)]), (277, [(277, 4, 0.3011)]), (313, [(313, 4, 0.2833)]), (328, [(328, 16, 4.428)]), (337, [(337, -20, 6.825)]), (373, [(373, -12, 2.335)]), (397, [(397, 4, 0.2515)]), (412, [(412, -8, 0.9876)]), (433, [(433, -20, 6.021)]), (457, [(457, 4, 0.2344)]), (472, [(472, 24, 8.305)]), (493, [(493, -8, 0.9029)]), (508, [(508, 8, 0.8894)]), (517, [(517, -16, 3.527)]), (553, [(553, 0, 0)]), (568, [(568, 16, 3.365)]), (577, [(577, 4, 0.2086)]), (613, [(613, -4, 0.2024)]), (652, [(652, 16, 3.140)]), (673, [(673, -20, 4.830)]), (697, [(697, -8, 0.7593)]), (712, [(712, 0, 0)]), (733, [(733, -12, 1.666)]), (748, [(748, 0, 0)]), (757, [(757, -4, 0.1822)]), (793, [(793, 16, 2.848)]), (808, [(808, -8, 0.7052)]), (817, [(817, -8, 0.7014)]), (853, [(853, -4, 0.1716)]), (877, [(877, -12, 1.523)]), (892, [(892, -8, 0.6712)]), (913, [(913, -24, 5.971)]), (937, [(937, 20, 4.093)]), (952, [(952, -16, 2.599)]), (973, [(973, 8, 0.6427)]), (988, [(988, 16, 2.551)]), (997, [(997, 4, 0.1587)]), (1033, [(1033, 28, 7.641)]), (1048, [(1048, 8, 0.6192)]), (1057, [(1057, 0, 0)]), (1093, [(1093, 4, 0.1516)]), (1117, [(1117, 20, 3.749)]), (1132, [(1132, 0, 0)]), (1153, [(1153, -4, 0.1476)]), (1177, [(1177, -8, 0.5843)]), (1192, [(1192, 8, 0.5806)]), (1213, [(1213, 4, 0.1439)]), (1228, [(1228, -16, 2.288)]), (1237, [(1237, -4, 0.1425)]), (1273, [(1273, 16, 2.247)]), (1288, [(1288, -16, 2.234)]), (1297, [(1297, -20, 3.479)]), (1333, [(1333, 16, 2.196)]), (1357, [(1357, 8, 0.5442)]), (1393, [(1393, -8, 0.5371)]), (1417, [(1417, 8, 0.5326)]), (1432, [(1432, -24, 4.768)]), (1453, [(1453, 12, 1.183)]), (1468, [(1468, -24, 4.709)]), (1477, [(1477, 16, 2.086)]), (1513, [(1513, 16, 2.062)]), (1528, [(1528, -16, 2.051)]), (1537, [(1537, 32, 8.181)]), (1597, [(1597, -20, 3.135)]), (1612, [(1612, 0, 0)]), (1633, [(1633, 8, 0.4961)]), (1657, [(1657, 12, 1.108)]), (1672, [(1672, -16, 1.961)]), (1693, [(1693, 12, 1.096)]), (1708, [(1708, 0, 0)]), (1717, [(1717, 0, 0)]), (1753, [(1753, 20, 2.992)]), (1768, [(1768, -16, 1.907)]), (1777, [(1777, -20, 2.972)]), (1837, [(1837, -8, 0.4677)]), (1852, [(1852, 8, 0.4658)]), (1873, [(1873, -12, 1.042)]), (1897, [(1897, 24, 4.142)]), (1912, [(1912, 16, 1.834)]), (1933, [(1933, -12, 1.026)]), (1948, [(1948, -8, 0.4542)]), (1957, [(1957, 16, 1.813)]), (1993, [(1993, 12, 1.010)]), (2008, [(2008, -8, 0.4474)]), (2017, [(2017, -12, 1.004)]), (2053, [(2053, -12, 0.9955)]), (2077, [(2077, -8, 0.4399)]), (2092, [(2092, 0, 0)]), (2113, [(2113, 12, 0.9812)]), (2137, [(2137, -12, 0.9757)]), (2152, [(2152, -8, 0.4321)]), (2173, [(2173, 8, 0.4300)]), (2188, [(2188, 16, 1.714)]), (2233, [(2233, 0, 0)]), (2248, [(2248, -16, 1.691)]), (2257, [(2257, -24, 3.798)]), (2293, [(2293, 12, 0.9419)]), (2317, [(2317, 16, 1.666)]), (2332, [(2332, 32, 6.642)]), (2353, [(2353, -32, 6.612)]), (2377, [(2377, 28, 5.037)]), (2392, [(2392, -16, 1.640)]), (2413, [(2413, 0, 0)]), (2428, [(2428, 24, 3.662)]), (2437, [(2437, -20, 2.538)]), (2473, [(2473, -20, 2.520)]), (2488, [(2488, 16, 1.608)]), (2497, [(2497, 24, 3.611)]), (2533, [(2533, -16, 1.593)]), (2557, [(2557, -12, 0.8920)]), (2572, [(2572, 16, 1.581)]), (2593, [(2593, -28, 4.823)]), (2617, [(2617, -28, 4.800)]), (2632, [(2632, -16, 1.563)]), (2653, [(2653, 0, 0)]), (2668, [(2668, 16, 1.552)]), (2677, [(2677, 4, 0.09686)]), (2713, [(2713, 12, 0.8660)]), (2728, [(2728, 32, 6.141)]), (2737, [(2737, -32, 6.131)]), (2773, [(2773, -8, 0.3807)]), (2797, [(2797, 4, 0.09476)]), (2812, [(2812, 16, 1.512)]), (2833, [(2833, -20, 2.354)]), (2857, [(2857, -20, 2.344)]), (2872, [(2872, 0, 0)]), (2893, [(2893, -24, 3.354)]), (2908, [(2908, 8, 0.3717)]), (2917, [(2917, -12, 0.8351)]), (2953, [(2953, 28, 4.519)]), (2968, [(2968, 16, 1.472)]), (2977, [(2977, 24, 3.307)]), (3013, [(3013, -24, 3.287)]), (3037, [(3037, 12, 0.8185)]), (3052, [(3052, 0, 0)]), (3073, [(3073, 8, 0.3616)]), (3097, [(3097, 8, 0.3602)]), (3112, [(3112, -24, 3.234)]), (3133, [(3133, -24, 3.223)]), (3148, [(3148, 32, 5.717)]), (3157, [(3157, 0, 0)]), (3193, [(3193, -24, 3.193)]), (3208, [(3208, 32, 5.663)]), (3217, [(3217, 12, 0.7952)]), (3253, [(3253, 12, 0.7908)]), (3277, [(3277, -24, 3.152)]), (3292, [(3292, 8, 0.3494)]), (3313, [(3313, -12, 0.7836)]), (3337, [(3337, -8, 0.3470)]), (3352, [(3352, -8, 0.3463)]), (3373, [(3373, -4, 0.08629)]), (3397, [(3397, -16, 1.376)]), (3433, [(3433, -4, 0.08554)]), (3448, [(3448, -32, 5.462)]), (3457, [(3457, 4, 0.08524)]), (3493, [(3493, 0, 0)]), (3517, [(3517, 4, 0.08451)]), (3532, [(3532, -16, 1.349)]), (3553, [(3553, -16, 1.345)]), (3592, [(3592, 48, 12.04)]), (3613, [(3613, 12, 0.7504)]), (3628, [(3628, 0, 0)]), (3637, [(3637, -12, 0.7479)]), (3673, [(3673, -4, 0.08270)]), (3688, [(3688, 8, 0.3301)]), (3697, [(3697, -36, 6.676)]), (3733, [(3733, 20, 2.051)]), (3772, [(3772, 0, 0)]), (3793, [(3793, -4, 0.08138)]), (3817, [(3817, 8, 0.3245)]), (3832, [(3832, 16, 1.295)]), (3853, [(3853, -4, 0.08074)]), (3868, [(3868, 8, 0.3223)]), (3877, [(3877, 12, 0.7244)]), (3913, [(3913, 16, 1.282)]), (3928, [(3928, -24, 2.879)]), (3937, [(3937, 32, 5.112)]), (3973, [(3973, 8, 0.3180)]), (3997, [(3997, 16, 1.268)]), (4012, [(4012, 32, 5.064)]), (4033, [(4033, 24, 2.841)]), (4057, [(4057, -4, 0.07868)]), (4072, [(4072, -24, 2.827)]), (4093, [(4093, 4, 0.07834)]), (4108, [(4108, -32, 5.004)]), (4117, [(4117, -8, 0.3124)]), (4153, [(4153, -12, 0.6999)]), (4168, [(4168, -16, 1.242)]), (4177, [(4177, -52, 13.11)]), (4213, [(4213, -16, 1.235)]), (4237, [(4237, 16, 1.232)]), (4252, [(4252, -40, 7.686)]), (4273, [(4273, 36, 6.210)]), (4297, [(4297, 12, 0.6881)]), (4333, [(4333, 24, 2.741)]), (4348, [(4348, 24, 2.736)]), (4357, [(4357, 4, 0.07593)]), (4393, [(4393, 16, 1.210)]), (4408, [(4408, -32, 4.831)]), (4417, [(4417, 32, 4.826)]), (4453, [(4453, -16, 1.202)]), (4492, [(4492, -16, 1.196)]), (4513, [(4513, 4, 0.07460)]), (4537, [(4537, -8, 0.2976)]), (4552, [(4552, 32, 4.754)]), (4573, [(4573, 8, 0.2964)]), (4588, [(4588, -32, 4.735)]), (4597, [(4597, 4, 0.07392)]), (4633, [(4633, -16, 1.178)]), (4648, [(4648, 0, 0)]), (4657, [(4657, 12, 0.6610)]), (4717, [(4717, -16, 1.168)]), (4777, [(4777, -16, 1.160)]), (4792, [(4792, -32, 4.633)]), (4813, [(4813, 36, 5.851)]), (4828, [(4828, -16, 1.154)]), (4837, [(4837, 24, 2.594)]), (4873, [(4873, 16, 1.149)]), (4888, [(4888, 32, 4.588)]), (4897, [(4897, 8, 0.2865)]), (4933, [(4933, 28, 3.496)]), (4957, [(4957, -44, 8.613)]), (4972, [(4972, 0, 0)]), (4993, [(4993, 44, 8.582)]), (5017, [(5017, 16, 1.132)]), (5032, [(5032, 0, 0)]), (5053, [(5053, 8, 0.2820)]), (5068, [(5068, -32, 4.506)]), (5077, [(5077, -12, 0.6330)]), (5113, [(5113, -28, 3.434)]), (5128, [(5128, -32, 4.479)]), (5137, [(5137, 0, 0)]), (5173, [(5173, -16, 1.115)]), (5197, [(5197, 12, 0.6257)]), (5212, [(5212, -24, 2.499)]), (5233, [(5233, 12, 0.6235)]), (5257, [(5257, 48, 9.954)]), (5272, [(5272, 8, 0.2761)]), (5293, [(5293, -24, 2.480)]), (5308, [(5308, -8, 0.2752)]), (5317, [(5317, 8, 0.2749)]), (5353, [(5353, -8, 0.2740)]), (5368, [(5368, 16, 1.094)]), (5377, [(5377, 24, 2.460)]), (5413, [(5413, 28, 3.338)]), (5437, [(5437, 12, 0.6117)]), (5452, [(5452, -16, 1.086)]), (5473, [(5473, -8, 0.2710)]), (5497, [(5497, -40, 6.760)]), (5512, [(5512, -32, 4.320)]), (5533, [(5533, -8, 0.2695)]), (5548, [(5548, -16, 1.077)]), (5557, [(5557, 20, 1.681)]), (5593, [(5593, 32, 4.289)]), (5608, [(5608, 24, 2.409)]), (5617, [(5617, -40, 6.687)]), (5653, [(5653, 12, 0.5999)]), (5677, [(5677, -8, 0.2661)]), (5692, [(5692, -8, 0.2657)]), (5713, [(5713, -16, 1.061)]), (5737, [(5737, -4, 0.06617)]), (5752, [(5752, 32, 4.229)]), (5773, [(5773, -32, 4.221)]), (5788, [(5788, -8, 0.2635)]), (5797, [(5797, -16, 1.053)]), (5833, [(5833, -16, 1.050)]), (5848, [(5848, 16, 1.049)]), (5857, [(5857, 36, 5.304)]), (5893, [(5893, 0, 0)]), (5917, [(5917, 0, 0)]), (5932, [(5932, 32, 4.165)]), (5953, [(5953, 60, 14.62)]), (5977, [(5977, -16, 1.037)]), (5992, [(5992, 16, 1.036)]), (6013, [(6013, 8, 0.2585)]), (6028, [(6028, 32, 4.131)]), (6037, [(6037, -4, 0.06450)]), (6073, [(6073, -12, 0.5788)]), (6088, [(6088, -16, 1.028)]), (6097, [(6097, 0, 0)]), (6133, [(6133, -20, 1.600)]), (6157, [(6157, -8, 0.2555)]), (6172, [(6172, 24, 2.297)]), (6193, [(6193, -8, 0.2547)]), (6217, [(6217, -4, 0.06356)]), (6232, [(6232, 16, 1.016)]), (6268, [(6268, 24, 2.279)]), (6277, [(6277, 28, 3.100)]), (6313, [(6313, -48, 9.083)]), (6328, [(6328, 16, 1.008)]), (6337, [(6337, -4, 0.06296)]), (6373, [(6373, -4, 0.06278)]), (6397, [(6397, -12, 0.5639)]), (6412, [(6412, -64, 16.02)]), (6433, [(6433, -16, 0.9998)]), (6457, [(6457, -32, 3.992)]), (6472, [(6472, 0, 0)]), (6493, [(6493, -8, 0.2488)]), (6508, [(6508, 16, 0.9940)]), (6553, [(6553, -12, 0.5572)]), (6568, [(6568, -24, 2.226)]), (6577, [(6577, 20, 1.545)]), (6613, [(6613, -32, 3.944)]), (6637, [(6637, -4, 0.06152)]), (6652, [(6652, 8, 0.2458)]), (6673, [(6673, -28, 3.006)]), (6697, [(6697, -16, 0.9799)]), (6712, [(6712, 32, 3.915)]), (6733, [(6733, 28, 2.993)]), (6748, [(6748, -16, 0.9762)]), (6757, [(6757, -16, 0.9755)]), (6793, [(6793, -20, 1.520)]), (6808, [(6808, 0, 0)]), (6817, [(6817, 24, 2.185)]), (6853, [(6853, -16, 0.9687)]), (6892, [(6892, 0, 0)]), (6913, [(6913, 16, 0.9644)]), (6937, [(6937, -16, 0.9628)]), (6952, [(6952, 48, 8.656)]), (6973, [(6973, -8, 0.2401)]), (6988, [(6988, 16, 0.9593)]), (6997, [(6997, 28, 2.936)]), (7033, [(7033, -8, 0.2390)]), (7048, [(7048, 32, 3.821)]), (7057, [(7057, -36, 4.832)]), (7093, [(7093, -16, 0.9521)]), (7117, [(7117, -16, 0.9505)]), (7132, [(7132, -8, 0.2374)]), (7153, [(7153, 8, 0.2370)]), (7177, [(7177, 4, 0.05916)]), (7192, [(7192, 0, 0)]), (7213, [(7213, -12, 0.5311)]), (7228, [(7228, 0, 0)]), (7237, [(7237, -20, 1.473)]), (7273, [(7273, -8, 0.2351)]), (7288, [(7288, 32, 3.757)]), (7297, [(7297, 28, 2.875)]), (7333, [(7333, -12, 0.5267)]), (7357, [(7357, 0, 0)]), (7372, [(7372, 16, 0.9339)]), (7393, [(7393, 12, 0.5246)]), (7417, [(7417, 4, 0.05819)]), (7432, [(7432, 16, 0.9302)]), (7453, [(7453, -32, 3.715)]), (7468, [(7468, 32, 3.712)]), (7477, [(7477, -20, 1.449)]), (7513, [(7513, -16, 0.9251)]), (7528, [(7528, 8, 0.2311)]), (7537, [(7537, -20, 1.443)]), (7573, [(7573, 12, 0.5183)]), (7597, [(7597, 0, 0)]), (7612, [(7612, 16, 0.9191)]), (7633, [(7633, -8, 0.2295)]), (7657, [(7657, 0, 0)]), (7672, [(7672, -16, 0.9155)]), (7708, [(7708, -16, 0.9133)]), (7717, [(7717, -28, 2.796)]), (7753, [(7753, -44, 6.887)]), (7768, [(7768, 24, 2.047)]), (7777, [(7777, 0, 0)]), (7813, [(7813, 0, 0)]), (7837, [(7837, 16, 0.9058)]), (7852, [(7852, -32, 3.620)]), (7873, [(7873, 44, 6.834)]), (7897, [(7897, 0, 0)]), (7912, [(7912, 16, 0.9015)]), (7933, [(7933, -12, 0.5064)]), (7948, [(7948, -16, 0.8995)]), (7957, [(7957, 0, 0)]), (7993, [(7993, -44, 6.783)]), (8008, [(8008, 32, 3.584)]), (8017, [(8017, -4, 0.05597)]), (8053, [(8053, 4, 0.05585)]), (8077, [(8077, -16, 0.8922)]), (8113, [(8113, 48, 8.012)]), (8137, [(8137, 48, 8.000)]), (8152, [(8152, -24, 1.998)]), (8173, [(8173, -8, 0.2217)]), (8188, [(8188, -16, 0.8862)]), (8197, [(8197, 0, 0)]), (8233, [(8233, -12, 0.4971)]), (8248, [(8248, 32, 3.532)]), (8257, [(8257, 32, 3.530)]), (8293, [(8293, 20, 1.376)]), (8317, [(8317, 4, 0.05495)]), (8332, [(8332, -32, 3.514)]), (8353, [(8353, -4, 0.05484)]), (8377, [(8377, -36, 4.435)]), (8392, [(8392, 0, 0)]), (8413, [(8413, -16, 0.8742)]), (8437, [(8437, 0, 0)]), (8473, [(8473, -16, 0.8711)]), (8488, [(8488, -40, 5.440)]), (8497, [(8497, -8, 0.2175)]), (8533, [(8533, -16, 0.8681)]), (8557, [(8557, 40, 5.418)]), (8572, [(8572, -8, 0.2165)]), (8593, [(8593, 24, 1.946)]), (8617, [(8617, -8, 0.2160)]), (8632, [(8632, 0, 0)]), (8653, [(8653, 16, 0.8620)]), (8668, [(8668, 16, 0.8613)]), (8677, [(8677, 4, 0.05380)]), (8713, [(8713, 44, 6.497)]), (8728, [(8728, -56, 10.51)]), (8737, [(8737, -20, 1.340)]), (8773, [(8773, 24, 1.926)]), (8797, [(8797, -8, 0.2137)]), (8812, [(8812, 16, 0.8542)]), (8857, [(8857, -40, 5.325)]), (8872, [(8872, -24, 1.915)]), (8893, [(8893, 28, 2.604)]), (8908, [(8908, 32, 3.398)]), (8917, [(8917, 24, 1.911)]), (8953, [(8953, -40, 5.297)]), (8968, [(8968, -16, 0.8468)]), (8977, [(8977, 8, 0.2116)]), (9013, [(9013, 12, 0.4751)]), (9037, [(9037, 8, 0.2109)]), (9052, [(9052, 32, 3.371)]), (9073, [(9073, -8, 0.2105)]), (9097, [(9097, -8, 0.2102)]), (9112, [(9112, 16, 0.8400)]), (9133, [(9133, 12, 0.4720)]), (9148, [(9148, -24, 1.886)]), (9157, [(9157, -4, 0.05237)]), (9193, [(9193, -56, 10.25)]), (9208, [(9208, -16, 0.8357)]), (9217, [(9217, 24, 1.879)]), (9253, [(9253, 16, 0.8336)]), (9277, [(9277, 12, 0.4683)]), (9292, [(9292, 48, 7.487)]), (9313, [(9313, 8, 0.2077)]), (9337, [(9337, 12, 0.4668)]), (9352, [(9352, -48, 7.463)]), (9373, [(9373, 32, 3.313)]), (9388, [(9388, -32, 3.310)]), (9397, [(9397, -12, 0.4653)]), (9433, [(9433, 28, 2.528)]), (9448, [(9448, -8, 0.2062)]), (9493, [(9493, -16, 0.8230)]), (9517, [(9517, 24, 1.849)]), (9532, [(9532, -24, 1.848)]), (9553, [(9553, 24, 1.846)]), (9577, [(9577, 24, 1.844)]), (9592, [(9592, -48, 7.369)]), (9613, [(9613, -4, 0.05112)]), (9628, [(9628, 16, 0.8172)]), (9637, [(9637, -16, 0.8168)]), (9673, [(9673, 32, 3.261)]), (9688, [(9688, -32, 3.259)]), (9697, [(9697, 36, 4.122)]), (9733, [(9733, -4, 0.05080)]), (9757, [(9757, -8, 0.2029)]), (9772, [(9772, -32, 3.245)]), (9793, [(9793, 24, 1.823)]), (9817, [(9817, -12, 0.4552)]), (9832, [(9832, 24, 1.820)]), (9853, [(9853, 16, 0.8078)]), (9868, [(9868, -32, 3.229)]), (9877, [(9877, -32, 3.227)]), (9913, [(9913, 0, 0)]), (9928, [(9928, 16, 0.8048)]), (9937, [(9937, 0, 0)]), (9973, [(9973, 20, 1.255)]), (9997, [(9997, 8, 0.2005)])]]

# map: (1 |-> 1.0) -> 1, Fractional ideal (3) -> 1, Fractional ideal (5) -> 1
[-31, -9/2 + (-339/2)*i + (-5)*j - k, [(1, [(1, -4, 1.253)]), (61, [(61, -16, 2.567)]), (76, [(76, 16, 2.300)]), (109, [(109, 0, 0)]), (124, [(124, 16, 1.800)]), (136, [(136, 16, 1.719)]), (181, [(181, 0, 0)]), (184, [(184, -32, 5.912)]), (229, [(229, 16, 1.325)]), (241, [(241, 16, 1.291)]), (301, [(301, 0, 0)]), (316, [(316, -16, 1.128)]), (349, [(349, -16, 1.073)]), (364, [(364, 0, 0)]), (376, [(376, 0, 0)]), (409, [(409, 32, 3.965)]), (421, [(421, 16, 0.9771)]), (424, [(424, 16, 0.9736)]), (469, [(469, -32, 3.703)]), (481, [(481, 48, 8.227)]), (541, [(541, 32, 3.448)]), (556, [(556, -48, 7.652)]), (589, [(589, 32, 3.304)]), (601, [(601, -16, 0.8178)]), (604, [(604, 16, 0.8158)]), (616, [(616, -32, 3.231)]), (649, [(649, -32, 3.148)]), (661, [(661, -16, 0.7798)]), (664, [(664, 0, 0)]), (709, [(709, 16, 0.7529)]), (721, [(721, 32, 2.987)]), (769, [(769, -16, 0.7230)]), (781, [(781, 32, 2.870)]), (796, [(796, 16, 0.7106)]), (829, [(829, 0, 0)]), (844, [(844, 48, 6.211)]), (856, [(856, -32, 2.741)]), (889, [(889, 0, 0)]), (901, [(901, -16, 0.6679)]), (904, [(904, -48, 6.001)]), (949, [(949, -16, 0.6508)]), (1009, [(1009, 48, 5.680)]), (1021, [(1021, 0, 0)]), (1036, [(1036, 32, 2.491)]), (1069, [(1069, -32, 2.453)]), (1081, [(1081, 0, 0)]), (1084, [(1084, -48, 5.480)]), (1096, [(1096, 16, 0.6056)]), (1129, [(1129, 32, 2.387)]), (1141, [(1141, 0, 0)]), (1144, [(1144, 32, 2.371)]), (1189, [(1189, 0, 0)]), (1201, [(1201, -16, 0.5785)]), (1249, [(1249, -48, 5.105)]), (1261, [(1261, -48, 5.081)]), (1276, [(1276, 32, 2.245)]), (1309, [(1309, 32, 2.216)]), (1321, [(1321, -48, 4.964)]), (1324, [(1324, -16, 0.5510)]), (1336, [(1336, 64, 8.776)]), (1381, [(1381, 16, 0.5395)]), (1384, [(1384, -16, 0.5389)]), (1429, [(1429, 32, 2.121)]), (1441, [(1441, 32, 2.113)]), (1489, [(1489, 32, 2.078)]), (1501, [(1501, -32, 2.070)]), (1516, [(1516, -16, 0.5149)]), (1549, [(1549, -16, 0.5094)]), (1561, [(1561, -64, 8.119)]), (1564, [(1564, -32, 2.028)]), (1576, [(1576, 16, 0.5050)]), (1609, [(1609, 32, 1.999)]), (1621, [(1621, 0, 0)]), (1624, [(1624, 64, 7.960)]), (1669, [(1669, -16, 0.4907)]), (1729, [(1729, -32, 1.929)]), (1741, [(1741, 0, 0)]), (1756, [(1756, -16, 0.4784)]), (1789, [(1789, -16, 0.4740)]), (1801, [(1801, -48, 4.252)]), (1804, [(1804, -32, 1.888)]), (1816, [(1816, 32, 1.882)]), (1861, [(1861, -32, 1.859)]), (1864, [(1864, 16, 0.4644)]), (1909, [(1909, 32, 1.835)]), (1921, [(1921, 16, 0.4574)]), (1969, [(1969, 0, 0)]), (1981, [(1981, 0, 0)]), (1996, [(1996, 16, 0.4487)]), (2029, [(2029, 16, 0.4451)]), (2041, [(2041, 16, 0.4438)]), (2044, [(2044, 64, 7.095)]), (2056, [(2056, -48, 3.979)]), (2089, [(2089, -16, 0.4386)]), (2101, [(2101, 0, 0)]), (2104, [(2104, 0, 0)]), (2149, [(2149, -32, 1.730)]), (2161, [(2161, -16, 0.4313)]), (2221, [(2221, -16, 0.4254)]), (2236, [(2236, 0, 0)]), (2269, [(2269, 0, 0)]), (2281, [(2281, 16, 0.4198)]), (2284, [(2284, -48, 3.775)]), (2296, [(2296, -64, 6.694)]), (2329, [(2329, 48, 3.739)]), (2341, [(2341, 48, 3.729)]), (2344, [(2344, 16, 0.4141)]), (2389, [(2389, 16, 0.4102)]), (2449, [(2449, 32, 1.620)]), (2461, [(2461, 0, 0)]), (2476, [(2476, 48, 3.626)]), (2509, [(2509, 16, 0.4002)]), (2521, [(2521, -16, 0.3993)]), (2524, [(2524, 16, 0.3990)]), (2536, [(2536, 48, 3.583)]), (2569, [(2569, -64, 6.329)]), (2581, [(2581, 64, 6.314)]), (2584, [(2584, -64, 6.310)]), (2629, [(2629, -32, 1.564)]), (2641, [(2641, 32, 1.560)]), (2689, [(2689, 0, 0)]), (2701, [(2701, 16, 0.3858)]), (2716, [(2716, -64, 6.155)]), (2749, [(2749, -32, 1.529)]), (2761, [(2761, -32, 1.526)]), (2764, [(2764, -48, 3.432)]), (2776, [(2776, -32, 1.522)]), (2821, [(2821, -32, 1.510)]), (2824, [(2824, 80, 9.431)]), (2869, [(2869, 0, 0)]), (2881, [(2881, 32, 1.494)]), (2929, [(2929, 32, 1.482)]), (2941, [(2941, 16, 0.3697)]), (2956, [(2956, -16, 0.3687)]), (3001, [(3001, 32, 1.464)]), (3004, [(3004, -48, 3.292)]), (3016, [(3016, -32, 1.460)]), (3049, [(3049, -48, 3.268)]), (3061, [(3061, -16, 0.3624)]), (3064, [(3064, 32, 1.449)]), (3109, 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[(8956, 112, 10.38)]), (8989, [(8989, 32, 0.8458)]), (9001, [(9001, 64, 3.381)]), (9004, [(9004, 16, 0.2113)]), (9049, [(9049, 32, 0.8430)]), (9061, [(9061, 0, 0)]), (9064, [(9064, 64, 3.369)]), (9109, [(9109, -16, 0.2101)]), (9121, [(9121, 32, 0.8397)]), (9169, [(9169, 112, 10.26)]), (9181, [(9181, -32, 0.8369)]), (9229, [(9229, -32, 0.8347)]), (9241, [(9241, -80, 5.214)]), (9244, [(9244, 16, 0.2085)]), (9256, [(9256, 32, 0.8335)]), (9289, [(9289, -64, 3.328)]), (9301, [(9301, -32, 0.8315)]), (9304, [(9304, -64, 3.326)]), (9349, [(9349, 16, 0.2073)]), (9361, [(9361, 0, 0)]), (9421, [(9421, -16, 0.2065)]), (9436, [(9436, -32, 0.8255)]), (9469, [(9469, -16, 0.2060)]), (9481, [(9481, -32, 0.8236)]), (9484, [(9484, 48, 1.853)]), (9496, [(9496, -32, 0.8229)]), (9529, [(9529, 48, 1.848)]), (9541, [(9541, 0, 0)]), (9544, [(9544, -80, 5.130)]), (9589, [(9589, 0, 0)]), (9601, [(9601, -48, 1.841)]), (9649, [(9649, 64, 3.266)]), (9661, [(9661, 32, 0.8159)]), (9676, [(9676, 64, 3.261)]), (9709, [(9709, -32, 0.8139)]), (9721, [(9721, 48, 1.830)]), (9724, [(9724, -64, 3.253)]), (9736, [(9736, -16, 0.2032)]), (9769, [(9769, 16, 0.2028)]), (9781, [(9781, -64, 3.243)]), (9784, [(9784, 32, 0.8107)]), (9829, [(9829, -48, 1.820)]), (9841, [(9841, -80, 5.052)]), (9889, [(9889, 0, 0)]), (9901, [(9901, -32, 0.8059)]), (9916, [(9916, 64, 3.221)]), (9949, [(9949, 32, 0.8040)]), (9961, [(9961, 96, 7.231)]), (9964, [(9964, 64, 3.213)]), (9976, [(9976, 0, 0)])]]