# label = 58.2.a.a
# Base field F = Number Field in a with defining polynomial x - 1
# Quaternion algebra given by i^2 = -1, j^2 = -1
# Order with basis over the integers given by [1, 29*i, 8*i + j, 1/2 + (-7/2)*i + 1/2*j + 1/2*k]

# Nmax = 10000

[(1, [29*i, 8*i + j, 1/2 + (-7/2)*i + 1/2*j + 1/2*k]), (-1, [29*i, 8*i + j, 1/2 + (-7/2)*i + 1/2*j + 1/2*k])]
[((2,), -3/2 + 63/2*i + (-5/2)*j + (-3/2)*k), ((29,), -41/2 + 97/2*i + (-43/2)*j + (-41/2)*k)]

# map: (1 |-> 1.0) -> -1, Fractional ideal (2) -> -1, Fractional ideal (29) -> -1
[17, -9/2 + (-7/2)*i + 1/2*j + 1/2*k, [(-3, [(-3, 4, 2.568)]), (-11, [(-11, 4, 1.341)]), (-19, [(-19, -8, 4.082)]), (-43, [(-43, 20, 16.96)]), (-131, [(-131, 8, 1.554)]), (-155, [(-155, 4, 0.3573)]), (-163, [(-163, -36, 28.22)]), (-195, [(-195, -4, 0.3185)]), (-211, [(-211, -20, 7.655)]), (-235, [(-235, -36, 23.50)]), (-251, [(-251, 4, 0.2808)]), (-259, [(-259, -8, 1.106)]), (-307, [(-307, -4, 0.2539)]), (-331, [(-331, -20, 6.112)]), (-379, [(-379, 0, 0)]), (-395, [(-395, -4, 0.2238)]), (-403, [(-403, 44, 26.81)]), (-427, [(-427, -40, 21.53)]), (-443, [(-443, 16, 3.381)]), (-467, [(-467, -20, 5.146)]), (-483, [(-483, -24, 7.286)]), (-491, [(-491, -12, 1.807)]), (-563, [(-563, -12, 1.687)]), (-595, [(-595, -48, 26.26)]), (-611, [(-611, -4, 0.1799)]), (-619, [(-619, 20, 4.469)]), (-627, [(-627, 32, 11.37)]), (-635, [(-635, -8, 0.7060)]), (-659, [(-659, 4, 0.1733)]), (-699, [(-699, -4, 0.1682)]), (-707, [(-707, 0, 0)]), (-715, [(-715, -28, 8.151)]), (-723, [(-723, -20, 4.135)]), (-739, [(-739, 12, 1.473)]), (-771, [(-771, -28, 7.849)]), (-795, [(-795, 28, 7.730)]), (-827, [(-827, 12, 1.392)]), (-843, [(-843, -36, 12.41)]), (-851, [(-851, -8, 0.6099)]), (-859, [(-859, -36, 12.29)]), (-907, [(-907, -56, 28.95)]), (-939, [(-939, 12, 1.306)]), (-947, [(-947, 20, 3.613)]), (-955, [(-955, 32, 9.212)]), (-971, [(-971, -8, 0.5710)]), (-1003, [(-1003, -24, 5.056)]), (-1027, [(-1027, 52, 23.46)]), (-1059, [(-1059, 0, 0)]), (-1091, [(-1091, 4, 0.1347)]), (-1099, [(-1099, -24, 4.830)]), (-1123, [(-1123, 24, 4.778)]), (-1139, [(-1139, 8, 0.5272)]), (-1163, [(-1163, -28, 6.391)]), (-1171, [(-1171, -28, 6.369)]), (-1187, [(-1187, -24, 4.648)]), (-1203, [(-1203, 20, 3.206)]), (-1235, [(-1235, -16, 2.025)]), (-1259, [(-1259, -8, 0.5014)]), (-1291, [(-1291, 12, 1.114)]), (-1307, [(-1307, -4, 0.1230)]), (-1315, [(-1315, 44, 14.84)]), (-1355, [(-1355, 28, 5.921)]), (-1371, [(-1371, -8, 0.4805)]), (-1403, [(-1403, 24, 4.275)]), (-1411, [(-1411, -16, 1.895)]), (-1419, [(-1419, -4, 0.1181)]), (-1435, [(-1435, -8, 0.4697)]), (-1491, [(-1491, -24, 4.147)]), (-1523, [(-1523, 28, 5.585)]), (-1547, [(-1547, 16, 1.809)]), (-1555, [(-1555, 24, 4.061)]), (-1563, [(-1563, -28, 5.513)]), (-1603, [(-1603, 80, 44.44)]), (-1627, [(-1627, 28, 5.403)]), (-1635, [(-1635, 28, 5.390)]), (-1643, [(-1643, 12, 0.9876)]), (-1651, [(-1651, -16, 1.751)]), (-1667, [(-1667, -28, 5.338)]), (-1699, [(-1699, 20, 2.698)]), (-1723, [(-1723, -48, 15.43)]), (-1771, [(-1771, 40, 10.57)]), (-1779, [(-1779, -4, 0.1055)]), (-1787, [(-1787, 16, 1.684)]), (-1795, [(-1795, 60, 23.62)]), (-1819, [(-1819, 32, 6.674)]), (-1835, [(-1835, 16, 1.661)]), (-1867, [(-1867, -56, 20.18)]), (-1883, [(-1883, -16, 1.640)]), (-1931, [(-1931, 4, 0.1012)]), (-1955, [(-1955, -8, 0.4024)]), (-1987, [(-1987, 16, 1.597)]), (-2003, [(-2003, -12, 0.8945)]), (-2011, [(-2011, -56, 19.44)]), (-2019, [(-2019, 20, 2.475)]), (-2027, [(-2027, -12, 0.8891)]), (-2051, [(-2051, -16, 1.571)]), (-2067, [(-2067, 28, 4.794)]), (-2091, [(-2091, -16, 1.556)]), (-2099, [(-2099, 8, 0.3883)]), (-2131, [(-2131, -36, 7.805)]), (-2163, [(-2163, -24, 3.443)]), (-2219, [(-2219, 8, 0.3777)]), (-2235, [(-2235, -44, 11.38)]), (-2243, [(-2243, -24, 3.381)]), (-2251, [(-2251, 28, 4.594)]), (-2283, [(-2283, 8, 0.3724)]), (-2323, [(-2323, 88, 44.67)]), (-2339, [(-2339, -4, 0.09197)]), (-2347, [(-2347, 64, 23.50)]), (-2363, [(-2363, -24, 3.294)]), (-2395, [(-2395, 68, 26.27)]), (-2419, [(-2419, 64, 23.15)]), (-2451, [(-2451, 16, 1.437)]), (-2467, [(-2467, -52, 15.13)]), (-2483, [(-2483, -16, 1.428)]), (-2491, [(-2491, -4, 0.08912)]), (-2515, [(-2515, 36, 7.184)]), (-2531, [(-2531, 4, 0.08841)]), (-2555, [(-2555, -32, 5.632)]), (-2563, [(-2563, -68, 25.39)]), (-2571, [(-2571, -28, 4.298)]), (-2579, [(-2579, 0, 0)]), (-2595, [(-2595, -24, 3.143)]), (-2627, [(-2627, -40, 8.678)]), (-2651, [(-2651, 4, 0.08639)]), (-2683, [(-2683, -76, 31.00)]), (-2699, [(-2699, -28, 4.195)]), (-2707, [(-2707, -52, 14.45)]), (-2715, [(-2715, 20, 2.134)]), (-2723, [(-2723, -32, 5.455)]), (-2747, [(-2747, 0, 0)]), (-2787, [(-2787, 0, 0)]), (-2795, [(-2795, 28, 4.122)]), (-2803, [(-2803, 44, 10.17)]), (-2811, [(-2811, 16, 1.342)]), (-2827, [(-2827, 52, 14.14)]), (-2859, [(-2859, -4, 0.08319)]), (-2915, [(-2915, 20, 2.060)]), (-2931, [(-2931, 28, 4.026)]), (-2939, [(-2939, -4, 0.08205)]), (-2947, [(-2947, 72, 26.55)]), (-2955, [(-2955, -16, 1.309)]), (-2995, [(-2995, 12, 0.7315)]), (-3019, [(-3019, 76, 29.22)]), (-3027, [(-3027, 28, 3.961)]), (-3035, [(-3035, -12, 0.7266)]), (-3043, [(-3043, 48, 11.61)]), (-3059, [(-3059, -16, 1.287)]), (-3091, [(-3091, 28, 3.920)]), (-3115, [(-3115, -32, 5.100)]), (-3147, [(-3147, 32, 5.074)]), (-3163, [(-3163, 68, 22.86)]), (-3171, [(-3171, -16, 1.264)]), (-3187, [(-3187, -36, 6.382)]), (-3227, [(-3227, 56, 15.35)]), (-3251, [(-3251, 8, 0.3120)]), (-3259, [(-3259, 36, 6.311)]), (-3291, [(-3291, -4, 0.07753)]), (-3323, [(-3323, -8, 0.3086)]), (-3347, [(-3347, 8, 0.3075)]), (-3379, [(-3379, 20, 1.913)]), (-3395, [(-3395, -8, 0.3053)]), (-3403, [(-3403, 72, 24.70)]), (-3419, [(-3419, 4, 0.07607)]), (-3443, [(-3443, 4, 0.07580)]), (-3459, [(-3459, 12, 0.6806)]), (-3491, [(-3491, -4, 0.07528)]), (-3499, [(-3499, 12, 0.6768)]), (-3507, [(-3507, -56, 14.72)]), (-3523, [(-3523, -4, 0.07494)]), (-3579, [(-3579, 0, 0)]), (-3611, [(-3611, 8, 0.2961)]), (-3635, [(-3635, -8, 0.2951)]), (-3643, [(-3643, 16, 1.179)]), (-3651, [(-3651, -4, 0.07361)]), (-3691, [(-3691, -4, 0.07321)]), (-3715, [(-3715, -40, 7.298)]), (-3723, [(-3723, 32, 4.665)]), (-3731, [(-3731, 24, 2.621)]), (-3739, [(-3739, 0, 0)]), (-3755, [(-3755, 0, 0)]), (-3787, [(-3787, 80, 28.91)]), (-3811, [(-3811, -48, 10.38)]), (-3859, [(-3859, 48, 10.31)]), (-3867, [(-3867, 12, 0.6437)]), (-3883, [(-3883, -104, 48.25)]), (-3907, [(-3907, 52, 12.03)]), (-3923, [(-3923, -28, 3.480)]), (-3947, [(-3947, -8, 0.2832)]), (-3955, [(-3955, -24, 2.546)]), (-3963, [(-3963, 52, 11.94)]), (-4019, [(-4019, -20, 1.754)]), (-4043, [(-4043, -8, 0.2798)]), (-4091, [(-4091, -24, 2.503)]), (-4099, [(-4099, 20, 1.737)]), (-4115, [(-4115, -8, 0.2774)]), (-4139, [(-4139, 16, 1.106)]), (-4155, [(-4155, 32, 4.416)]), (-4179, [(-4179, -8, 0.2752)]), (-4187, [(-4187, 36, 5.568)]), (-4195, [(-4195, 36, 5.563)]), (-4219, [(-4219, -4, 0.06848)]), (-4251, [(-4251, -28, 3.343)]), (-4307, [(-4307, 40, 6.777)]), (-4323, [(-4323, 8, 0.2706)]), (-4331, [(-4331, 0, 0)]), (-4339, [(-4339, -56, 13.23)]), (-4371, [(-4371, 28, 3.297)]), (-4387, [(-4387, -56, 13.16)]), (-4411, [(-4411, 12, 0.6027)]), (-4427, [(-4427, -8, 0.2674)]), (-4435, [(-4435, 36, 5.410)]), (-4451, [(-4451, -4, 0.06667)]), (-4483, [(-4483, -4, 0.06643)]), (-4507, [(-4507, 44, 8.017)]), (-4539, [(-4539, -8, 0.2641)]), (-4555, [(-4555, -4, 0.06590)]), (-4571, [(-4571, 8, 0.2632)]), (-4579, [(-4579, -48, 9.465)]), (-4603, [(-4603, -124, 63.00)]), (-4619, [(-4619, 12, 0.5890)]), (-4643, [(-4643, -32, 4.178)]), (-4651, [(-4651, -20, 1.631)]), (-4659, [(-4659, 8, 0.2607)]), (-4667, [(-4667, 12, 0.5860)]), (-4683, [(-4683, -56, 12.74)]), (-4715, [(-4715, -24, 2.332)]), (-4739, [(-4739, -8, 0.2584)]), (-4771, [(-4771, -40, 6.440)]), (-4787, [(-4787, -24, 2.314)]), (-4795, [(-4795, -56, 12.59)]), (-4803, [(-4803, 20, 1.605)]), (-4811, [(-4811, -16, 1.026)]), (-4835, [(-4835, 20, 1.599)]), (-4883, [(-4883, 16, 1.018)]), (-4891, [(-4891, 32, 4.070)]), (-4899, [(-4899, -32, 4.067)]), (-4915, [(-4915, 44, 7.677)]), (-4947, [(-4947, -16, 1.012)]), (-4971, [(-4971, -4, 0.06309)]), (-5003, [(-5003, -24, 2.264)]), (-5019, [(-5019, 0, 0)]), (-5027, [(-5027, -64, 16.06)]), (-5035, [(-5035, 32, 4.012)]), (-5083, [(-5083, -40, 6.239)]), (-5107, [(-5107, 20, 1.556)]), (-5115, [(-5115, -44, 7.525)]), (-5123, [(-5123, -4, 0.06214)]), (-5131, [(-5131, 40, 6.209)]), (-5147, [(-5147, 20, 1.550)]), (-5179, [(-5179, 20, 1.545)]), (-5235, [(-5235, 12, 0.5533)]), (-5251, [(-5251, -56, 12.03)]), (-5259, [(-5259, 12, 0.5520)]), (-5267, [(-5267, 24, 2.206)]), (-5299, [(-5299, -64, 15.64)]), (-5315, [(-5315, -12, 0.5491)]), (-5339, [(-5339, -16, 0.9740)]), (-5347, [(-5347, 32, 3.893)]), (-5363, [(-5363, -40, 6.074)]), (-5379, [(-5379, 4, 0.06065)]), (-5411, [(-5411, -8, 0.2419)]), (-5435, [(-5435, 20, 1.508)]), (-5467, [(-5467, -56, 11.79)]), (-5483, [(-5483, -44, 7.268)]), (-5507, [(-5507, 8, 0.2397)]), (-5531, [(-5531, 4, 0.05981)]), (-5579, [(-5579, 16, 0.9528)]), (-5587, [(-5587, -128, 60.93)]), (-5595, [(-5595, -52, 10.05)]), (-5611, [(-5611, 44, 7.185)]), (-5667, [(-5667, -52, 9.985)]), (-5699, [(-5699, 0, 0)]), (-5723, [(-5723, 16, 0.9407)]), (-5731, [(-5731, 4, 0.05875)]), (-5739, [(-5739, -4, 0.05871)]), (-5763, [(-5763, -16, 0.9375)]), (-5779, [(-5779, 40, 5.851)]), (-5803, [(-5803, 0, 0)]), (-5811, [(-5811, 60, 13.13)]), (-5827, [(-5827, 20, 1.457)]), (-5843, [(-5843, -20, 1.455)]), (-5899, [(-5899, 8, 0.2316)]), (-5947, [(-5947, -8, 0.2307)]), (-5955, [(-5955, 28, 2.824)]), (-5963, [(-5963, 48, 8.294)]), (-5971, [(-5971, 80, 23.02)]), (-5995, [(-5995, -36, 4.653)]), (-6011, [(-6011, 12, 0.5163)]), (-6035, [(-6035, 16, 0.9161)]), (-6043, [(-6043, -12, 0.5150)]), (-6051, [(-6051, -20, 1.429)]), (-6059, [(-6059, 0, 0)]), (-6107, [(-6107, -24, 2.049)]), (-6131, [(-6131, 4, 0.05681)]), (-6163, [(-6163, -52, 9.575)]), (-6179, [(-6179, 24, 2.037)]), (-6187, [(-6187, -8, 0.2262)]), (-6195, [(-6195, 16, 0.9042)]), (-6203, [(-6203, -36, 4.574)]), (-6227, [(-6227, -28, 2.762)]), (-6243, [(-6243, 48, 8.106)]), (-6267, [(-6267, -100, 35.12)]), (-6283, [(-6283, 56, 11.00)]), (-6307, [(-6307, 80, 22.40)]), (-6339, [(-6339, 12, 0.5028)]), (-6395, [(-6395, -12, 0.5006)]), (-6411, [(-6411, 4, 0.05555)]), (-6427, [(-6427, -92, 29.35)]), (-6459, [(-6459, 12, 0.4981)]), (-6499, [(-6499, -24, 1.986)]), (-6515, [(-6515, -20, 1.378)]), (-6523, [(-6523, -116, 46.32)]), (-6539, [(-6539, 4, 0.05500)]), (-6571, [(-6571, -40, 5.487)]), (-6595, [(-6595, 8, 0.2191)]), (-6643, [(-6643, -48, 7.858)]), (-6659, [(-6659, -16, 0.8721)]), (-6667, [(-6667, 96, 31.38)]), (-6691, [(-6691, 20, 1.359)]), (-6707, [(-6707, 0, 0)]), (-6731, [(-6731, -24, 1.952)]), (-6739, [(-6739, 8, 0.2167)]), (-6747, [(-6747, 32, 3.466)]), (-6755, [(-6755, -8, 0.2165)]), (-6771, [(-6771, -32, 3.459)]), (-6803, [(-6803, -44, 6.525)]), (-6827, [(-6827, 12, 0.4845)]), (-6883, [(-6883, 92, 28.36)]), (-6891, [(-6891, -32, 3.429)]), (-6899, [(-6899, -16, 0.8568)]), (-6923, [(-6923, 24, 1.924)]), (-6963, [(-6963, -4, 0.05330)]), (-6971, [(-6971, 4, 0.05327)]), (-6979, [(-6979, -24, 1.917)]), (-6987, [(-6987, 48, 7.663)]), (-7003, [(-7003, -52, 8.983)]), (-7035, [(-7035, 56, 10.39)]), (-7059, [(-7059, -12, 0.4765)]), (-7091, [(-7091, 24, 1.902)]), (-7107, [(-7107, 80, 21.10)]), (-7115, [(-7115, -20, 1.318)]), (-7123, [(-7123, -152, 76.10)]), (-7131, [(-7131, 8, 0.2107)]), (-7171, [(-7171, -32, 3.362)]), (-7195, [(-7195, -32, 3.356)]), (-7211, [(-7211, 8, 0.2095)]), (-7219, [(-7219, 8, 0.2094)]), (-7235, [(-7235, -12, 0.4706)]), (-7291, [(-7291, 40, 5.209)]), (-7323, [(-7323, -4, 0.05198)]), (-7339, [(-7339, 8, 0.2077)]), (-7347, [(-7347, -4, 0.05189)]), (-7355, [(-7355, -24, 1.867)]), (-7363, [(-7363, -64, 13.27)]), (-7387, [(-7387, 56, 10.14)]), (-7403, [(-7403, 28, 2.533)]), (-7427, [(-7427, -8, 0.2064)]), (-7435, [(-7435, -104, 34.87)]), (-7451, [(-7451, -16, 0.8244)]), (-7467, [(-7467, -32, 3.294)]), (-7499, [(-7499, 0, 0)]), (-7523, [(-7523, 4, 0.05128)]), (-7555, [(-7555, 76, 18.47)]), (-7571, [(-7571, -24, 1.840)]), (-7579, [(-7579, 4, 0.05109)]), (-7619, [(-7619, -16, 0.8153)]), (-7635, [(-7635, -36, 4.123)]), (-7667, [(-7667, 32, 3.251)]), (-7683, [(-7683, -80, 20.30)]), (-7699, [(-7699, 60, 11.41)]), (-7755, [(-7755, 12, 0.4546)]), (-7787, [(-7787, -12, 0.4536)]), (-7811, [(-7811, 8, 0.2013)]), (-7819, [(-7819, 32, 3.219)]), (-7827, [(-7827, 52, 8.497)]), (-7851, [(-7851, 36, 4.066)]), (-7867, [(-7867, -52, 8.475)]), (-7891, [(-7891, -84, 22.08)]), (-7899, [(-7899, 20, 1.251)]), (-7907, [(-7907, 16, 0.8003)]), (-7915, [(-7915, -52, 8.449)]), (-7931, [(-7931, 8, 0.1998)]), (-7963, [(-7963, -104, 33.69)]), (-8035, [(-8035, 92, 26.25)]), (-8043, [(-8043, 64, 12.70)]), (-8051, [(-8051, 24, 1.785)]), (-8059, [(-8059, 76, 17.89)]), (-8083, [(-8083, -48, 7.124)]), (-8099, [(-8099, -16, 0.7908)]), (-8123, [(-8123, 36, 3.997)]), (-8131, [(-8131, 8, 0.1973)]), (-8139, [(-8139, 20, 1.233)]), (-8147, [(-8147, 4, 0.04928)]), (-8195, [(-8195, -4, 0.04913)]), (-8219, [(-8219, 20, 1.227)]), (-8251, [(-8251, -40, 4.897)]), (-8267, [(-8267, -8, 0.1957)]), (-8283, [(-8283, -28, 2.395)]), (-8291, [(-8291, -20, 1.221)]), (-8315, [(-8315, -8, 0.1951)]), (-8331, [(-8331, 52, 8.236)]), (-8355, [(-8355, -8, 0.1946)]), (-8363, [(-8363, 32, 3.113)]), (-8371, [(-8371, -24, 1.750)]), (-8395, [(-8395, -24, 1.748)]), (-8483, [(-8483, 24, 1.739)]), (-8499, [(-8499, -32, 3.088)]), (-8507, [(-8507, 4, 0.04822)]), (-8515, [(-8515, 56, 9.448)]), (-8547, [(-8547, -40, 4.811)]), (-8563, [(-8563, 20, 1.202)]), (-8587, [(-8587, 48, 6.912)]), (-8603, [(-8603, -40, 4.795)]), (-8611, [(-8611, 28, 2.349)]), (-8627, [(-8627, 4, 0.04789)]), (-8659, [(-8659, -48, 6.883)]), (-8683, [(-8683, -32, 3.055)]), (-8715, [(-8715, 64, 12.20)]), (-8731, [(-8731, 28, 2.332)]), (-8747, [(-8747, -4, 0.04756)]), (-8755, [(-8755, 40, 4.754)]), (-8779, [(-8779, 20, 1.187)]), (-8795, [(-8795, 8, 0.1897)]), (-8819, [(-8819, 20, 1.184)]), (-8827, [(-8827, 88, 22.91)]), (-8835, [(-8835, -8, 0.1893)]), (-8843, [(-8843, 8, 0.1892)]), (-8859, [(-8859, 4, 0.04726)]), (-8891, [(-8891, 16, 0.7547)]), (-8915, [(-8915, -36, 3.816)]), (-8947, [(-8947, -112, 36.87)]), (-8963, [(-8963, -20, 1.175)]), (-8971, [(-8971, 64, 12.02)]), (-8979, [(-8979, 32, 3.004)]), (-8987, [(-8987, -8, 0.1877)]), (-9011, [(-9011, -12, 0.4217)]), (-9051, [(-9051, 0, 0)]), (-9059, [(-9059, -8, 0.1869)]), (-9067, [(-9067, -168, 82.40)]), (-9091, [(-9091, 48, 6.718)]), (-9123, [(-9123, 28, 2.282)]), (-9147, [(-9147, 4, 0.04651)]), (-9179, [(-9179, 0, 0)]), (-9195, [(-9195, -36, 3.757)]), (-9203, [(-9203, -32, 2.967)]), (-9211, [(-9211, -16, 0.7415)]), (-9219, [(-9219, -8, 0.1853)]), (-9259, [(-9259, -32, 2.958)]), (-9283, [(-9283, 16, 0.7386)]), (-9291, [(-9291, 16, 0.7383)]), (-9299, [(-9299, -16, 0.7380)]), (-9307, [(-9307, -104, 31.17)]), (-9323, [(-9323, 28, 2.257)]), (-9355, [(-9355, -40, 4.599)]), (-9379, [(-9379, 16, 0.7348)]), (-9411, [(-9411, -44, 5.548)]), (-9427, [(-9427, 12, 0.4123)]), (-9435, [(-9435, 24, 1.648)]), (-9443, [(-9443, 16, 0.7323)]), (-9451, [(-9451, 0, 0)]), (-9491, [(-9491, -12, 0.4109)]), (-9515, [(-9515, 8, 0.1824)]), (-9523, [(-9523, -96, 26.25)]), (-9539, [(-9539, -12, 0.4099)]), (-9587, [(-9587, -44, 5.497)]), (-9611, [(-9611, 24, 1.633)]), (-9643, [(-9643, -108, 33.02)]), (-9659, [(-9659, -8, 0.1810)]), (-9667, [(-9667, -48, 6.514)]), (-9683, [(-9683, 48, 6.509)]), (-9707, [(-9707, 48, 6.501)]), (-9723, [(-9723, -16, 0.7217)]), (-9755, [(-9755, 28, 2.207)]), (-9763, [(-9763, 64, 11.52)]), (-9771, [(-9771, 4, 0.04500)]), (-9787, [(-9787, -108, 32.78)]), (-9843, [(-9843, -88, 21.70)]), (-9899, [(-9899, 16, 0.7153)]), (-9907, [(-9907, 44, 5.407)]), (-9915, [(-9915, -8, 0.1787)]), (-9939, [(-9939, -20, 1.115)]), (-9955, [(-9955, -100, 27.86)]), (-9979, [(-9979, 64, 11.40)]), (-9987, [(-9987, 36, 3.605)]), (-9995, [(-9995, 0, 0)])]]

# map: (1 |-> 1.0) -> -1, Fractional ideal (2) -> 1, Fractional ideal (29) -> 1
[5, 1/2 + (-47/2)*i + (-15/2)*j + (-1/2)*k, [(-4, [(-4, 2, 2.224)]), (-7, [(-7, 4, 3.362)]), (-20, [(-20, 2, 0.9946)]), (-23, [(-23, -4, 1.855)]), (-24, [(-24, -2, 0.9079)]), (-52, [(-52, 6, 5.552)]), (-71, [(-71, 0, 0)]), (-87, [(-87, 4, 1.908)]), (-88, [(-88, 10, 11.85)]), (-103, [(-103, 8, 3.506)]), (-111, [(-111, 0, 0)]), (-116, [(-116, 2, 0.8260)]), (-120, [(-120, -6, 3.654)]), (-132, [(-132, -2, 0.3871)]), (-136, [(-136, 0, 0)]), (-151, [(-151, 4, 0.7239)]), (-152, [(-152, 0, 0)]), (-167, [(-167, 0, 0)]), (-168, [(-168, -8, 5.491)]), (-183, [(-183, -4, 0.6576)]), (-199, [(-199, -12, 5.676)]), (-212, [(-212, 2, 0.3055)]), (-223, [(-223, -8, 2.383)]), (-228, [(-228, 8, 4.713)]), (-231, [(-231, -4, 0.5853)]), (-232, [(-232, -8, 9.345)]), (-239, [(-239, 4, 0.5754)]), (-248, [(-248, -6, 2.542)]), (-255, [(-255, 4, 0.5571)]), (-260, [(-260, -2, 0.2759)]), (-295, [(-295, 12, 4.662)]), (-296, [(-296, 0, 0)]), (-303, [(-303, 8, 2.044)]), (-312, [(-312, 6, 2.266)]), (-319, [(-319, 4, 0.9962)]), (-328, [(-328, 16, 15.72)]), (-335, [(-335, 0, 0)]), (-344, [(-344, 2, 0.2398)]), (-372, [(-372, 10, 5.765)]), (-376, [(-376, -2, 0.2294)]), (-383, [(-383, 4, 0.4546)]), (-399, [(-399, -8, 1.781)]), (-407, [(-407, -8, 1.764)]), (-415, [(-415, -20, 10.92)]), (-431, [(-431, 4, 0.4285)]), (-436, [(-436, -2, 0.2130)]), (-439, [(-439, -4, 0.4246)]), (-440, [(-440, -2, 0.2120)]), (-455, [(-455, -4, 0.4170)]), (-463, [(-463, 20, 10.34)]), (-471, [(-471, -4, 0.4099)]), (-487, [(-487, -12, 3.628)]), (-488, [(-488, 4, 0.8054)]), (-516, [(-516, 6, 1.762)]), (-527, [(-527, -4, 0.3875)]), (-535, [(-535, 4, 0.3846)]), (-551, [(-551, 0, 0)]), (-552, [(-552, -4, 0.7573)]), (-564, [(-564, -6, 1.686)]), (-580, [(-580, 2, 0.3694)]), (-584, [(-584, 4, 0.7362)]), (-596, [(-596, -2, 0.1822)]), (-615, [(-615, 12, 3.228)]), (-616, [(-616, -8, 2.867)]), (-631, [(-631, 16, 5.666)]), (-632, [(-632, 6, 1.592)]), (-644, [(-644, 4, 0.7011)]), (-647, [(-647, 4, 0.3497)]), (-660, [(-660, -2, 0.1731)]), (-663, [(-663, -12, 3.109)]), (-671, [(-671, 4, 0.3434)]), (-680, [(-680, 4, 0.6823)]), (-687, [(-687, -12, 3.055)]), (-692, [(-692, -4, 0.6764)]), (-695, [(-695, -4, 0.3374)]), (-696, [(-696, 2, 0.3372)]), (-703, [(-703, 16, 5.368)]), (-712, [(-712, -12, 6.001)]), (-719, [(-719, 0, 0)]), (-724, [(-724, 6, 1.488)]), (-759, [(-759, -4, 0.3229)]), (-760, [(-760, -16, 10.33)]), (-767, [(-767, -4, 0.3212)]), (-776, [(-776, -4, 0.6387)]), (-788, [(-788, 0, 0)]), (-799, [(-799, -12, 2.832)]), (-807, [(-807, -4, 0.3132)]), (-808, [(-808, 4, 0.6259)]), (-836, [(-836, -4, 0.6154)]), (-840, [(-840, -4, 0.6139)]), (-863, [(-863, 8, 1.211)]), (-871, [(-871, -8, 1.206)]), (-879, [(-879, 8, 1.200)]), (-895, [(-895, 8, 1.189)]), (-903, [(-903, -4, 0.2960)]), (-904, [(-904, 12, 5.326)]), (-919, [(-919, 16, 4.695)]), (-932, [(-932, -10, 3.642)]), (-935, [(-935, -4, 0.2909)]), (-948, [(-948, -2, 0.1445)]), (-951, [(-951, -4, 0.2885)]), (-952, [(-952, -8, 2.307)]), (-964, [(-964, -2, 0.1433)]), (-991, [(-991, -16, 4.521)]), (-1015, [(-1015, 12, 5.026)]), (-1016, [(-1016, 0, 0)]), (-1028, [(-1028, 6, 1.249)]), (-1031, [(-1031, 8, 1.108)]), (-1039, [(-1039, 12, 2.484)]), (-1048, [(-1048, 8, 2.198)]), (-1060, [(-1060, 14, 6.694)]), (-1064, [(-1064, 0, 0)]), (-1079, [(-1079, -4, 0.2708)]), (-1095, [(-1095, 0, 0)]), (-1096, [(-1096, 12, 4.837)]), (-1103, [(-1103, 0, 0)]), (-1108, [(-1108, 28, 26.19)]), (-1111, [(-1111, 0, 0)]), (-1124, [(-1124, -2, 0.1327)]), (-1135, [(-1135, 0, 0)]), (-1140, [(-1140, 0, 0)]), (-1144, [(-1144, -14, 6.444)]), (-1151, [(-1151, 4, 0.2622)]), (-1159, [(-1159, 8, 1.045)]), (-1160, [(-1160, 4, 1.045)]), (-1167, [(-1167, -8, 1.042)]), (-1223, [(-1223, 8, 1.018)]), (-1231, [(-1231, -12, 2.282)]), (-1240, [(-1240, 6, 1.137)]), (-1247, [(-1247, 4, 0.5038)]), (-1252, [(-1252, -26, 21.24)]), (-1256, [(-1256, 0, 0)]), (-1263, [(-1263, 4, 0.2503)]), (-1271, [(-1271, -4, 0.2495)]), (-1272, [(-1272, -2, 0.1247)]), (-1304, [(-1304, -2, 0.1232)]), (-1311, [(-1311, 0, 0)]), (-1327, [(-1327, -32, 15.63)]), (-1335, [(-1335, 12, 2.191)]), (-1343, [(-1343, -4, 0.2428)]), (-1364, [(-1364, 2, 0.1204)]), (-1367, [(-1367, -8, 0.9624)]), (-1383, [(-1383, 16, 3.827)]), (-1391, [(-1391, -4, 0.2385)]), (-1396, [(-1396, 2, 0.1190)]), (-1399, [(-1399, 4, 0.2378)]), (-1412, [(-1412, -4, 0.4735)]), (-1415, [(-1415, -4, 0.2365)]), (-1416, [(-1416, 0, 0)]), (-1428, [(-1428, 0, 0)]), (-1455, [(-1455, 12, 2.099)]), (-1463, [(-1463, 0, 0)]), (-1479, [(-1479, 4, 0.4626)]), (-1480, [(-1480, -16, 7.400)]), (-1492, [(-1492, 10, 2.879)]), (-1495, [(-1495, -20, 5.752)]), (-1508, [(-1508, 2, 0.2291)]), (-1524, [(-1524, 4, 0.4558)]), (-1528, [(-1528, 8, 1.821)]), (-1543, [(-1543, -24, 8.153)]), (-1544, [(-1544, 4, 0.4528)]), (-1559, [(-1559, -8, 0.9012)]), (-1560, [(-1560, -6, 1.014)]), (-1567, [(-1567, 28, 11.01)]), (-1572, [(-1572, -4, 0.4487)]), (-1588, [(-1588, 6, 1.005)]), (-1591, [(-1591, 16, 3.568)]), (-1599, [(-1599, 4, 0.2225)]), (-1604, [(-1604, 2, 0.1111)]), (-1608, [(-1608, 4, 0.4437)]), (-1615, [(-1615, -16, 3.542)]), (-1623, [(-1623, -8, 0.8833)]), (-1624, [(-1624, -8, 3.532)]), (-1631, [(-1631, 4, 0.2203)]), (-1640, [(-1640, 4, 0.4393)]), (-1652, [(-1652, 8, 1.751)]), (-1687, [(-1687, 12, 1.949)]), (-1688, [(-1688, -10, 2.707)]), (-1695, [(-1695, 8, 0.8643)]), (-1704, [(-1704, -4, 0.4310)]), (-1711, [(-1711, -12, 3.871)]), (-1716, [(-1716, 2, 0.1074)]), (-1720, [(-1720, 6, 0.9653)]), (-1727, [(-1727, -12, 1.927)]), (-1735, [(-1735, -16, 3.417)]), (-1736, [(-1736, -4, 0.4270)]), (-1768, [(-1768, -28, 20.73)]), (-1799, [(-1799, 4, 0.2097)]), (-1807, [(-1807, 20, 5.232)]), (-1823, [(-1823, 0, 0)]), (-1828, [(-1828, -20, 10.40)]), (-1831, [(-1831, -8, 0.8316)]), (-1832, [(-1832, 8, 1.663)]), (-1847, [(-1847, 0, 0)]), (-1855, [(-1855, -4, 0.2065)]), (-1860, [(-1860, -6, 0.9282)]), (-1876, [(-1876, -12, 3.697)]), (-1879, [(-1879, -4, 0.2052)]), (-1880, [(-1880, -2, 0.1026)]), (-1892, [(-1892, 10, 2.556)]), (-1919, [(-1919, -8, 0.8123)]), (-1927, [(-1927, 4, 0.2027)]), (-1943, [(-1943, -8, 1.615)]), (-1956, [(-1956, 2, 0.1006)]), (-1959, [(-1959, -4, 0.2010)]), (-1967, [(-1967, -4, 0.2006)]), (-1972, [(-1972, 12, 7.212)]), (-1976, [(-1976, 4, 0.4002)]), (-1988, [(-1988, 4, 0.3990)]), (-1992, [(-1992, -16, 6.378)]), (-2008, [(-2008, 6, 0.8934)]), (-2024, [(-2024, -4, 0.3955)]), (-2031, [(-2031, -8, 0.7896)]), (-2036, [(-2036, -2, 0.09858)]), (-2039, [(-2039, 4, 0.1970)]), (-2055, [(-2055, 8, 0.7850)]), (-2063, [(-2063, -4, 0.1959)]), (-2068, [(-2068, -22, 11.84)]), (-2072, [(-2072, -4, 0.3909)]), (-2084, [(-2084, 2, 0.09743)]), (-2087, [(-2087, 12, 1.753)]), (-2095, [(-2095, -8, 0.7774)]), (-2104, [(-2104, 6, 0.8727)]), (-2111, [(-2111, 0, 0)]), (-2152, [(-2152, 20, 9.588)]), (-2159, [(-2159, 0, 0)]), (-2168, [(-2168, -2, 0.09553)]), (-2180, [(-2180, -2, 0.09527)]), (-2184, [(-2184, -4, 0.3807)]), (-2191, [(-2191, 12, 1.710)]), (-2199, [(-2199, 8, 0.7588)]), (-2228, [(-2228, 12, 3.392)]), (-2239, [(-2239, 8, 0.7520)]), (-2255, [(-2255, -4, 0.1873)]), (-2263, [(-2263, 16, 2.992)]), (-2271, [(-2271, 4, 0.1867)]), (-2287, [(-2287, 24, 6.697)]), (-2292, [(-2292, 0, 0)]), (-2296, [(-2296, 4, 0.3713)]), (-2311, [(-2311, 0, 0)]), (-2319, [(-2319, 4, 0.1847)]), (-2324, [(-2324, 8, 1.476)]), (-2327, [(-2327, 0, 0)]), (-2343, [(-2343, 16, 2.941)]), (-2344, [(-2344, 4, 0.3675)]), (-2356, [(-2356, -8, 1.466)]), (-2372, [(-2372, 10, 2.283)]), (-2383, [(-2383, 28, 8.930)]), (-2391, [(-2391, -20, 4.548)]), (-2407, [(-2407, -12, 3.264)]), (-2408, [(-2408, -8, 1.450)]), (-2423, [(-2423, 0, 0)]), (-2431, [(-2431, 12, 1.624)]), (-2436, [(-2436, 8, 2.884)]), (-2440, [(-2440, -16, 5.763)]), (-2452, [(-2452, 10, 2.246)]), (-2456, [(-2456, 2, 0.08975)]), (-2471, [(-2471, -8, 0.7158)]), (-2472, [(-2472, 12, 3.221)]), (-2487, [(-2487, 28, 8.741)]), (-2488, [(-2488, 4, 0.3567)]), (-2495, [(-2495, 12, 1.603)]), (-2503, [(-2503, 0, 0)]), (-2516, [(-2516, -4, 0.3547)]), (-2519, [(-2519, -4, 0.1772)]), (-2532, [(-2532, -2, 0.08840)]), (-2536, [(-2536, 24, 12.72)]), (-2543, [(-2543, 4, 0.1764)]), (-2551, [(-2551, -12, 1.585)]), (-2552, [(-2552, -6, 1.585)]), (-2559, [(-2559, 0, 0)]), (-2568, [(-2568, -12, 3.160)]), (-2580, [(-2580, -2, 0.08757)]), (-2615, [(-2615, 0, 0)]), (-2616, [(-2616, 2, 0.08697)]), (-2623, [(-2623, -28, 8.511)]), (-2632, [(-2632, 20, 8.670)]), (-2639, [(-2639, -4, 0.3463)]), (-2644, [(-2644, -4, 0.3460)]), (-2648, [(-2648, -2, 0.08644)]), (-2663, [(-2663, 4, 0.1724)]), (-2692, [(-2692, 14, 4.201)]), (-2696, [(-2696, -8, 1.371)]), (-2703, [(-2703, -28, 8.384)]), (-2719, [(-2719, 0, 0)]), (-2735, [(-2735, -4, 0.1701)]), (-2751, [(-2751, 8, 0.6784)]), (-2756, [(-2756, -2, 0.08473)]), (-2759, [(-2759, 12, 1.524)]), (-2760, [(-2760, -16, 5.419)]), (-2788, [(-2788, 24, 12.13)]), (-2791, [(-2791, 20, 4.210)]), (-2804, [(-2804, -2, 0.08400)]), (-2807, [(-2807, 12, 1.511)]), (-2820, [(-2820, -2, 0.08376)]), (-2836, [(-2836, 22, 10.11)]), (-2847, [(-2847, 0, 0)]), (-2855, [(-2855, 8, 0.6660)]), (-2872, [(-2872, 22, 10.04)]), (-2884, [(-2884, -4, 0.3313)]), (-2887, [(-2887, -16, 2.649)]), (-2895, [(-2895, -4, 0.1653)]), (-2920, [(-2920, -12, 2.963)]), (-2935, [(-2935, -12, 1.478)]), (-2936, [(-2936, -4, 0.3284)]), (-2951, [(-2951, 8, 0.6550)]), (-2959, [(-2959, 4, 0.1635)]), (-2964, [(-2964, -4, 0.3268)]), (-2967, [(-2967, -4, 0.1633)]), (-2980, [(-2980, 22, 9.859)]), (-2983, [(-2983, 16, 2.606)]), (-2991, [(-2991, -8, 0.6506)]), (-2996, [(-2996, 0, 0)]), (-3007, [(-3007, 36, 13.14)]), (-3012, [(-3012, -14, 3.971)]), (-3016, [(-3016, -4, 0.6479)]), (-3023, [(-3023, -8, 0.6472)]), (-3032, [(-3032, 12, 2.908)]), (-3039, [(-3039, 0, 0)]), (-3044, [(-3044, 0, 0)]), (-3079, [(-3079, 12, 1.443)]), (-3080, [(-3080, 4, 0.3206)]), (-3103, [(-3103, 28, 15.65)]), (-3108, [(-3108, 20, 7.979)]), (-3112, [(-3112, -4, 0.3189)]), (-3119, [(-3119, 0, 0)]), (-3127, [(-3127, 20, 3.977)]), (-3128, [(-3128, -12, 2.863)]), (-3156, [(-3156, -6, 0.7126)]), (-3160, [(-3160, 22, 9.574)]), (-3167, [(-3167, 4, 0.1581)]), (-3183, [(-3183, 4, 0.1577)]), (-3191, [(-3191, 4, 0.1575)]), (-3199, [(-3199, -16, 2.517)]), (-3215, [(-3215, -12, 1.412)]), (-3220, [(-3220, -20, 7.839)]), (-3223, [(-3223, 8, 0.6268)]), (-3224, [(-3224, -6, 0.7050)]), (-3239, [(-3239, -4, 0.1563)]), (-3247, [(-3247, 8, 0.6245)]), (-3252, [(-3252, -6, 0.7020)]), (-3255, [(-3255, -4, 0.1559)]), (-3268, [(-3268, -12, 2.801)]), (-3271, [(-3271, -8, 0.6222)]), (-3272, [(-3272, -4, 0.3110)]), (-3284, [(-3284, 6, 0.6986)]), (-3311, [(-3311, 4, 0.1546)]), (-3319, [(-3319, -4, 0.1544)]), (-3335, [(-3335, 4, 0.3081)]), (-3336, [(-3336, 12, 2.772)]), (-3351, [(-3351, 4, 0.1537)]), (-3359, [(-3359, -8, 0.6140)]), (-3368, [(-3368, -16, 4.905)]), (-3399, [(-3399, 16, 2.441)]), (-3415, [(-3415, -24, 5.480)]), (-3416, [(-3416, -4, 0.3044)]), (-3423, [(-3423, -12, 1.368)]), (-3428, [(-3428, -6, 0.6837)]), (-3431, [(-3431, 8, 0.6075)]), (-3444, [(-3444, -4, 0.3032)]), (-3455, [(-3455, -8, 0.6054)]), (-3460, [(-3460, -16, 4.840)]), (-3464, 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2, 0.05366)]), (-6879, [(-6879, 12, 0.9653)]), (-6895, [(-6895, -48, 15.43)]), (-6911, [(-6911, 0, 0)]), (-6927, [(-6927, -12, 0.9620)]), (-6932, [(-6932, -6, 0.4808)]), (-6935, [(-6935, -8, 0.4273)]), (-6951, [(-6951, 4, 0.1067)]), (-6959, [(-6959, 8, 0.4266)]), (-6964, [(-6964, -14, 2.612)]), (-6967, [(-6967, 4, 0.1066)]), (-6980, [(-6980, 2, 0.05324)]), (-6983, [(-6983, -8, 0.4258)]), (-6996, [(-6996, 2, 0.05318)]), (-7012, [(-7012, 14, 2.603)]), (-7023, [(-7023, 4, 0.1062)]), (-7031, [(-7031, -4, 0.1061)]), (-7048, [(-7048, -4, 0.2119)]), (-7060, [(-7060, -32, 13.55)]), (-7063, [(-7063, -20, 2.646)]), (-7071, [(-7071, 8, 0.4232)]), (-7076, [(-7076, 4, 0.4230)]), (-7080, [(-7080, -4, 0.2115)]), (-7096, [(-7096, 18, 4.277)]), (-7111, [(-7111, -28, 5.169)]), (-7112, [(-7112, -24, 7.595)]), (-7127, [(-7127, 4, 0.1054)]), (-7135, [(-7135, 24, 3.791)]), (-7140, [(-7140, 0, 0)]), (-7143, [(-7143, 0, 0)]), (-7156, [(-7156, -6, 0.4732)]), (-7159, [(-7159, -8, 0.4206)]), (-7167, [(-7167, -4, 0.1051)]), (-7172, [(-7172, 18, 4.254)]), (-7176, [(-7176, 8, 0.8401)]), (-7183, [(-7183, -60, 23.62)]), (-7188, [(-7188, 22, 6.348)]), (-7192, [(-7192, -2, 0.1049)]), (-7199, [(-7199, 4, 0.1048)]), (-7208, [(-7208, -4, 0.2096)]), (-7215, [(-7215, 8, 0.4189)]), (-7255, [(-7255, 4, 0.1044)]), (-7256, [(-7256, 0, 0)]), (-7279, [(-7279, 4, 0.2085)]), (-7284, [(-7284, -18, 4.221)]), (-7288, [(-7288, -14, 2.553)]), (-7295, [(-7295, 0, 0)]), (-7303, [(-7303, 32, 6.662)]), (-7304, [(-7304, 0, 0)]), (-7332, [(-7332, 22, 6.286)]), (-7336, [(-7336, 8, 0.8309)]), (-7343, [(-7343, 24, 3.737)]), (-7359, [(-7359, -8, 0.4148)]), (-7367, [(-7367, 12, 0.9328)]), (-7391, [(-7391, 0, 0)]), (-7415, [(-7415, 8, 0.4132)]), (-7423, [(-7423, 16, 1.652)]), (-7428, [(-7428, 6, 0.4645)]), (-7431, [(-7431, 0, 0)]), (-7444, [(-7444, -8, 0.8249)]), (-7447, [(-7447, 24, 3.711)]), (-7460, [(-7460, -6, 0.4635)]), (-7476, [(-7476, 8, 0.8231)]), (-7487, [(-7487, 8, 0.4112)]), (-7495, [(-7495, 20, 2.569)]), (-7511, [(-7511, -8, 0.8212)]), (-7512, [(-7512, -14, 2.515)]), (-7527, [(-7527, 12, 0.9228)]), (-7535, [(-7535, -8, 0.4099)]), (-7540, [(-7540, -22, 12.40)]), (-7544, [(-7544, 4, 0.2048)]), (-7556, [(-7556, -2, 0.05117)]), (-7576, [(-7576, -2, 0.05110)]), (-7591, [(-7591, 8, 0.4084)]), (-7592, [(-7592, -12, 1.838)]), (-7599, [(-7599, -4, 0.1021)]), (-7604, [(-7604, 2, 0.05101)]), (-7607, [(-7607, 12, 0.9180)]), (-7620, [(-7620, 16, 3.261)]), (-7631, [(-7631, -4, 0.1018)]), (-7636, [(-7636, -16, 3.258)]), (-7640, [(-7640, -8, 0.8142)]), (-7647, [(-7647, 16, 1.628)]), (-7652, [(-7652, -14, 2.492)]), (-7655, [(-7655, -8, 0.4067)]), (-7656, [(-7656, 0, 0)]), (-7663, [(-7663, 20, 2.541)]), (-7672, [(-7672, 36, 16.45)]), (-7679, [(-7679, 4, 0.1015)]), (-7684, [(-7684, -16, 3.248)]), (-7719, [(-7719, 4, 0.1013)]), (-7720, [(-7720, 24, 7.290)]), (-7727, [(-7727, 4, 0.1012)]), (-7736, [(-7736, -2, 0.05057)]), (-7743, [(-7743, 12, 1.820)]), (-7748, [(-7748, 10, 1.263)]), (-7752, [(-7752, 16, 3.233)]), (-7759, [(-7759, 12, 0.9089)]), (-7768, [(-7768, -32, 12.92)]), (-7796, [(-7796, -6, 0.4534)]), (-7807, [(-7807, -8, 0.4027)]), (-7823, [(-7823, 4, 0.1006)]), (-7831, [(-7831, -24, 3.619)]), (-7855, [(-7855, -28, 4.918)]), (-7860, [(-7860, -4, 0.2007)]), (-7863, [(-7863, 8, 0.4013)]), (-7864, [(-7864, -22, 6.069)]), (-7879, [(-7879, -8, 0.4009)]), (-7887, [(-7887, -20, 2.504)]), (-7892, [(-7892, 2, 0.05007)]), (-7895, [(-7895, 0, 0)]), (-7908, [(-7908, -18, 4.052)]), (-7912, [(-7912, -20, 5.001)]), (-7924, [(-7924, 12, 1.799)]), (-7940, [(-7940, -14, 2.446)]), (-7951, [(-7951, -16, 1.596)]), (-7959, [(-7959, 8, 0.3989)]), (-7976, [(-7976, -4, 0.1992)]), (-7988, [(-7988, 8, 0.7963)]), (-7991, [(-7991, 8, 0.3981)]), (-7999, [(-7999, 0, 0)]), (-8004, [(-8004, -4, 0.3977)]), (-8008, [(-8008, 4, 0.1988)]), (-8020, [(-8020, -2, 0.04967)]), (-8024, [(-8024, -12, 1.788)]), (-8039, [(-8039, 0, 0)]), (-8040, [(-8040, -12, 1.786)]), (-8056, [(-8056, -4, 0.1982)]), (-8063, [(-8063, -24, 3.567)]), (-8068, [(-8068, -22, 5.992)]), (-8071, [(-8071, 12, 0.8912)]), (-8084, [(-8084, 6, 0.4452)]), (-8087, [(-8087, 8, 0.3957)]), (-8095, [(-8095, 24, 3.560)]), (-8104, [(-8104, -12, 1.779)]), (-8111, [(-8111, 12, 0.8890)]), (-8116, [(-8116, 6, 0.4444)]), (-8119, [(-8119, 0, 0)]), (-8120, [(-8120, 0, 0)]), (-8143, [(-8143, 4, 0.09858)]), (-8148, [(-8148, -4, 0.1971)]), (-8184, [(-8184, 2, 0.04917)]), (-8191, [(-8191, -28, 4.816)]), (-8207, [(-8207, -4, 0.1964)]), (-8212, [(-8212, 30, 11.04)]), (-8216, [(-8216, 2, 0.04907)]), (-8223, [(-8223, -16, 1.570)]), (-8231, [(-8231, 0, 0)]), (-8260, [(-8260, 16, 3.132)]), (-8264, [(-8264, 0, 0)]), (-8287, [(-8287, 4, 0.09772)]), (-8295, [(-8295, -20, 2.442)]), (-8319, [(-8319, 12, 0.8778)]), (-8324, [(-8324, -4, 0.1950)]), (-8327, [(-8327, 4, 0.09749)]), (-8328, [(-8328, 4, 0.1950)]), (-8351, [(-8351, 0, 0)]), (-8356, [(-8356, -2, 0.04866)]), (-8359, [(-8359, -12, 0.8757)]), (-8372, [(-8372, 4, 0.1945)]), (-8376, [(-8376, -22, 5.881)]), (-8404, [(-8404, -20, 4.852)]), (-8423, [(-8423, -8, 0.3877)]), (-8439, [(-8439, 4, 0.1937)]), (-8440, [(-8440, 2, 0.04842)]), (-8452, [(-8452, 26, 8.177)]), (-8455, [(-8455, -24, 3.483)]), (-8463, [(-8463, -12, 0.8703)]), (-8468, [(-8468, 0, 0)]), (-8472, [(-8472, -24, 6.959)]), (-8484, [(-8484, 0, 0)]), (-8488, [(-8488, -36, 15.64)]), (-8503, [(-8503, -12, 0.8683)]), (-8504, [(-8504, 2, 0.04823)]), (-8519, [(-8519, 4, 0.09638)]), (-8520, [(-8520, -12, 1.735)]), (-8527, [(-8527, 28, 4.721)]), (-8535, [(-8535, 8, 0.3852)]), (-8548, [(-8548, -46, 25.45)]), (-8551, [(-8551, 36, 7.792)]), (-8564, [(-8564, -4, 0.1923)]), (-8580, [(-8580, 10, 1.200)]), (-8583, [(-8583, -8, 0.3841)]), (-8584, [(-8584, 16, 6.145)]), (-8607, [(-8607, 16, 1.534)]), (-8612, [(-8612, -2, 0.04793)]), (-8647, [(-8647, -4, 0.09567)]), (-8648, [(-8648, 8, 0.7653)]), (-8655, [(-8655, 4, 0.09562)]), (-8671, [(-8671, -20, 4.777)]), (-8680, [(-8680, 32, 12.22)]), (-8687, [(-8687, 16, 1.527)]), (-8695, [(-8695, 8, 0.3816)]), (-8696, [(-8696, 2, 0.04770)]), (-8724, [(-8724, 4, 0.1905)]), (-8728, [(-8728, 30, 10.71)]), (-8735, [(-8735, 0, 0)]), (-8751, [(-8751, 16, 1.522)]), (-8759, [(-8759, 0, 0)]), (-8767, [(-8767, 12, 0.8551)]), (-8783, [(-8783, 16, 1.519)]), (-8791, [(-8791, -12, 0.8539)]), (-8792, [(-8792, -12, 1.708)]), (-8807, [(-8807, 0, 0)]), (-8815, [(-8815, -12, 0.8528)]), (-8823, [(-8823, -32, 6.061)]), (-8839, [(-8839, 4, 0.09462)]), (-8840, [(-8840, 0, 0)]), (-8852, [(-8852, -14, 2.317)]), (-8868, [(-8868, 6, 0.4251)]), (-8879, [(-8879, 0, 0)]), (-8887, [(-8887, -24, 3.397)]), (-8903, [(-8903, 12, 1.697)]), (-8904, [(-8904, -4, 0.1886)]), (-8916, [(-8916, 0, 0)]), (-8927, [(-8927, 24, 3.390)]), (-8932, [(-8932, 24, 13.55)]), (-8936, [(-8936, 0, 0)]), (-8948, [(-8948, 6, 0.4232)]), (-8952, [(-8952, 6, 0.4231)]), (-8968, [(-8968, 8, 0.7515)]), (-8983, [(-8983, 8, 0.3754)]), (-8984, [(-8984, 8, 0.7508)]), (-8996, [(-8996, 12, 1.688)]), (-8999, [(-8999, -16, 1.500)]), (-9012, [(-9012, -12, 1.687)]), (-9015, [(-9015, -20, 2.342)]), (-9023, [(-9023, 4, 0.09365)]), (-9028, [(-9028, 8, 0.7490)]), (-9032, [(-9032, 20, 4.680)]), (-9039, [(-9039, -16, 1.497)]), (-9044, [(-9044, 8, 0.7483)]), (-9047, [(-9047, -20, 2.338)]), (-9048, [(-9048, 14, 4.583)]), (-9055, [(-9055, -28, 4.581)]), (-9064, [(-9064, 12, 1.682)]), (-9071, [(-9071, -4, 0.09340)]), (-9076, [(-9076, 12, 1.681)]), (-9111, [(-9111, 8, 0.3728)]), (-9112, [(-9112, 44, 22.55)]), (-9119, [(-9119, -4, 0.09316)]), (-9128, [(-9128, -8, 0.7449)]), (-9140, [(-9140, 8, 0.7444)]), (-9151, [(-9151, 24, 3.348)]), (-9159, [(-9159, -8, 0.3718)]), (-9160, [(-9160, -4, 0.1859)]), (-9188, [(-9188, -12, 1.671)]), (-9192, [(-9192, 4, 0.1856)]), (-9199, [(-9199, 12, 0.8348)]), (-9215, [(-9215, 0, 0)]), (-9223, [(-9223, 12, 0.8337)]), (-9231, [(-9231, 12, 0.8333)]), (-9247, [(-9247, 28, 4.533)]), (-9255, [(-9255, -24, 3.329)]), (-9256, [(-9256, -8, 0.7397)]), (-9271, [(-9271, 0, 0)]), (-9284, [(-9284, -2, 0.04616)]), (-9287, [(-9287, -8, 0.3692)]), (-9303, [(-9303, -8, 0.3689)]), (-9304, [(-9304, -6, 0.4150)]), (-9316, [(-9316, -16, 2.949)]), (-9332, [(-9332, 4, 0.1842)]), (-9343, [(-9343, -16, 1.473)]), (-9367, [(-9367, 8, 0.7353)]), (-9368, [(-9368, 14, 2.252)]), (-9380, [(-9380, -4, 0.1837)]), (-9383, [(-9383, -8, 0.3674)]), (-9391, [(-9391, 8, 0.3672)]), (-9412, [(-9412, -10, 1.146)]), (-9416, [(-9416, -12, 1.650)]), (-9431, [(-9431, 0, 0)]), (-9447, [(-9447, -40, 9.153)]), (-9448, [(-9448, -20, 4.576)]), (-9455, [(-9455, 4, 0.09149)]), (-9460, [(-9460, -22, 5.534)]), (-9463, [(-9463, 8, 0.3658)]), (-9476, [(-9476, -8, 0.7311)]), (-9479, [(-9479, 0, 0)]), (-9487, [(-9487, -8, 0.3653)]), (-9492, [(-9492, -20, 4.565)]), (-9496, [(-9496, 16, 2.921)]), (-9503, [(-9503, -12, 0.8213)]), (-9508, [(-9508, -4, 0.1825)]), (-9511, [(-9511, 4, 0.09122)]), (-9512, [(-9512, -4, 0.3649)]), (-9519, [(-9519, 8, 0.3647)]), (-9528, [(-9528, 14, 2.233)]), (-9535, [(-9535, 36, 7.379)]), (-9592, [(-9592, 6, 0.4087)]), (-9599, [(-9599, -4, 0.1816)]), (-9608, [(-9608, 0, 0)]), (-9615, [(-9615, -20, 2.268)]), (-9623, [(-9623, 12, 0.8162)]), (-9624, [(-9624, 2, 0.04534)]), (-9652, [(-9652, 8, 0.7244)]), (-9656, [(-9656, 8, 0.7242)]), (-9663, [(-9663, 8, 0.3620)]), (-9679, [(-9679, 16, 1.447)]), (-9687, [(-9687, 32, 5.785)]), (-9695, [(-9695, 8, 0.3614)]), (-9716, [(-9716, -8, 0.7220)]), (-9719, [(-9719, -4, 0.09024)]), (-9735, [(-9735, -4, 0.09016)]), (-9743, [(-9743, -4, 0.09013)]), (-9748, [(-9748, 54, 32.84)]), (-9764, [(-9764, -6, 0.4051)]), (-9767, [(-9767, -20, 2.250)]), (-9768, [(-9768, 16, 2.880)]), (-9780, [(-9780, 22, 5.442)]), (-9796, [(-9796, 10, 1.124)]), (-9807, [(-9807, -12, 0.8085)]), (-9815, [(-9815, -12, 0.8082)]), (-9831, [(-9831, 0, 0)]), (-9832, [(-9832, -4, 0.1794)]), (-9844, [(-9844, -8, 0.7173)]), (-9847, [(-9847, -12, 0.8068)]), (-9860, [(-9860, 4, 0.3584)]), (-9876, [(-9876, 4, 0.1790)]), (-9880, [(-9880, -12, 1.611)]), (-9895, [(-9895, 4, 0.08943)]), (-9896, [(-9896, 4, 0.1789)]), (-9911, [(-9911, 4, 0.08936)]), (-9912, [(-9912, -8, 0.7148)]), (-9919, [(-9919, 12, 0.8039)]), (-9924, [(-9924, -6, 0.4018)]), (-9940, [(-9940, 28, 8.744)]), (-9943, [(-9943, 12, 0.8029)]), (-9951, [(-9951, -4, 0.08918)]), (-9956, [(-9956, 0, 0)]), (-9960, [(-9960, -4, 0.1783)]), (-9967, [(-9967, 32, 5.703)]), (-9976, [(-9976, 10, 2.227)]), (-9983, [(-9983, -8, 0.3561)]), (-9992, [(-9992, 4, 0.1780)])]]

# map: (1 |-> 1.0) -> 1, Fractional ideal (2) -> -1, Fractional ideal (29) -> 1
[-7, -1/2 + (-227/2)*i + (-23/2)*j + (-1/2)*k, [(5, [(5, 4, 4.889)]), (13, [(13, 4, 3.032)]), (29, [(29, -4, 4.060)]), (53, [(53, 12, 13.51)]), (93, [(93, 4, 1.134)]), (109, [(109, -4, 1.047)]), (141, [(141, -4, 0.9206)]), (149, [(149, 4, 0.8956)]), (165, [(165, 12, 7.660)]), (173, [(173, -24, 29.92)]), (181, [(181, -4, 0.8126)]), (197, [(197, -16, 12.46)]), (237, [(237, -12, 6.391)]), (277, [(277, 8, 2.627)]), (285, [(285, 8, 2.590)]), (341, [(341, -20, 14.80)]), (349, [(349, -4, 0.5852)]), (357, [(357, -16, 9.257)]), (373, [(373, 4, 0.5660)]), (381, [(381, 0, 0)]), (397, [(397, -4, 0.5487)]), (413, [(413, -32, 34.43)]), (429, [(429, -4, 0.5278)]), (469, [(469, 8, 2.019)]), (493, [(493, -8, 3.939)]), (509, [(509, 4, 0.4846)]), (517, [(517, 4, 0.4808)]), (557, [(557, -8, 1.853)]), (573, [(573, 24, 16.44)]), (581, [(581, -16, 7.257)]), (589, [(589, 8, 1.802)]), (613, [(613, 4, 0.4415)]), (629, [(629, 24, 15.69)]), (645, [(645, 12, 3.874)]), (661, [(661, -8, 1.701)]), (701, [(701, -12, 3.716)]), (709, [(709, 4, 0.4106)]), (741, [(741, -16, 6.426)]), (749, [(749, 0, 0)]), (789, [(789, 20, 9.730)]), (805, [(805, -8, 1.541)]), (813, [(813, 20, 9.585)]), (821, [(821, -12, 3.434)]), (861, [(861, 8, 1.490)]), (869, [(869, 12, 3.338)]), (877, [(877, -4, 0.3691)]), (893, [(893, 32, 23.41)]), (933, [(933, -16, 5.726)]), (941, [(941, -20, 8.909)]), (957, [(957, 12, 6.361)]), (973, [(973, 8, 1.402)]), (1021, [(1021, 4, 0.3421)]), (1037, [(1037, 16, 5.432)]), (1045, [(1045, 0, 0)]), (1069, [(1069, 0, 0)]), (1077, [(1077, -12, 2.998)]), (1093, [(1093, -16, 5.291)]), (1101, [(1101, -8, 1.318)]), (1109, [(1109, 20, 8.207)]), (1165, [(1165, 12, 2.883)]), (1173, [(1173, -8, 1.277)]), (1189, [(1189, 0, 0)]), (1205, [(1205, -4, 0.3149)]), (1213, [(1213, -16, 5.022)]), (1253, [(1253, -40, 30.88)]), (1277, [(1277, -28, 14.99)]), (1285, [(1285, 4, 0.3050)]), (1301, [(1301, -16, 4.849)]), (1309, [(1309, 0, 0)]), (1333, [(1333, 12, 2.695)]), (1357, [(1357, 16, 4.748)]), (1397, [(1397, 40, 29.25)]), (1405, [(1405, 4, 0.2917)]), (1437, [(1437, -20, 7.210)]), (1501, [(1501, -8, 1.129)]), (1509, [(1509, -4, 0.2814)]), (1517, [(1517, 8, 1.123)]), (1533, [(1533, -16, 4.467)]), (1541, [(1541, -24, 10.03)]), (1565, [(1565, 4, 0.2763)]), (1589, [(1589, 32, 17.55)]), (1637, [(1637, -48, 38.91)]), (1653, [(1653, 0, 0)]), (1669, [(1669, -8, 1.070)]), (1677, [(1677, 4, 0.2670)]), (1717, [(1717, -16, 4.221)]), (1733, [(1733, 20, 6.565)]), (1741, [(1741, -20, 6.550)]), (1749, [(1749, -4, 0.2614)]), (1765, [(1765, 0, 0)]), (1789, [(1789, 4, 0.2585)]), (1797, [(1797, 4, 0.2579)]), (1821, [(1821, -4, 0.2562)]), (1861, [(1861, 0, 0)]), (1869, [(1869, -16, 4.046)]), (1885, [(1885, 4, 0.5036)]), (1901, [(1901, 4, 0.2507)]), (1909, [(1909, 0, 0)]), (1949, [(1949, 12, 2.229)]), (1965, [(1965, 16, 3.946)]), (1973, [(1973, 28, 12.06)]), (1981, [(1981, 8, 0.9825)]), (1997, [(1997, -32, 15.66)]), (2005, [(2005, -4, 0.2441)]), (2021, [(2021, 12, 2.189)]), (2029, [(2029, -12, 2.184)]), (2037, [(2037, 24, 8.720)]), (2053, [(2053, -4, 0.2413)]), (2093, [(2093, 24, 8.603)]), (2101, [(2101, 0, 0)]), (2117, [(2117, 32, 30.41)]), (2141, [(2141, -24, 8.505)]), (2181, [(2181, 16, 3.745)]), (2213, [(2213, 20, 5.810)]), (2229, [(2229, 8, 0.9262)]), (2237, [(2237, 52, 39.06)]), (2253, [(2253, -16, 3.685)]), (2261, [(2261, -16, 3.679)]), (2269, [(2269, 8, 0.9180)]), (2285, [(2285, 32, 14.64)]), (2333, [(2333, -24, 8.148)]), (2365, [(2365, 12, 2.023)]), (2373, [(2373, -8, 0.8977)]), (2413, [(2413, 0, 0)]), (2429, [(2429, -16, 3.549)]), (2437, [(2437, 12, 1.993)]), (2445, [(2445, 20, 5.527)]), (2461, [(2461, 16, 3.526)]), (2469, [(2469, -16, 3.520)]), (2485, [(2485, -8, 0.8772)]), (2501, [(2501, 8, 0.8744)]), (2517, [(2517, -4, 0.2179)]), (2557, [(2557, -12, 1.946)]), (2581, [(2581, 0, 0)]), (2605, [(2605, 12, 1.928)]), (2661, [(2661, -12, 1.907)]), (2669, [(2669, -24, 7.618)]), (2677, [(2677, 12, 1.902)]), (2693, [(2693, 52, 35.60)]), (2701, [(2701, -8, 0.8414)]), (2717, [(2717, 8, 0.8389)]), (2733, [(2733, -12, 1.882)]), (2749, [(2749, -8, 0.8340)]), (2789, [(2789, 20, 5.175)]), (2797, [(2797, -4, 0.2067)]), (2813, [(2813, 16, 6.596)]), (2829, [(2829, 8, 0.8221)]), (2837, [(2837, 12, 1.847)]), (2877, [(2877, -24, 7.337)]), (2893, [(2893, -4, 0.2032)]), (2901, [(2901, -12, 1.827)]), (2909, [(2909, 0, 0)]), (2933, [(2933, 8, 0.8074)]), (2949, [(2949, 4, 0.2013)]), (2957, [(2957, 12, 1.809)]), (2965, [(2965, -4, 0.2008)]), (2981, [(2981, 28, 9.811)]), (3021, [(3021, 0, 0)]), (3029, [(3029, 36, 16.09)]), (3045, [(3045, -16, 6.340)]), (3061, [(3061, -4, 0.1976)]), (3109, [(3109, 12, 1.765)]), (3133, [(3133, 4, 0.1953)]), (3157, [(3157, -24, 7.004)]), (3165, [(3165, 4, 0.1943)]), (3181, [(3181, 4, 0.1938)]), (3189, [(3189, -4, 0.1936)]), (3197, [(3197, -56, 37.90)]), (3253, [(3253, 8, 0.7667)]), (3261, [(3261, 20, 4.786)]), (3277, [(3277, -8, 1.528)]), (3293, [(3293, -56, 37.34)]), (3301, [(3301, -4, 0.1903)]), (3341, [(3341, -4, 0.1891)]), (3365, [(3365, -44, 22.80)]), (3373, [(3373, -24, 6.776)]), (3389, [(3389, 28, 9.202)]), (3397, [(3397, 12, 1.688)]), (3413, [(3413, 28, 9.169)]), (3421, [(3421, -8, 0.7476)]), (3445, [(3445, 4, 0.1863)]), (3485, [(3485, -32, 11.85)]), (3493, [(3493, -8, 0.7399)]), (3533, [(3533, 76, 66.40)]), (3589, [(3589, 8, 0.7299)]), (3597, [(3597, 36, 14.76)]), (3605, [(3605, -40, 18.21)]), (3621, [(3621, 16, 2.907)]), (3629, [(3629, -16, 2.904)]), (3653, [(3653, -4, 0.1809)]), (3661, [(3661, 8, 0.7227)]), (3677, [(3677, -36, 14.60)]), (3741, [(3741, -4, 0.3575)]), (3765, [(3765, -20, 4.454)]), (3805, [(3805, 0, 0)]), (3821, [(3821, -28, 8.666)]), (3829, [(3829, 0, 0)]), (3837, [(3837, -12, 1.588)]), (3853, [(3853, -8, 0.7045)]), (3877, [(3877, 12, 1.580)]), (3885, [(3885, -8, 0.7016)]), (3893, [(3893, -32, 11.21)]), (3909, [(3909, 12, 1.574)]), (3949, [(3949, -4, 0.1740)]), (3957, [(3957, 16, 2.781)]), (3973, [(3973, 16, 5.550)]), (3989, [(3989, 24, 6.231)]), (3997, [(3997, -8, 0.6917)]), (4037, [(4037, 24, 6.194)]), (4053, [(4053, -24, 6.182)]), (4061, [(4061, -8, 0.6862)]), (4069, [(4069, -12, 1.542)]), (4085, [(4085, -16, 2.737)]), (4093, [(4093, 4, 0.1709)]), (4109, [(4109, 24, 6.140)]), (4117, [(4117, -24, 6.134)]), (4141, [(4141, 8, 0.6795)]), (4181, [(4181, 8, 0.6763)]), (4189, [(4189, 8, 0.6756)]), (4229, [(4229, 4, 0.1681)]), (4269, [(4269, -12, 1.506)]), (4285, [(4285, -12, 1.503)]), (4301, [(4301, -8, 0.6668)]), (4317, [(4317, 8, 0.6655)]), (4341, [(4341, -4, 0.1659)]), (4349, [(4349, -28, 8.123)]), (4357, [(4357, -16, 2.650)]), (4373, [(4373, -52, 27.94)]), (4413, [(4413, 24, 5.924)]), (4421, [(4421, 40, 16.44)]), (4453, [(4453, 8, 0.6553)]), (4461, [(4461, -8, 0.6547)]), (4501, [(4501, 8, 0.6518)]), (4517, [(4517, 4, 0.1627)]), (4533, [(4533, 20, 4.059)]), (4549, [(4549, 12, 1.459)]), (4573, [(4573, 24, 5.820)]), (4589, [(4589, 32, 10.33)]), (4605, [(4605, -12, 1.450)]), (4645, [(4645, -8, 0.6416)]), (4669, [(4669, -8, 1.280)]), (4685, [(4685, 40, 15.97)]), (4733, [(4733, -52, 26.85)]), (4749, [(4749, -28, 7.773)]), (4757, [(4757, 16, 2.536)]), (4765, [(4765, -4, 0.1584)]), (4781, [(4781, 32, 10.12)]), (4789, [(4789, 4, 0.1580)]), (4813, [(4813, 12, 1.418)]), (4821, [(4821, 4, 0.1574)]), (4837, [(4837, -16, 2.515)]), (4877, [(4877, 40, 15.65)]), (4885, [(4885, -12, 1.408)]), (4917, [(4917, 20, 3.898)]), (4965, [(4965, 4, 0.1551)]), (4981, [(4981, 8, 0.6196)]), (4989, [(4989, -16, 2.476)]), (4997, [(4997, 16, 2.474)]), (5021, [(5021, -8, 0.6171)]), (5037, [(5037, -24, 5.545)]), (5045, [(5045, -60, 34.63)]), (5053, [(5053, 4, 0.1538)]), (5069, [(5069, 24, 5.528)]), (5109, [(5109, 0, 0)]), (5117, [(5117, 32, 9.781)]), (5133, [(5133, -8, 1.221)]), (5149, [(5149, 0, 0)]), (5197, [(5197, 36, 12.28)]), (5213, [(5213, -20, 3.785)]), (5221, [(5221, 8, 0.6052)]), (5245, [(5245, 8, 0.6038)]), (5253, [(5253, 8, 0.6033)]), (5269, [(5269, -4, 0.1506)]), (5277, [(5277, 56, 29.50)]), (5285, [(5285, -48, 21.65)]), (5349, [(5349, 20, 3.737)]), (5365, [(5365, 0, 0)]), (5381, [(5381, 4, 0.1490)]), (5389, [(5389, -8, 0.5957)]), (5429, [(5429, 24, 5.341)]), (5453, [(5453, 64, 37.90)]), (5461, [(5461, -16, 2.367)]), (5477, [(5477, -56, 28.95)]), (5485, [(5485, -20, 3.690)]), (5501, [(5501, 40, 14.74)]), (5509, [(5509, -8, 0.5891)]), (5533, [(5533, -4, 0.1470)]), (5573, [(5573, 20, 3.661)]), (5581, [(5581, 4, 0.1463)]), (5597, [(5597, 0, 0)]), (5613, [(5613, 32, 9.339)]), (5621, [(5621, 0, 0)]), (5677, [(5677, 32, 9.286)]), (5685, [(5685, -16, 2.320)]), (5693, [(5693, -56, 28.40)]), (5709, [(5709, 8, 0.5787)]), (5717, [(5717, -4, 0.1446)]), (5741, [(5741, -40, 14.43)]), (5749, [(5749, 4, 0.1442)]), (5765, [(5765, -12, 1.296)]), (5813, [(5813, -64, 36.71)]), (5829, [(5829, -16, 4.582)]), (5845, [(5845, -24, 5.148)]), (5853, [(5853, 20, 3.572)]), (5893, [(5893, -32, 9.114)]), (5909, [(5909, 0, 0)]), (5917, [(5917, -8, 0.5685)]), (5941, [(5941, 0, 0)]), (5965, [(5965, 16, 2.265)]), (5973, [(5973, -4, 0.1415)]), (5981, [(5981, 60, 31.81)]), (5997, [(5997, -48, 20.33)]), (6037, [(6037, -32, 9.005)]), (6045, [(6045, 20, 3.515)]), (6061, [(6061, 8, 1.123)]), (6077, [(6077, -24, 5.049)]), (6085, [(6085, -4, 0.1401)]), (6141, [(6141, 8, 0.5580)]), (6149, [(6149, -12, 1.255)]), (6157, [(6157, -8, 0.5573)]), (6173, [(6173, -12, 1.252)]), (6181, [(6181, 0, 0)]), (6197, [(6197, -24, 4.999)]), (6205, [(6205, -16, 2.220)]), (6213, [(6213, -16, 2.219)]), (6229, [(6229, 12, 1.247)]), (6269, [(6269, -36, 11.18)]), (6277, [(6277, -4, 0.1380)]), (6293, [(6293, -32, 17.64)]), (6317, [(6317, -4, 0.1375)]), (6357, [(6357, -20, 3.428)]), (6373, [(6373, 16, 2.191)]), (6389, [(6389, 4, 0.1368)]), (6405, [(6405, -8, 0.5464)]), (6429, [(6429, -12, 1.227)]), (6437, [(6437, 8, 0.5450)]), (6445, [(6445, 20, 3.404)]), (6461, [(6461, 24, 4.896)]), (6501, [(6501, 16, 2.169)]), (6509, [(6509, -8, 0.5420)]), (6541, [(6541, 4, 0.1352)]), (6549, [(6549, -16, 2.161)]), (6589, [(6589, -4, 0.1347)]), (6605, [(6605, -44, 16.28)]), (6613, [(6613, 16, 2.151)]), (6621, [(6621, 12, 1.209)]), (6637, [(6637, -4, 0.1342)]), (6645, [(6645, 16, 2.146)]), (6661, [(6661, 8, 0.5358)]), (6677, [(6677, -52, 22.61)]), (6693, [(6693, 16, 2.138)]), (6733, [(6733, 4, 0.1332)]), (6757, [(6757, 4, 0.2660)]), (6773, [(6773, 20, 3.321)]), (6781, [(6781, 8, 0.5310)]), (6821, [(6821, 16, 2.118)]), (6837, [(6837, -44, 16.00)]), (6853, [(6853, 16, 2.113)]), (6869, [(6869, -8, 0.5276)]), (6893, [(6893, -72, 42.66)]), (6901, [(6901, 8, 0.5264)]), (6965, [(6965, -40, 13.10)]), (6973, [(6973, -16, 2.095)]), (6989, [(6989, 12, 2.354)]), (7005, [(7005, -4, 0.1306)]), (7013, [(7013, -68, 37.73)]), (7053, [(7053, -20, 3.254)]), (7069, [(7069, -20, 3.251)]), (7077, [(7077, -8, 0.5198)]), (7085, [(7085, -4, 0.1299)]), (7109, [(7109, -40, 12.97)]), (7133, [(7133, 88, 62.65)]), (7141, [(7141, 0, 0)]), (7157, [(7157, -8, 0.5169)]), (7197, [(7197, 44, 15.59)]), (7205, [(7205, -16, 2.061)]), (7221, [(7221, -8, 1.029)]), (7237, [(7237, 4, 0.1285)]), (7285, [(7285, 20, 3.202)]), (7309, [(7309, -8, 0.5115)]), (7333, [(7333, -28, 6.255)]), (7341, [(7341, 12, 1.148)]), (7357, [(7357, -8, 0.5098)]), (7365, [(7365, -4, 0.1274)]), (7373, [(7373, 8, 0.5093)]), (7429, [(7429, 0, 0)]), (7437, [(7437, -24, 4.564)]), (7453, [(7453, 20, 6.332)]), (7469, [(7469, 8, 0.5060)]), (7477, [(7477, 4, 0.1264)]), (7517, [(7517, -76, 45.52)]), (7541, [(7541, -44, 15.23)]), (7549, [(7549, -8, 0.5033)]), (7565, [(7565, 8, 0.5028)]), (7573, [(7573, 4, 0.1256)]), (7589, [(7589, 44, 15.18)]), (7597, [(7597, 0, 0)]), (7621, [(7621, 20, 3.131)]), (7661, [(7661, -4, 0.1249)]), (7669, [(7669, -4, 0.1248)]), (7685, [(7685, -20, 6.235)]), (7701, [(7701, 8, 0.4983)]), (7709, [(7709, -36, 10.09)]), (7765, [(7765, 8, 0.4962)]), (7773, [(7773, -28, 6.076)]), (7781, [(7781, 20, 3.098)]), (7797, [(7797, 16, 1.981)]), (7805, [(7805, -40, 12.37)]), (7829, [(7829, 12, 1.112)]), (7837, [(7837, -8, 0.4940)]), (7853, [(7853, 28, 6.045)]), (7901, [(7901, 28, 6.026)]), (7917, [(7917, 32, 15.73)]), (7933, [(7933, -32, 7.855)]), (7941, [(7941, -4, 0.1227)]), (7981, [(7981, 0, 0)]), (7997, [(7997, 64, 31.30)]), (8005, [(8005, -4, 0.1222)]), (8013, [(8013, 40, 12.21)]), (8029, [(8029, -8, 0.4880)]), (8053, [(8053, -4, 0.1218)]), (8061, [(8061, 24, 4.383)]), (8069, [(8069, 12, 1.095)]), (8133, [(8133, 36, 9.819)]), (8149, [(8149, 4, 0.2422)]), (8165, [(8165, -80, 48.39)]), (8173, [(8173, 8, 0.4837)]), (8213, [(8213, 40, 12.06)]), (8229, [(8229, -4, 0.1205)]), (8237, [(8237, 28, 5.902)]), (8245, [(8245, -16, 1.926)]), (8261, [(8261, 0, 0)]), (8269, [(8269, -8, 0.4809)]), (8285, [(8285, -28, 5.885)]), (8293, [(8293, -20, 3.001)]), (8301, [(8301, 24, 4.320)]), (8317, [(8317, 20, 2.997)]), (8357, [(8357, 0, 0)]), (8365, [(8365, 0, 0)]), (8445, [(8445, -4, 0.1190)]), (8461, [(8461, -8, 0.4754)]), (8493, [(8493, -8, 0.4745)]), (8501, [(8501, -16, 1.897)]), (8517, [(8517, -16, 1.895)]), (8533, [(8533, 8, 0.4734)]), (8549, [(8549, 32, 7.567)]), (8589, [(8589, 8, 0.4718)]), (8597, [(8597, -60, 26.53)]), (8629, [(8629, 4, 0.1177)]), (8637, [(8637, 4, 0.1176)]), (8677, [(8677, 20, 2.934)]), (8693, [(8693, 72, 37.99)]), (8701, [(8701, 24, 4.219)]), (8709, [(8709, -12, 1.054)]), (8733, [(8733, -16, 1.872)]), (8749, [(8749, 12, 1.052)]), (8765, [(8765, 4, 0.1168)]), (8781, [(8781, 12, 1.050)]), (8821, [(8821, 4, 0.1164)]), (8845, [(8845, -8, 0.9299)]), (8861, [(8861, 12, 1.045)]), (8909, [(8909, 16, 1.853)]), (8933, [(8933, -40, 11.57)]), (8941, [(8941, 4, 0.1156)]), (8965, [(8965, -4, 0.1155)]), (8981, [(8981, 32, 7.383)]), (8989, [(8989, 16, 1.845)]), (8997, [(8997, 12, 1.037)]), (9013, [(9013, -20, 2.879)]), (9053, [(9053, -32, 7.353)]), (9061, [(9061, 0, 0)]), (9077, [(9077, 52, 38.78)]), (9093, [(9093, 8, 0.4586)]), (9101, [(9101, -16, 1.833)]), (9141, [(9141, 16, 1.829)]), (9157, [(9157, 12, 1.028)]), (9165, [(9165, 4, 0.1142)]), (9173, [(9173, 84, 50.34)]), (9197, [(9197, -24, 4.104)]), (9213, [(9213, -16, 1.822)]), (9221, [(9221, 12, 1.025)]), (9229, [(9229, 12, 1.024)]), (9285, [(9285, 4, 0.1135)]), (9293, [(9293, -4, 0.1134)]), (9309, [(9309, -16, 3.626)]), (9373, [(9373, 8, 0.4517)]), (9389, [(9389, -40, 11.28)]), (9397, [(9397, 0, 0)]), (9421, [(9421, -16, 1.802)]), (9429, [(9429, 8, 0.4503)]), (9445, [(9445, -4, 0.1125)]), (9453, [(9453, -40, 11.24)]), (9461, [(9461, 24, 4.046)]), (9517, [(9517, 12, 1.009)]), (9541, [(9541, -16, 3.581)]), (9557, [(9557, 32, 7.157)]), (9565, [(9565, -36, 9.054)]), (9605, [(9605, -32, 7.139)]), (9629, [(9629, 4, 0.1114)]), (9637, [(9637, 24, 4.009)]), (9661, [(9661, 8, 0.4449)]), (9677, [(9677, -24, 4.001)]), (9685, [(9685, 20, 2.777)]), (9709, [(9709, 16, 1.775)]), (9749, [(9749, 20, 2.768)]), (9757, [(9757, -20, 2.767)]), (9773, [(9773, 8, 0.8847)]), (9789, [(9789, -12, 0.9944)]), (9797, [(9797, -72, 35.79)]), (9853, [(9853, 0, 0)]), (9861, [(9861, -16, 1.761)]), (9869, [(9869, 24, 3.962)]), (9885, [(9885, -4, 0.1100)]), (9893, [(9893, 40, 10.99)]), (9917, [(9917, -44, 13.28)]), (9941, [(9941, -8, 0.4386)]), (9989, [(9989, 40, 10.94)])]]

# map: (1 |-> 1.0) -> 1, Fractional ideal (2) -> 1, Fractional ideal (29) -> -1
[-3, 13/2 + (-7/2)*i + 5/2*j + 7/2*k, [(8, [(8, -2, 3.865)]), (12, [(12, 2, 3.156)]), (17, [(17, 4, 5.303)]), (40, [(40, 2, 1.728)]), (41, [(41, 4, 3.415)]), (44, [(44, 2, 1.648)]), (56, [(56, 4, 5.843)]), (60, [(60, -2, 1.411)]), (73, [(73, 0, 0)]), (76, [(76, 0, 0)]), (89, [(89, 4, 2.318)]), (97, [(97, -4, 2.220)]), (104, [(104, 2, 1.072)]), (105, [(105, 4, 2.134)]), (113, [(113, -8, 8.227)]), (124, [(124, 2, 0.9817)]), (137, [(137, 0, 0)]), (156, [(156, 2, 0.8753)]), (172, [(172, 2, 0.8335)]), (177, [(177, 4, 1.643)]), (184, [(184, 0, 0)]), (185, [(185, 8, 6.430)]), (188, [(188, 6, 7.176)]), (193, [(193, 4, 1.574)]), (201, [(201, 0, 0)]), (217, [(217, 4, 1.484)]), (220, [(220, -2, 0.7370)]), (249, [(249, 4, 1.386)]), (264, [(264, 2, 0.6728)]), (273, [(273, 4, 1.323)]), (280, [(280, 0, 0)]), (305, [(305, -4, 1.252)]), (316, [(316, -2, 0.6150)]), (321, [(321, -4, 1.220)]), (329, [(329, 4, 1.205)]), (337, [(337, 4, 1.191)]), (345, [(345, 4, 1.177)]), (380, [(380, 8, 8.973)]), (385, [(385, -4, 1.114)]), (408, [(408, -4, 2.165)]), (409, [(409, 0, 0)]), (417, [(417, -4, 1.071)]), (424, [(424, -2, 0.5309)]), (433, [(433, 0, 0)]), (449, [(449, 0, 0)]), (456, [(456, 0, 0)]), (472, [(472, 4, 2.013)]), (476, [(476, 0, 0)]), (481, [(481, 0, 0)]), (505, [(505, 0, 0)]), (508, [(508, -4, 1.940)]), (520, [(520, 2, 0.4794)]), (524, [(524, 8, 7.641)]), (536, [(536, -4, 1.889)]), (537, [(537, 8, 3.774)]), (553, [(553, 4, 0.9297)]), (561, [(561, -4, 0.9231)]), (568, [(568, -4, 1.835)]), (569, [(569, -8, 3.666)]), (572, [(572, 14, 22.40)]), (577, [(577, 4, 0.9102)]), (601, [(601, 4, 0.8918)]), (617, [(617, -8, 3.521)]), (620, [(620, -6, 3.951)]), (636, [(636, 2, 0.4335)]), (641, [(641, 4, 0.8636)]), (649, [(649, -4, 0.8582)]), (652, [(652, -2, 0.4281)]), (664, [(664, -4, 1.697)]), (665, [(665, 8, 3.391)]), (681, [(681, 0, 0)]), (713, [(713, -12, 7.369)]), (728, [(728, -8, 6.483)]), (737, [(737, -16, 12.89)]), (744, [(744, 2, 0.4008)]), (764, [(764, 4, 1.582)]), (769, [(769, 4, 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[(1505, 4, 0.5636)]), (1516, [(1516, 4, 1.123)]), (1529, [(1529, 4, 0.5591)]), (1545, [(1545, 0, 0)]), (1564, [(1564, 4, 1.106)]), (1569, [(1569, -8, 2.208)]), (1576, [(1576, 4, 1.101)]), (1577, [(1577, -8, 2.202)]), (1580, [(1580, 6, 2.475)]), (1585, [(1585, -4, 0.5492)]), (1592, [(1592, 16, 17.53)]), (1609, [(1609, 0, 0)]), (1612, [(1612, 2, 0.2723)]), (1641, [(1641, -4, 0.5397)]), (1672, [(1672, -4, 1.069)]), (1697, [(1697, -4, 0.5307)]), (1708, [(1708, -4, 1.058)]), (1713, [(1713, 16, 8.452)]), (1721, [(1721, 4, 0.5270)]), (1729, [(1729, 0, 0)]), (1752, [(1752, -4, 1.045)]), (1761, [(1761, 4, 0.5210)]), (1772, [(1772, -4, 1.039)]), (1777, [(1777, 0, 0)]), (1784, [(1784, 0, 0)]), (1788, [(1788, 10, 6.463)]), (1801, [(1801, 0, 0)]), (1816, [(1816, -4, 1.026)]), (1817, [(1817, 20, 12.82)]), (1841, [(1841, 4, 0.5096)]), (1848, [(1848, -4, 1.017)]), (1864, [(1864, -2, 0.2532)]), (1868, [(1868, -6, 2.276)]), (1873, [(1873, 4, 0.5052)]), (1896, [(1896, 6, 2.260)]), (1897, [(1897, 4, 0.5020)]), (1912, [(1912, -4, 1.000)]), (1916, [(1916, -2, 0.2497)]), (1928, [(1928, 18, 20.17)]), (1929, [(1929, -4, 0.4978)]), (1932, [(1932, -12, 8.953)]), (1945, [(1945, 0, 0)]), (1961, [(1961, 8, 1.975)]), (1964, [(1964, 2, 0.2467)]), (1969, [(1969, 0, 0)]), (1993, [(1993, -4, 0.4897)]), (2012, [(2012, 14, 11.94)]), (2033, [(2033, -16, 7.759)]), (2040, [(2040, -8, 3.873)]), (2041, [(2041, -4, 0.4839)]), (2044, [(2044, 0, 0)]), (2049, [(2049, 0, 0)]), (2056, [(2056, -2, 0.2411)]), (2073, [(2073, 8, 1.921)]), (2076, [(2076, 0, 0)]), (2105, [(2105, 20, 11.91)]), (2120, [(2120, 2, 0.2374)]), (2129, [(2129, 4, 0.4738)]), (2136, [(2136, 0, 0)]), (2161, [(2161, 4, 0.4703)]), (2172, [(2172, -2, 0.2346)]), (2177, [(2177, -8, 1.874)]), (2185, [(2185, 0, 0)]), (2193, [(2193, -4, 0.4669)]), (2201, [(2201, -8, 1.864)]), (2216, [(2216, 8, 3.716)]), (2236, [(2236, 2, 0.2312)]), (2248, [(2248, 2, 0.2306)]), (2252, [(2252, -22, 27.87)]), (2264, [(2264, 0, 0)]), (2265, [(2265, 4, 0.4594)]), (2273, [(2273, 24, 16.51)]), (2280, [(2280, 0, 0)]), (2281, [(2281, 0, 0)]), (2289, [(2289, 4, 0.4570)]), (2305, [(2305, 0, 0)]), (2328, [(2328, 8, 3.625)]), (2332, [(2332, 2, 0.2264)]), (2337, [(2337, 8, 1.809)]), (2360, [(2360, -8, 3.600)]), (2361, [(2361, 0, 0)]), (2364, [(2364, -4, 0.8993)]), (2380, [(2380, 0, 0)]), (2392, [(2392, -4, 0.8941)]), (2393, [(2393, -12, 4.023)]), (2396, [(2396, 6, 2.010)]), (2409, [(2409, -8, 1.782)]), (2417, [(2417, 4, 0.4447)]), (2424, [(2424, -4, 0.8882)]), (2428, [(2428, 2, 0.2219)]), (2433, [(2433, -4, 0.4433)]), (2444, [(2444, -6, 1.990)]), (2473, [(2473, -4, 0.4397)]), (2476, [(2476, -2, 0.2197)]), (2492, [(2492, 24, 31.53)]), (2497, [(2497, 8, 1.750)]), (2504, [(2504, -6, 1.966)]), (2505, [(2505, 0, 0)]), (2508, [(2508, 12, 7.858)]), (2513, [(2513, -12, 3.925)]), (2521, [(2521, 0, 0)]), (2537, [(2537, -4, 0.4341)]), (2540, [(2540, 16, 13.88)]), (2569, [(2569, 0, 0)]), (2584, [(2584, 0, 0)]), (2593, [(2593, 4, 0.4294)]), (2620, [(2620, 0, 0)]), (2636, [(2636, -10, 5.323)]), (2641, [(2641, 0, 0)]), (2649, [(2649, -12, 3.823)]), (2657, [(2657, 4, 0.4242)]), (2665, [(2665, -4, 0.4235)]), (2680, [(2680, 4, 0.8447)]), (2689, [(2689, 0, 0)]), (2705, [(2705, 0, 0)]), (2712, [(2712, 4, 0.8397)]), (2716, [(2716, -4, 0.8391)]), (2728, [(2728, 2, 0.2093)]), (2729, [(2729, 16, 6.696)]), (2737, [(2737, 0, 0)]), (2753, [(2753, 16, 6.667)]), (2769, [(2769, -8, 1.662)]), (2776, [(2776, -4, 0.8299)]), (2792, [(2792, 22, 25.03)]), (2796, [(2796, -2, 0.2067)]), (2801, [(2801, 4, 0.4131)]), (2824, [(2824, 4, 0.8229)]), (2828, [(2828, -8, 3.289)]), (2840, [(2840, -4, 0.8205)]), (2856, [(2856, 0, 0)]), (2857, [(2857, -4, 0.4090)]), (2860, [(2860, 2, 0.2044)]), (2881, [(2881, 0, 0)]), (2892, [(2892, 2, 0.2033)]), (2897, [(2897, -8, 1.625)]), (2908, [(2908, 4, 0.8109)]), (2921, [(2921, -16, 6.473)]), (2937, [(2937, 4, 0.4034)]), (2956, [(2956, 2, 0.2011)]), (2968, [(2968, -8, 3.211)]), (2969, [(2969, 8, 1.605)]), (2972, [(2972, -12, 7.219)]), (2977, [(2977, -4, 0.4007)]), (2984, [(2984, 2, 0.2001)]), (2985, [(2985, -4, 0.4002)]), (3001, [(3001, 0, 0)]), (3004, [(3004, 4, 0.7978)]), (3048, [(3048, 0, 0)]), (3057, [(3057, 4, 0.3954)]), (3064, [(3064, 0, 0)]), (3084, [(3084, -6, 1.772)]), (3089, [(3089, 0, 0)]), (3113, [(3113, -4, 0.3919)]), (3121, [(3121, -4, 0.3914)]), (3129, [(3129, 4, 0.3909)]), (3144, [(3144, 4, 0.7798)]), (3153, [(3153, -16, 6.230)]), (3164, [(3164, -4, 0.7774)]), (3169, [(3169, 0, 0)]), (3176, [(3176, -14, 9.505)]), (3180, [(3180, -6, 1.745)]), (3192, [(3192, 8, 3.096)]), (3193, [(3193, 0, 0)]), (3201, [(3201, 4, 0.3864)]), (3208, [(3208, 6, 1.737)]), (3209, [(3209, 0, 0)]), (3217, [(3217, -4, 0.3855)]), (3233, [(3233, 36, 31.15)]), (3256, [(3256, 0, 0)]), (3260, [(3260, 6, 1.723)]), (3265, [(3265, 4, 0.3826)]), (3288, [(3288, 4, 0.7626)]), (3289, [(3289, -4, 0.3812)]), (3292, [(3292, -4, 0.7621)]), (3304, [(3304, 0, 0)]), (3308, [(3308, 22, 23.00)]), (3320, [(3320, 0, 0)]), (3324, [(3324, 12, 6.826)]), (3337, [(3337, -8, 1.514)]), (3345, [(3345, 8, 1.512)]), (3352, [(3352, -8, 3.021)]), (3353, [(3353, -20, 9.439)]), (3356, [(3356, 2, 0.1887)]), (3361, [(3361, 0, 0)]), (3372, [(3372, 6, 1.694)]), (3385, [(3385, 0, 0)]), (3401, [(3401, -8, 1.500)]), (3404, [(3404, 4, 0.7495)]), (3432, [(3432, 6, 1.679)]), (3433, [(3433, 8, 1.493)]), (3436, [(3436, 2, 0.1865)]), (3441, [(3441, 8, 1.491)]), (3448, [(3448, 0, 0)]), (3449, [(3449, 12, 3.351)]), (3497, [(3497, 12, 3.328)]), (3512, [(3512, 8, 2.951)]), (3521, [(3521, -4, 0.3685)]), (3548, [(3548, -22, 22.21)]), (3553, [(3553, -8, 1.467)]), (3569, [(3569, -4, 0.3660)]), (3585, [(3585, 4, 0.3652)]), (3593, [(3593, 8, 1.459)]), (3608, [(3608, -12, 6.552)]), (3617, [(3617, -16, 5.817)]), (3628, [(3628, -8, 2.904)]), (3633, [(3633, 0, 0)]), (3640, [(3640, 4, 0.7248)]), (3644, [(3644, 14, 8.874)]), (3656, [(3656, 4, 0.7232)]), (3657, [(3657, 4, 0.3615)]), (3665, [(3665, -8, 1.445)]), (3673, [(3673, 8, 1.443)]), (3697, [(3697, 0, 0)]), (3704, [(3704, 12, 6.466)]), (3720, [(3720, -14, 8.782)]), (3729, [(3729, -8, 1.432)]), (3752, [(3752, 12, 6.425)]), (3756, [(3756, -2, 0.1784)]), (3768, [(3768, -4, 0.7124)]), (3772, [(3772, -4, 0.7120)]), (3784, [(3784, 2, 0.1777)]), (3785, [(3785, 12, 3.198)]), (3788, [(3788, -2, 0.1776)]), (3801, [(3801, -4, 0.3546)]), (3809, [(3809, -8, 1.417)]), (3817, [(3817, 0, 0)]), (3820, [(3820, -4, 0.7075)]), (3836, [(3836, 4, 0.7060)]), (3849, [(3849, 8, 1.410)]), (3865, [(3865, 4, 0.3517)]), (3868, [(3868, 2, 0.1758)]), (3884, [(3884, -8, 2.807)]), (3889, [(3889, 0, 0)]), (3896, [(3896, 4, 0.7006)]), (3905, [(3905, -16, 5.598)]), (3912, [(3912, 2, 0.1748)]), (3913, [(3913, 12, 3.146)]), (3929, [(3929, 8, 1.395)]), (3932, [(3932, 2, 0.1743)]), (3961, [(3961, -4, 0.3474)]), (3976, [(3976, 4, 0.6935)]), (3985, [(3985, -4, 0.3463)]), (3992, [(3992, -16, 11.07)]), (4012, [(4012, -4, 0.6904)]), (4017, [(4017, -8, 1.380)]), (4028, [(4028, -4, 0.6890)]), (4033, [(4033, 0, 0)]), (4049, [(4049, 12, 3.092)]), (4057, [(4057, -8, 1.373)]), (4072, [(4072, -2, 0.1713)]), (4081, [(4081, -4, 0.3422)]), (4092, [(4092, -6, 1.538)]), (4097, [(4097, -20, 8.540)]), (4108, [(4108, 6, 1.535)]), (4120, [(4120, 4, 0.6812)]), (4121, [(4121, -20, 8.515)]), (4129, [(4129, 0, 0)]), (4136, [(4136, -6, 1.530)]), (4137, [(4137, -16, 5.439)]), (4145, [(4145, -12, 3.056)]), (4161, [(4161, -8, 1.356)]), (4168, [(4168, 10, 4.233)]), (4184, [(4184, 8, 2.704)]), (4188, [(4188, -2, 0.1689)]), (4193, [(4193, -12, 3.039)]), (4216, [(4216, 0, 0)]), (4217, [(4217, 8, 1.347)]), (4220, [(4220, 22, 20.36)]), (4236, [(4236, 0, 0)]), (4249, [(4249, -4, 0.3354)]), (4252, [(4252, 2, 0.1676)]), (4265, [(4265, 0, 0)]), (4273, [(4273, -8, 1.338)]), (4280, [(4280, 12, 6.016)]), (4281, [(4281, 8, 1.337)]), (4289, [(4289, -4, 0.3338)]), (4313, [(4313, 16, 5.327)]), (4348, [(4348, -2, 0.1658)]), (4353, [(4353, 12, 2.982)]), (4360, [(4360, 2, 0.1656)]), (4364, [(4364, -14, 8.109)]), (4369, [(4369, 4, 0.3308)]), (4376, [(4376, -4, 0.6610)]), (4377, [(4377, 0, 0)]), (4393, [(4393, -8, 1.319)]), (4396, [(4396, 4, 0.6595)]), (4440, [(4440, 0, 0)]), (4449, [(4449, 0, 0)]), (4456, [(4456, 0, 0)]), (4476, [(4476, -2, 0.1634)]), (4481, [(4481, 12, 2.940)]), (4492, [(4492, 8, 2.610)]), (4497, [(4497, -20, 8.151)]), (4505, [(4505, 4, 0.3257)]), (4513, [(4513, -4, 0.3255)]), (4521, [(4521, 0, 0)]), (4556, [(4556, -12, 5.831)]), (4561, [(4561, 4, 0.3237)]), (4568, [(4568, -20, 16.17)]), (4584, [(4584, -4, 0.6459)]), (4585, [(4585, 0, 0)]), (4593, [(4593, 0, 0)]), (4601, [(4601, -20, 8.058)]), (4609, [(4609, 0, 0)]), (4632, [(4632, 0, 0)]), (4648, [(4648, -8, 2.566)]), (4652, [(4652, 2, 0.1603)]), (4657, [(4657, -12, 2.883)]), (4681, [(4681, -4, 0.3196)]), (4684, [(4684, 2, 0.1597)]), (4696, [(4696, -4, 0.6381)]), (4712, [(4712, -8, 2.548)]), (4713, [(4713, 4, 0.3185)]), (4729, [(4729, 0, 0)]), (4737, [(4737, 8, 1.271)]), (4744, [(4744, 2, 0.1587)]), (4745, [(4745, -16, 5.078)]), (4748, [(4748, -16, 10.15)]), (4764, [(4764, -2, 0.1584)]), (4777, [(4777, 4, 0.3163)]), (4793, [(4793, -8, 1.263)]), (4796, [(4796, 10, 3.946)]), (4812, [(4812, -2, 0.1576)]), (4817, [(4817, 8, 1.260)]), (4828, [(4828, 8, 2.517)]), (4841, [(4841, 0, 0)]), (4857, [(4857, -16, 5.019)]), (4889, [(4889, -12, 2.814)]), (4904, [(4904, -10, 3.903)]), (4920, [(4920, 8, 2.494)]), (4940, [(4940, 12, 5.599)]), (4945, [(4945, -4, 0.3109)]), (4956, [(4956, 8, 2.485)]), (4969, [(4969, 4, 0.3102)]), (4985, [(4985, 16, 4.955)]), (5009, [(5009, 16, 4.943)]), (5020, [(5020, -2, 0.1543)]), (5032, [(5032, -4, 0.6164)]), (5036, [(5036, -8, 2.465)]), (5048, [(5048, 0, 0)]), (5057, [(5057, -24, 11.07)]), (5064, [(5064, 6, 1.383)]), (5065, [(5065, 0, 0)]), (5073, [(5073, 8, 1.228)]), (5089, [(5089, 0, 0)]), (5116, [(5116, -2, 0.1528)]), (5144, [(5144, 16, 9.755)]), (5160, [(5160, -2, 0.1522)]), (5164, [(5164, 2, 0.1521)]), (5176, [(5176, 4, 0.6078)]), (5177, [(5177, -8, 1.215)]), (5180, [(5180, -4, 0.6076)]), (5201, [(5201, 0, 0)]), (5208, [(5208, -8, 2.424)]), (5209, [(5209, -8, 1.212)]), (5212, [(5212, 10, 3.786)]), (5217, [(5217, 0, 0)]), (5228, [(5228, -14, 7.408)]), (5241, [(5241, 8, 1.208)]), (5257, [(5257, 8, 1.206)]), (5260, [(5260, -2, 0.1507)]), (5276, [(5276, -16, 9.632)]), (5281, [(5281, -8, 1.203)]), (5288, [(5288, -8, 2.405)]), (5289, [(5289, 4, 0.3006)]), (5297, [(5297, 28, 14.72)]), (5304, [(5304, 8, 2.402)]), (5305, [(5305, -4, 0.3002)]), (5321, [(5321, -4, 0.2997)]), (5353, [(5353, -8, 1.195)]), (5368, [(5368, -8, 2.387)]), (5377, [(5377, 0, 0)]), (5384, [(5384, -6, 1.341)]), (5404, [(5404, -4, 0.5948)]), (5420, [(5420, 14, 7.276)]), (5433, [(5433, 20, 7.416)]), (5441, [(5441, 8, 1.186)]), (5449, [(5449, 4, 0.2962)]), (5464, [(5464, 4, 0.5916)]), (5473, [(5473, -4, 0.2955)]), (5484, [(5484, 12, 5.314)]), (5489, [(5489, 4, 0.2951)]), (5496, [(5496, 4, 0.5898)]), (5512, [(5512, 6, 1.325)]), (5513, [(5513, -24, 10.60)]), (5521, [(5521, 0, 0)]), (5528, [(5528, -32, 37.64)]), (5529, [(5529, 0, 0)]), (5560, [(5560, -4, 0.5864)]), (5576, [(5576, 8, 2.342)]), (5585, [(5585, 4, 0.2926)]), (5608, [(5608, 2, 0.1460)]), (5609, [(5609, 0, 0)]), (5612, [(5612, 4, 0.5837)]), (5624, [(5624, -8, 2.332)]), (5628, [(5628, -4, 0.5829)]), (5640, [(5640, -2, 0.1456)]), (5641, [(5641, -4, 0.2911)]), (5644, [(5644, 0, 0)]), (5657, [(5657, 20, 7.267)]), (5665, [(5665, 8, 1.162)]), (5672, [(5672, -26, 24.53)]), (5673, [(5673, -12, 2.613)]), (5676, [(5676, 6, 1.306)]), (5681, [(5681, -8, 1.160)]), (5692, [(5692, -2, 0.1449)]), (5705, [(5705, 4, 0.2895)]), (5721, [(5721, -4, 0.2891)]), (5740, [(5740, 4, 0.5772)]), (5745, [(5745, -4, 0.2885)]), (5752, [(5752, -12, 5.189)]), (5753, [(5753, -24, 10.38)]), (5756, [(5756, 4, 0.5764)]), (5761, [(5761, 0, 0)]), (5768, [(5768, 20, 14.39)]), (5785, [(5785, -4, 0.2875)]), (5788, [(5788, -2, 0.1437)]), (5817, [(5817, 0, 0)]), (5848, [(5848, 4, 0.5718)]), (5873, [(5873, 4, 0.2853)]), (5884, [(5884, 0, 0)]), (5889, [(5889, -4, 0.2849)]), (5897, [(5897, -8, 1.139)]), (5905, [(5905, 0, 0)]), (5928, [(5928, -20, 14.20)]), (5937, [(5937, 4, 0.2838)]), (5948, [(5948, 4, 0.5670)]), (5953, [(5953, 8, 1.133)]), (5960, [(5960, 10, 3.540)]), (5964, [(5964, 4, 0.5662)]), (5977, [(5977, -4, 0.2828)]), (5992, [(5992, 0, 0)]), (5993, [(5993, 24, 10.17)]), (6001, [(6001, 0, 0)]), (6017, [(6017, -20, 7.047)]), (6024, [(6024, 6, 1.268)]), (6040, [(6040, -4, 0.5626)]), (6044, [(6044, -10, 3.515)]), (6049, [(6049, -4, 0.2811)]), (6072, [(6072, -16, 8.979)]), (6073, [(6073, 4, 0.2806)]), (6088, [(6088, -8, 2.242)]), (6092, [(6092, 10, 3.502)]), (6104, [(6104, 8, 2.239)]), (6105, [(6105, 0, 0)]), (6108, [(6108, 2, 0.1399)]), (6121, [(6121, 4, 0.2795)]), (6136, [(6136, 0, 0)]), (6140, [(6140, 10, 3.488)]), (6145, [(6145, -4, 0.2789)]), (6169, [(6169, -4, 0.2784)]), (6185, [(6185, 28, 13.62)]), (6188, [(6188, 16, 8.894)]), (6204, [(6204, 6, 1.249)]), (6209, [(6209, 4, 0.2775)]), (6216, [(6216, -12, 4.992)]), (6217, [(6217, 4, 0.2773)]), (6220, [(6220, 0, 0)]), (6232, [(6232, 8, 2.216)]), 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[(6569, 24, 9.711)]), (6572, [(6572, 14, 6.608)]), (6585, [(6585, -12, 2.425)]), (6593, [(6593, -16, 4.308)]), (6601, [(6601, -8, 1.076)]), (6604, [(6604, -4, 0.5381)]), (6609, [(6609, 0, 0)]), (6620, [(6620, 6, 1.209)]), (6649, [(6649, 4, 0.2681)]), (6652, [(6652, -12, 4.825)]), (6668, [(6668, 2, 0.1339)]), (6673, [(6673, 4, 0.2676)]), (6680, [(6680, 8, 2.140)]), (6681, [(6681, 8, 1.070)]), (6684, [(6684, 8, 2.139)]), (6689, [(6689, 4, 0.2673)]), (6697, [(6697, 0, 0)]), (6716, [(6716, -12, 4.802)]), (6745, [(6745, 0, 0)]), (6769, [(6769, -4, 0.2657)]), (6796, [(6796, 2, 0.1326)]), (6801, [(6801, 0, 0)]), (6812, [(6812, 8, 2.119)]), (6817, [(6817, -4, 0.2648)]), (6833, [(6833, -4, 0.2645)]), (6841, [(6841, -4, 0.2643)]), (6856, [(6856, 2, 0.1320)]), (6865, [(6865, 0, 0)]), (6881, [(6881, -12, 2.372)]), (6888, [(6888, 4, 0.5269)]), (6892, [(6892, 4, 0.5267)]), (6904, [(6904, 0, 0)]), (6905, [(6905, 20, 6.578)]), (6913, [(6913, 8, 1.052)]), (6920, [(6920, 4, 0.5257)]), (6945, [(6945, 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0)]), (7305, [(7305, -4, 0.2558)]), (7320, [(7320, 4, 0.5111)]), (7329, [(7329, 4, 0.2554)]), (7340, [(7340, -4, 0.5104)]), (7345, [(7345, 0, 0)]), (7352, [(7352, 4, 0.5100)]), (7356, [(7356, 6, 1.147)]), (7368, [(7368, 18, 10.32)]), (7369, [(7369, 0, 0)]), (7377, [(7377, -8, 1.018)]), (7384, [(7384, -4, 0.5089)]), (7385, [(7385, -4, 0.2544)]), (7393, [(7393, 12, 2.289)]), (7409, [(7409, 12, 2.286)]), (7432, [(7432, -12, 4.565)]), (7441, [(7441, 4, 0.2535)]), (7464, [(7464, 0, 0)]), (7465, [(7465, -4, 0.2531)]), (7468, [(7468, 8, 2.024)]), (7480, [(7480, -8, 2.022)]), (7484, [(7484, 0, 0)]), (7496, [(7496, -16, 8.081)]), (7513, [(7513, 8, 1.009)]), (7521, [(7521, 4, 0.2521)]), (7528, [(7528, 2, 0.1260)]), (7529, [(7529, -4, 0.2520)]), (7532, [(7532, -24, 18.14)]), (7537, [(7537, -8, 1.007)]), (7548, [(7548, -4, 0.5033)]), (7561, [(7561, -4, 0.2514)]), (7577, [(7577, -16, 4.019)]), (7580, [(7580, 12, 4.520)]), (7601, [(7601, 0, 0)]), (7608, [(7608, -4, 0.5013)]), (7609, [(7609, -4, 0.2506)]), (7612, [(7612, 8, 2.005)]), (7617, [(7617, -8, 1.002)]), (7624, [(7624, -2, 0.1252)]), (7673, [(7673, -8, 0.9984)]), (7697, [(7697, 32, 15.95)]), (7724, [(7724, -10, 3.110)]), (7729, [(7729, 0, 0)]), (7745, [(7745, -16, 3.975)]), (7753, [(7753, 0, 0)]), (7761, [(7761, -4, 0.2482)]), (7769, [(7769, -8, 0.9922)]), (7784, [(7784, -4, 0.4956)]), (7793, [(7793, -24, 8.916)]), (7804, [(7804, 2, 0.1237)]), (7809, [(7809, 0, 0)]), (7816, [(7816, 2, 0.1237)]), (7820, [(7820, 4, 0.4945)]), (7832, [(7832, 0, 0)]), (7833, [(7833, -12, 2.223)]), (7841, [(7841, 4, 0.2469)]), (7849, [(7849, -8, 0.9871)]), (7873, [(7873, -8, 0.9856)]), (7880, [(7880, 8, 1.970)]), (7896, [(7896, 0, 0)]), (7905, [(7905, -12, 2.213)]), (7928, [(7928, 16, 7.858)]), (7932, [(7932, 4, 0.4910)]), (7944, [(7944, 10, 3.066)]), (7948, [(7948, -4, 0.4905)]), (7960, [(7960, -4, 0.4901)]), (7961, [(7961, -8, 0.9802)]), (7964, [(7964, -2, 0.1225)]), (7977, [(7977, 12, 2.203)]), (7985, [(7985, -20, 6.117)]), (7993, [(7993, -8, 0.9782)]), (7996, [(7996, -4, 0.4890)]), (8012, [(8012, 30, 27.48)]), (8041, [(8041, 4, 0.2438)]), (8044, [(8044, 0, 0)]), (8060, [(8060, 6, 1.096)]), (8065, [(8065, -4, 0.2435)]), (8072, [(8072, -14, 5.962)]), (8076, [(8076, 2, 0.1216)]), (8081, [(8081, 4, 0.2432)]), (8088, [(8088, -20, 12.16)]), (8089, [(8089, -4, 0.2431)]), (8105, [(8105, 12, 2.186)]), (8108, [(8108, -26, 20.52)]), (8137, [(8137, 8, 0.9695)]), (8152, [(8152, 0, 0)]), (8161, [(8161, -4, 0.2420)]), (8168, [(8168, 6, 1.089)]), (8188, [(8188, -4, 0.4832)]), (8193, [(8193, -16, 3.865)]), (8204, [(8204, -8, 1.931)]), (8209, [(8209, 0, 0)]), (8233, [(8233, 0, 0)]), (8248, [(8248, 0, 0)]), (8257, [(8257, 4, 0.2406)]), (8268, [(8268, -10, 3.006)]), (8273, [(8273, 28, 11.78)]), (8284, [(8284, -4, 0.4804)]), (8296, [(8296, 8, 1.920)]), (8297, [(8297, 12, 2.160)]), (8305, [(8305, 12, 2.159)]), (8312, [(8312, 24, 17.27)]), (8313, [(8313, -4, 0.2398)]), (8321, [(8321, 4, 0.2397)]), (8337, [(8337, 28, 11.73)]), (8344, [(8344, -8, 1.915)]), (8360, [(8360, 4, 0.4782)]), (8364, [(8364, 0, 0)]), (8369, [(8369, 16, 3.824)]), (8392, [(8392, -4, 0.4773)]), (8393, [(8393, -20, 5.966)]), (8396, [(8396, 8, 1.909)]), (8408, [(8408, 24, 17.17)]), (8412, [(8412, 18, 9.655)]), (8441, [(8441, -8, 0.9519)]), (8449, [(8449, 8, 0.9514)]), (8456, [(8456, 0, 0)]), (8457, [(8457, 0, 0)]), (8465, [(8465, 20, 5.941)]), (8476, [(8476, 2, 0.1187)]), (8489, [(8489, -20, 5.932)]), (8508, [(8508, -10, 2.963)]), (8524, [(8524, -6, 1.066)]), (8529, [(8529, 12, 2.131)]), (8536, [(8536, 0, 0)]), (8537, [(8537, -8, 0.9465)]), (8540, [(8540, -12, 4.259)]), (8545, [(8545, 0, 0)]), (8552, [(8552, -20, 11.82)]), (8553, [(8553, 4, 0.2364)]), (8569, [(8569, 0, 0)]), (8572, [(8572, 6, 1.063)]), (8601, [(8601, -4, 0.2357)]), (8616, [(8616, 10, 2.944)]), (8632, [(8632, 0, 0)]), (8652, [(8652, -4, 0.4701)]), (8657, [(8657, 40, 23.50)]), (8668, [(8668, 4, 0.4697)]), (8681, [(8681, -12, 2.112)]), (8689, [(8689, -4, 0.2346)]), (8697, [(8697, -24, 8.440)]), (8732, [(8732, 16, 7.487)]), (8737, [(8737, 4, 0.2339)]), (8744, [(8744, 4, 0.4676)]), (8760, [(8760, 4, 0.4672)]), (8761, [(8761, 4, 0.2336)]), (8769, [(8769, 8, 0.9339)]), (8776, [(8776, 2, 0.1167)]), (8777, [(8777, -16, 3.734)]), (8785, [(8785, 4, 0.2333)]), (8801, [(8801, 16, 3.729)]), (8808, [(8808, 4, 0.4659)]), (8824, [(8824, 4, 0.4655)]), (8828, [(8828, 30, 26.18)]), (8857, [(8857, 4, 0.2323)]), (8860, [(8860, 0, 0)]), (8872, [(8872, 10, 2.902)]), (8876, [(8876, -12, 4.177)]), (8888, [(8888, 28, 22.73)]), (8889, [(8889, -4, 0.2319)]), (8905, [(8905, -8, 0.9268)]), (8913, [(8913, -12, 2.084)]), (8920, [(8920, 0, 0)]), (8921, [(8921, 12, 2.083)]), (8924, [(8924, -8, 1.852)]), (8929, [(8929, -4, 0.2314)]), (8940, [(8940, 6, 1.041)]), (8953, [(8953, -12, 2.080)]), (8969, [(8969, -8, 0.9234)]), (8972, [(8972, -8, 1.847)]), (8988, [(8988, 0, 0)]), (9001, [(9001, -8, 0.9218)]), (9004, [(9004, 2, 0.1152)]), (9017, [(9017, 0, 0)]), (9033, [(9033, -12, 2.070)]), (9080, [(9080, -4, 0.4589)]), (9089, [(9089, 4, 0.2293)]), (9096, [(9096, 12, 4.126)]), (9116, [(9116, 2, 0.1145)]), (9121, [(9121, 4, 0.2289)]), (9132, [(9132, -4, 0.4576)]), (9137, [(9137, 0, 0)]), (9145, [(9145, 4, 0.2286)]), (9161, [(9161, 4, 0.2284)]), (9176, [(9176, 8, 1.826)]), (9185, [(9185, 0, 0)]), (9201, [(9201, 4, 0.2279)]), (9208, [(9208, 16, 7.291)]), (9224, [(9224, 10, 2.846)]), (9233, [(9233, 32, 14.56)]), (9240, [(9240, 0, 0)]), (9241, [(9241, -4, 0.2274)]), (9249, [(9249, 4, 0.2273)]), (9265, [(9265, -4, 0.2271)]), (9272, [(9272, 16, 7.266)]), (9292, [(9292, 12, 4.083)]), (9320, [(9320, 10, 2.831)]), (9321, [(9321, 4, 0.2265)]), (9336, [(9336, 4, 0.4526)]), (9340, [(9340, -2, 0.1131)]), (9352, [(9352, 4, 0.4522)]), (9353, [(9353, 4, 0.2261)]), (9356, [(9356, 18, 9.155)]), (9377, [(9377, 4, 0.2258)]), (9384, [(9384, -4, 0.4514)]), (9385, [(9385, 4, 0.2257)]), (9388, [(9388, 4, 0.4513)]), (9393, [(9393, 0, 0)]), (9404, [(9404, 22, 13.64)]), (9417, [(9417, -8, 0.9012)]), (9433, [(9433, 0, 0)]), (9436, [(9436, 4, 0.4502)]), (9452, [(9452, -20, 11.24)]), (9465, [(9465, 0, 0)]), (9473, [(9473, -16, 3.594)]), (9480, [(9480, 10, 2.807)]), (9481, [(9481, -8, 0.8982)]), (9497, [(9497, 24, 8.077)]), (9529, [(9529, 0, 0)]), (9544, [(9544, 4, 0.4476)]), (9553, [(9553, 12, 2.013)]), (9560, [(9560, 0, 0)]), (9580, [(9580, 2, 0.1117)]), (9596, [(9596, -2, 0.1116)]), (9601, [(9601, 0, 0)]), (9609, [(9609, 8, 0.8922)]), (9617, [(9617, 12, 2.007)]), (9640, [(9640, 2, 0.1113)]), (9649, [(9649, -8, 0.8903)]), (9660, [(9660, 4, 0.4449)]), (9665, [(9665, -16, 3.558)]), (9672, [(9672, -10, 2.779)]), (9676, [(9676, 0, 0)]), (9688, [(9688, -8, 1.777)]), (9689, [(9689, -16, 3.554)]), (9697, [(9697, 4, 0.2220)]), (9704, [(9704, -12, 3.995)]), (9705, [(9705, 12, 1.997)]), (9713, [(9713, -20, 5.546)]), (9736, [(9736, 6, 0.9971)]), (9752, [(9752, 4, 0.4428)]), (9761, [(9761, -16, 3.541)]), (9784, [(9784, -4, 0.4421)]), (9785, [(9785, 32, 14.15)]), (9788, [(9788, 14, 5.414)]), (9804, [(9804, 4, 0.4416)]), (9816, [(9816, 12, 3.972)]), (9817, [(9817, -4, 0.2207)]), (9820, [(9820, -6, 0.9929)]), (9833, [(9833, -36, 17.86)]), (9841, [(9841, 4, 0.2204)]), (9848, [(9848, 4, 0.4406)]), (9852, [(9852, -10, 2.753)]), (9857, [(9857, 28, 10.79)]), (9868, [(9868, -6, 0.9904)]), (9881, [(9881, -4, 0.2199)]), (9897, [(9897, -12, 1.978)]), (9916, [(9916, -4, 0.4391)]), (9921, [(9921, 0, 0)]), (9928, [(9928, 8, 1.755)]), (9929, [(9929, -8, 0.8777)]), (9932, [(9932, 12, 3.949)]), (9937, [(9937, 0, 0)]), (9944, [(9944, -12, 3.947)]), (9961, [(9961, 4, 0.2191)]), (9964, [(9964, -2, 0.1095)]), (9993, [(9993, 12, 1.968)])]]