# label = 2.2.12.1-47.2-b # Base field F = Number Field in a with defining polynomial x^2 - 3 # Quaternion algebra given by i^2 = -1, j^2 = -1 # Order with basis over the integers given by [1, (4*a - 1)*i, (1/2*a - 15)*i + 1/2*j, 1/2*a + i + 1/2*k] # Nmax = 10000 [(1, [(6*a - 25)*i, (1/2*a - 62)*i + 1/2*j, 1/2*a + (-8897/22*a - 2227/11)*i + (-3/11*a - 3/22)*j + (-1/11*a - 1/22)*k]), (-1, [(6*a - 25)*i, (1/2*a - 62)*i + 1/2*j, 1/2*a + (-8897/22*a - 2227/11)*i + (-3/11*a - 3/22)*j + (-1/11*a - 1/22)*k]), (-1, [(4*a - 1)*i, (1/2*a - 15)*i + 1/2*j, 1/2*a + i + 1/2*k]), (1, [(4*a - 1)*i, (1/2*a - 15)*i + 1/2*j, 1/2*a + i + 1/2*k])] [((4*a - 1,), a - 8 + (27/2*a + 95/2)*i + (-1/2*a - 1/2)*j + (-3*a)*k)] # map: (a |-> -1.73) -> -1, (a |-> 1.73) -> -1, Fractional ideal (4*a - 1) -> -1 [5, -a + 2 + (-95*a - 171/2)*i + 7/2*a*j + a*k, [(1, [(-1, 2, 1.400)]), (16, [(4*a - 8, -4, 1.400)]), (33, [(4*a - 9, 4, 0.9748)]), (49, [(-7, -4, 0.8000)]), (52, [(-2*a - 8, 0, 0)]), (73, [(-4*a - 11, 4, 0.6554)]), (177, [(4*a - 15, 12, 3.788), (-4*a - 15, 4, 0.4209)]), (193, [(-12*a - 25, -4, 0.4031)]), (208, [(-4*a - 16, 8, 1.553)]), (241, [(4*a - 17, -8, 1.443), (-4*a - 17, 4, 0.3607)]), (276, [(-10*a - 24, 0, 0)]), (289, [(-17, -4, 0.3294)]), (313, [(4*a - 19, 8, 1.266)]), (321, [(-16*a - 33, -4, 0.3126)]), (337, [(8*a - 23, 4, 0.3050), (-8*a - 23, 0, 0)]), (352, [(-4*a - 20, -8, 1.194), (12*a - 28, -16, 4.776)]), (409, [(-12*a - 29, 0, 0)]), (433, [(-8*a - 25, 16, 4.306)]), (436, [(-14*a - 32, 8, 1.073)]), (481, [(-4*a - 23, 4, 0.2553), (20*a - 41, -4, 0.2553)]), (528, [(-4*a - 24, -16, 3.899)]), (537, [(8*a - 27, -20, 6.041)]), (564, [(2*a - 24, 8, 1.886), (-2*a - 24, 8, 0.9432)]), (577, [(4*a - 25, -16, 3.730)]), (628, [(-18*a - 40, -24, 8.045), (18*a - 40, 24, 8.045)]), (649, [(8*a - 29, 4, 0.2198), (-20*a - 43, 4, 0.2198)]), (673, [(-24*a - 49, 12, 1.943)]), (681, [(-4*a - 27, -12, 1.931)]), (724, [(10*a - 32, -8, 0.8325)]), (736, [(4*a - 28, 16, 3.303), (-20*a - 44, 0, 0)]), (784, [(-28*a - 56, 0, 0)]), (793, [(4*a - 29, 20, 4.972), (12*a - 35, 4, 0.1989)]), (825, [(-20*a - 45, 0, 0)]), (897, [(28*a - 57, 8, 0.7479), (-28*a - 57, 8, 0.7479)]), (913, [(-4*a - 31, -16, 2.965), (16*a - 41, 8, 0.7413)]), (916, [(6*a - 32, -8, 0.7401)]), (937, [(12*a - 37, 16, 2.927)]), (1009, [(20*a - 47, 0, 0)]), (1012, [(2*a - 32, -16, 2.817), (-2*a - 32, 16, 2.817)]), (1033, [(-8*a - 35, 4, 0.1742)]), (1041, [(4*a - 33, 4, 0.1736), (-4*a - 33, 12, 1.562)]), (1081, [(-16*a - 43, 16, 5.450), (24*a - 53, -4, 0.3406), (-24*a - 53, 0, 0)]), (1104, [(-20*a - 48, 16, 2.697)]), (1168, [(12*a - 40, 16, 2.622)]), (1177, [(4*a - 35, -8, 0.6529), (-4*a - 35, -4, 0.1632)]), (1201, [(-20*a - 49, -12, 1.454)]), (1248, [(-4*a - 36, -8, 0.6341), (28*a - 60, 8, 0.6341)]), (1257, [(-16*a - 45, 12, 1.422)]), (1297, [(-24*a - 55, 24, 5.598), (24*a - 55, -16, 2.488)]), (1300, [(10*a - 40, 8, 0.6213)]), (1321, [(4*a - 37, -4, 0.1541)]), (1329, [(8*a - 39, -12, 1.383)]), (1369, [(-37, 4, 0.1514)]), (1396, [(-30*a - 64, -8, 0.5995)]), (1401, [(-20*a - 51, 4, 0.1496)]), (1417, [(32*a - 67, 32, 9.521), (-32*a - 67, 4, 0.1488)]), (1441, [(36*a - 73, 16, 2.360), (-16*a - 47, 0, 0)]), (1492, [(-6*a - 40, 24, 5.219)]), (1504, [(-12*a - 44, -4, 0.2888), (20*a - 52, 4, 0.2888)]), (1588, [(2*a - 40, -8, 0.5621), (-2*a - 40, -32, 8.994)]), (1609, [(20*a - 53, 4, 0.1396)]), (1617, [(28*a - 63, -16, 2.228)]), (1633, [(-4*a - 41, 0, 0), (-16*a - 49, 0, 0)]), (1684, [(22*a - 56, 0, 0)]), (1689, [(32*a - 69, -4, 0.1363)]), (1716, [(-14*a - 48, -16, 2.163), (14*a - 48, -16, 2.163)]), (1744, [(-28*a - 64, 0, 0)]), (1753, [(-24*a - 59, -8, 0.5350), (24*a - 59, -16, 2.140)]), (1761, [(40*a - 81, 4, 0.1334)]), (1777, [(-12*a - 47, 4, 0.1328)]), (1801, [(4*a - 43, 8, 0.5278)]), (1825, [(20*a - 55, -16, 2.097)]), (1833, [(-8*a - 45, -8, 1.046), (-16*a - 51, -24, 4.709), (16*a - 51, 20, 6.540)]), (1873, [(-28*a - 65, 8, 0.5176)]), (1969, [(-32*a - 71, -12, 1.136), (32*a - 71, 0, 0)]), (1993, [(24*a - 61, -4, 0.1254)]), (2004, [(-10*a - 48, 8, 0.5004)]), (2017, [(-8*a - 47, -12, 1.122)]), (2041, [(36*a - 77, -8, 0.4958), (16*a - 53, 0, 0)]), (2068, [(26*a - 64, 8, 0.4926), (-26*a - 64, 16, 3.941), (38*a - 80, 8, 0.9852)]), (2113, [(-44*a - 89, 8, 0.4873)]), (2137, [(-28*a - 67, -12, 1.090)]), (2161, [(-4*a - 47, 4, 0.1205)]), (2164, [(18*a - 56, 16, 1.926), (-18*a - 56, 0, 0)]), (2209, [(-47, 8, 0.9532)]), (2256, [(4*a - 48, 8, 0.9432), (-4*a - 48, -8, 0.4716)]), (2257, [(-16*a - 55, -4, 0.1179), (16*a - 55, 28, 5.776), (32*a - 73, -28, 5.776), (-32*a - 73, 4, 0.1179)]), (2272, [(12*a - 52, -16, 1.880), (-12*a - 52, 16, 1.880), (28*a - 68, -16, 1.880), (-28*a - 68, 16, 1.880)]), (2281, [(20*a - 59, -4, 0.1173), (-20*a - 59, 0, 0)]), (2292, [(2*a - 48, 8, 0.4679), (-2*a - 48, -16, 1.872)]), (2353, [(4*a - 49, 8, 0.4618), (-4*a - 49, 36, 9.351)]), (2377, [(-12*a - 53, 12, 1.034), (12*a - 53, 0, 0)]), (2400, [(-20*a - 60, -24, 4.115), (20*a - 60, 24, 4.115)]), (2409, [(8*a - 51, -16, 1.826), (-8*a - 51, 16, 1.826)]), (2425, [(-40*a - 85, -16, 1.819), (40*a - 85, 8, 0.4549)]), (2452, [(-42*a - 88, -40, 11.31), (42*a - 88, 16, 1.809)]), (2473, [(-44*a - 91, -4, 0.1126)]), (2481, [(-16*a - 57, -12, 1.012), (16*a - 57, 20, 2.811)]), (2497, [(-24*a - 65, -32, 7.172), (24*a - 65, 12, 1.009)]), (2512, [(36*a - 80, -16, 1.788), (-36*a - 80, 0, 0)]), (2521, [(20*a - 61, -4, 0.1115)]), (2548, [(-14*a - 56, -16, 1.775)]), (2553, [(4*a - 51, 16, 1.773), (-32*a - 75, -8, 0.4433)]), (2617, [(8*a - 53, -12, 0.9852), (-8*a - 53, 16, 1.751)]), (2656, [(4*a - 52, -8, 0.4346), (-4*a - 52, 16, 1.739), (44*a - 92, 8, 0.4346), (-44*a - 92, 0, 0)]), (2689, [(28*a - 71, -4, 0.1080)]), (2713, [(-16*a - 59, 24, 3.870), (16*a - 59, 4, 0.1075)]), (2761, [(-4*a - 53, -8, 0.4263), (24*a - 67, -16, 1.705)]), (2769, [(-20*a - 63, -8, 0.4257), (-40*a - 87, -16, 1.703)]), (2809, [(-53, 4, 0.1057)]), (2832, [(28*a - 72, -24, 3.788), (-28*a - 72, 8, 0.4209)]), (2833, [(8*a - 55, -12, 0.9469)]), (2868, [(-46*a - 96, -8, 0.4183), (46*a - 96, 32, 6.692)]), (2896, [(20*a - 64, 0, 0)]), (2913, [(-52*a - 105, -4, 0.1038)]), (2932, [(34*a - 80, 24, 3.723), (-34*a - 80, 8, 0.4137)]), (2953, [(-16*a - 61, -12, 0.9275)]), (2977, [(4*a - 55, -12, 0.9237), (-4*a - 55, 32, 6.569)]), (3001, [(36*a - 83, -8, 0.4089)]), (3025, [(-55, 0, 0)]), (3028, [(-6*a - 56, 0, 0)]), (3049, [(12*a - 59, -4, 0.1014)]), (3057, [(8*a - 57, 4, 0.1013), (-8*a - 57, -4, 0.1013)]), (3088, [(4*a - 56, 16, 1.612)]), (3121, [(40*a - 89, -12, 0.9022)]), (3124, [(2*a - 56, 0, 0), (18*a - 64, 0, 0)]), (3156, [(26*a - 72, -24, 3.589), (-26*a - 72, -16, 1.595)]), (3169, [(32*a - 79, 0, 0)]), (3201, [(4*a - 57, -8, 0.3959), (16*a - 63, 8, 0.3959)]), (3217, [(-44*a - 95, -4, 0.09873), (44*a - 95, -16, 1.580)]), (3273, [(28*a - 75, -12, 0.8810)]), (3289, [(-8*a - 59, 8, 0.3906), (-12*a - 61, -8, 0.3906), (48*a - 101, -8, 0.3906), (-20*a - 67, 0, 0)]), (3313, [(24*a - 71, 20, 2.432)]), (3316, [(50*a - 104, -16, 1.556)]), (3337, [(-36*a - 85, 12, 1.745), (52*a - 107, 0, 0)]), (3412, [(-38*a - 88, -16, 1.534), (38*a - 88, -32, 6.136)]), (3424, [(-28*a - 76, -8, 0.3828), (20*a - 68, 0, 0)]), (3457, [(16*a - 65, 0, 0)]), (3481, [(-59, 20, 2.373)]), (3489, [(-32*a - 81, -4, 0.09481)]), (3508, [(14*a - 64, -16, 1.513)]), (3529, [(8*a - 61, -20, 2.357), (-8*a - 61, -4, 0.09427)]), (3552, [(4*a - 60, -32, 6.014), (-4*a - 60, 8, 0.3758), (52*a - 108, -24, 3.383), (-52*a - 108, 16, 1.503)]), (3561, [(-20*a - 69, 28, 4.598), (20*a - 69, 4, 0.09384)]), (3577, [(-28*a - 77, 8, 0.3745)]), (3601, [(-24*a - 73, 12, 0.8399), (-44*a - 97, 12, 0.8399)]), (3664, [(12*a - 64, -32, 5.921)]), (3697, [(-48*a - 103, -4, 0.09210)]), (3700, [(30*a - 80, 8, 0.3683), (-30*a - 80, -8, 0.3683)]), (3721, [(-61, -12, 0.8262)]), (3732, [(-22*a - 72, 8, 0.3667)]), (3769, [(52*a - 109, 28, 4.470), (-52*a - 109, -32, 5.838)]), (3777, [(8*a - 63, 20, 2.278), (-8*a - 63, -20, 2.278)]), (3793, [(-12*a - 65, 8, 0.3637)]), (3796, [(54*a - 112, -8, 0.3636), (-54*a - 112, 0, 0)]), (3817, [(32*a - 83, -4, 0.09064), (56*a - 115, -12, 0.8158)]), (3841, [(60*a - 121, -16, 1.446), (-60*a - 121, 32, 5.783)]), (3849, [(-40*a - 93, 12, 0.8124), (40*a - 93, -12, 0.8124)]), (3856, [(36*a - 88, -16, 1.443), (-36*a - 88, -16, 1.443)]), (3889, [(28*a - 79, -8, 0.3592)]), (3921, [(-4*a - 63, -12, 0.8049)]), (3988, [(-6*a - 64, 8, 0.3547)]), (4033, [(8*a - 65, -28, 4.321), (-36*a - 89, -4, 0.08818)]), (4048, [(4*a - 64, -32, 5.633), (-4*a - 64, -16, 1.408)]), (4057, [(12*a - 67, -12, 0.7913)]), (4129, [(20*a - 73, -12, 0.7843)]), (4177, [(4*a - 65, -8, 0.3466)]), (4192, [(-12*a - 68, -24, 3.114), (-44*a - 100, 40, 8.649), (12*a - 68, 0, 0), (44*a - 100, 0, 0)]), (4201, [(-24*a - 77, -4, 0.08640), (24*a - 77, -8, 0.3456)]), (4209, [(28*a - 81, 8, 0.3453), (52*a - 111, 32, 5.524)]), (4225, [(-65, 8, 0.3446)]), (4273, [(-16*a - 71, -12, 0.7710)]), (4276, [(34*a - 88, -8, 0.3426)]), (4281, [(56*a - 117, -4, 0.08559), (-56*a - 117, -12, 0.7703)]), (4297, [(8*a - 67, 20, 2.136)]), (4308, [(-58*a - 120, 16, 1.365)]), (4353, [(-64*a - 129, -4, 0.08488)]), (4372, [(26*a - 80, -32, 5.420), (-26*a - 80, 8, 0.3388)]), (4393, [(-36*a - 91, 8, 0.3380), (-44*a - 101, -8, 0.3380)]), (4441, [(-4*a - 67, -8, 0.3361)]), (4497, [(32*a - 87, 20, 2.088), (-32*a - 87, 28, 4.092)]), (4537, [(-48*a - 107, 4, 0.08314), (48*a - 107, -8, 0.3326)]), (4569, [(-8*a - 69, -4, 0.08285)]), (4576, [(-20*a - 76, 16, 1.325), (20*a - 76, 16, 1.325), (36*a - 92, -16, 1.325), (-36*a - 92, 16, 1.325)]), (4609, [(12*a - 71, -4, 0.08249), (-12*a - 71, -16, 1.320)]), (4624, [(-68*a - 136, -24, 2.965)]), (4657, [(52*a - 113, 12, 0.7385), (-52*a - 113, -8, 0.3282)]), (4713, [(4*a - 69, 4, 0.08157)]), (4729, [(20*a - 77, 4, 0.08143)]), (4825, [(60*a - 125, 0, 0)]), (4849, [(32*a - 89, 12, 0.7238), (-32*a - 89, -8, 0.3217)]), (4852, [(62*a - 128, 16, 1.286)]), (4857, [(-16*a - 75, 36, 6.509), (16*a - 75, 28, 3.937)]), (4873, [(-64*a - 131, -28, 3.931), (64*a - 131, 0, 0)]), (4884, [(-10*a - 72, 32, 5.128), (38*a - 96, 16, 1.282)]), (4948, [(22*a - 80, -8, 0.3184)]), (4969, [(48*a - 109, 28, 3.893), (-48*a - 109, 0, 0)]), (4993, [(-4*a - 71, -8, 0.3170)]), (5001, [(40*a - 99, -12, 0.7127)]), (5008, [(-44*a - 104, 16, 1.266)]), (5041, [(-71, 8, 0.3155)]), (5044, [(-50*a - 112, 16, 1.262), (-30*a - 88, 0, 0)]), (5113, [(52*a - 115, -40, 7.832), (-52*a - 115, -12, 0.7048)]), (5136, [(4*a - 72, 8, 0.3126)]), (5137, [(8*a - 73, 36, 6.329), (-8*a - 73, 24, 2.813)]), (5161, [(-24*a - 83, -16, 1.247), (-16*a - 77, 0, 0)]), (5172, [(2*a - 72, 48, 11.21), (-2*a - 72, -8, 0.3115)]), (5200, [(20*a - 80, 8, 0.3106)]), (5209, [(32*a - 91, 8, 0.3104)]), (5217, [(-28*a - 87, 4, 0.1551), (44*a - 105, -12, 1.396)]), (5281, [(4*a - 73, 16, 1.233), (-4*a - 73, 28, 3.776)]), (5344, [(-12*a - 76, -8, 0.3064), (52*a - 116, 8, 0.3064)]), (5392, [(28*a - 88, 48, 10.98), (-28*a - 88, -32, 4.881)]), (5401, [(-64*a - 133, 32, 4.877), (-40*a - 101, 0, 0)]), (5428, [(66*a - 136, 16, 1.216), (-18*a - 80, 0, 0)]), (5449, [(68*a - 139, 0, 0)]), (5473, [(-16*a - 79, 4, 0.07570), (16*a - 79, -32, 4.845)]), (5497, [(12*a - 77, 24, 2.719), (24*a - 85, 8, 0.3021)]), (5521, [(-36*a - 97, -24, 2.713)]), (5569, [(-28*a - 89, -4, 0.07504)]), (5577, [(-52*a - 117, -16, 1.200)]), (5584, [(-60*a - 128, 0, 0)]), (5641, [(-44*a - 107, 12, 0.6710), (44*a - 107, 0, 0)]), (5716, [(-26*a - 88, -8, 0.2963)]), (5728, [(4*a - 76, 24, 2.664), (-68*a - 140, 16, 1.184)]), (5737, [(8*a - 77, 16, 1.183), (-8*a - 77, -16, 1.183)]), (5748, [(34*a - 96, -8, 0.2955), (-34*a - 96, 0, 0)]), (5812, [(14*a - 80, -16, 1.175)]), (5856, [(20*a - 84, -8, 0.2927), (-44*a - 108, -8, 0.2927), (44*a - 108, 32, 4.683), (-20*a - 84, 0, 0)]), (5857, [(48*a - 113, 4, 0.07317)]), (5937, [(64*a - 135, -12, 0.6541)]), (5953, [(-32*a - 95, 4, 0.07258)]), (5968, [(-12*a - 80, 16, 1.160)]), (6009, [(-68*a - 141, 4, 0.07224)]), (6036, [(70*a - 144, 8, 0.2883)]), (6049, [(-8*a - 79, -8, 0.2880), (52*a - 119, 0, 0)]), (6073, [(44*a - 109, -16, 1.150)]), (6100, [(10*a - 80, -8, 0.2868), (-10*a - 80, 24, 2.581)]), (6121, [(16*a - 83, -4, 0.07158)]), (6193, [(-24*a - 89, -36, 5.764), (24*a - 89, -24, 2.562)]), (6196, [(-46*a - 112, 8, 0.2846)]), (6217, [(56*a - 125, 4, 0.07102)]), (6225, [(-40*a - 105, 8, 0.2839), (40*a - 105, -24, 2.555)]), (6241, [(-79, 8, 0.2835)]), (6292, [(22*a - 88, 48, 10.17)]), (6297, [(-28*a - 93, 36, 5.716)]), (6313, [(-36*a - 101, 20, 1.762), (48*a - 115, 36, 5.709)]), (6337, [(32*a - 97, 4, 0.07035)]), (6352, [(4*a - 80, -16, 1.124), (-4*a - 80, -8, 0.2811)]), (6369, [(8*a - 81, -8, 0.2807), (-8*a - 81, -16, 1.123)]), (6388, [(2*a - 80, 16, 1.121)]), (6457, [(-16*a - 85, 12, 0.6272), (16*a - 85, 24, 2.509)]), (6481, [(-64*a - 137, 20, 1.739), (64*a - 137, 16, 1.113)]), (6484, [(38*a - 104, 8, 0.2782)]), (6513, [(-44*a - 111, -32, 4.441), (44*a - 111, 8, 0.2776)]), (6529, [(52*a - 121, 0, 0)]), (6544, [(20*a - 88, 0, 0)]), (6553, [(-24*a - 91, -48, 9.962)]), (6577, [(68*a - 143, 24, 2.486)]), (6649, [(40*a - 107, -4, 0.06868), (72*a - 149, 20, 1.717)]), (6673, [(-28*a - 95, 0, 0)]), (6676, [(-74*a - 152, -16, 1.097), (74*a - 152, -8, 0.2742)]), (6697, [(8*a - 83, -20, 1.711), (76*a - 155, 4, 0.06843)]), (6721, [(-20*a - 89, -8, 0.5465), (20*a - 89, 8, 0.2732), (36*a - 103, 8, 0.5465), (-36*a - 103, 32, 4.372), (-56*a - 127, -12, 1.230), (80*a - 161, -8, 0.5465)]), (6736, [(44*a - 112, 8, 0.2729)]), (6801, [(16*a - 87, -4, 0.06790)]), (6841, [(-4*a - 83, 0, 0)]), (6864, [(28*a - 96, -16, 1.081), (-28*a - 96, -32, 4.326)]), (6889, [(-83, -8, 0.2699)]), (6900, [(50*a - 120, -32, 4.315)]), (6928, [(36*a - 104, -16, 1.076)]), (6961, [(44*a - 113, -20, 1.678)]), (6964, [(62*a - 136, -24, 2.416), (-62*a - 136, 0, 0)]), (7008, [(4*a - 84, -8, 0.2676), (-76*a - 156, 8, 0.2676)]), (7017, [(52*a - 123, 4, 0.06685), (-52*a - 123, 36, 5.415)]), (7033, [(8*a - 85, 8, 0.2671), (-64*a - 139, 0, 0)]), (7081, [(-20*a - 91, -8, 0.2662), (-40*a - 109, 16, 1.065)]), (7153, [(-68*a - 145, 8, 0.2649), (68*a - 145, -16, 1.059)]), (7156, [(-14*a - 88, -24, 2.383), (14*a - 88, 8, 0.2648)]), (7177, [(4*a - 85, 0, 0)]), (7188, [(-26*a - 96, 40, 6.605)]), (7233, [(56*a - 129, 44, 7.967), (-56*a - 129, 4, 0.06585)]), (7249, [(-48*a - 119, 0, 0), (-72*a - 151, 0, 0)]), (7264, [(-20*a - 92, 16, 1.051), (52*a - 124, 8, 0.2628)]), (7297, [(-24*a - 95, -4, 0.06556), (24*a - 95, -8, 0.2622)]), (7348, [(34*a - 104, 24, 2.352), (-34*a - 104, 16, 1.045)]), (7369, [(80*a - 163, 12, 0.5871), (-80*a - 163, 20, 1.631)]), (7377, [(-8*a - 87, 4, 0.06520)]), (7393, [(84*a - 169, 40, 6.513), (-84*a - 169, -4, 0.06513)]), (7417, [(-44*a - 115, -16, 1.040)]), (7449, [(-20*a - 93, -8, 0.2595), (-28*a - 99, 8, 0.2595)]), (7513, [(-16*a - 91, -16, 1.034), (52*a - 125, -16, 1.034)]), (7521, [(-40*a - 111, 0, 0), (40*a - 111, 0, 0)]), (7537, [(32*a - 103, -8, 0.2580), (-32*a - 103, 8, 0.2580)]), (7561, [(36*a - 107, 8, 0.2576)]), (7593, [(-64*a - 141, 4, 0.06427)]), (7636, [(6*a - 88, 16, 1.025), (-54*a - 128, 0, 0)]), (7681, [(-24*a - 97, -24, 2.300)]), (7696, [(-4*a - 88, -48, 9.192), (60*a - 136, -8, 0.2553)]), (7732, [(2*a - 88, -16, 1.019), (-2*a - 88, 16, 1.019)]), (7737, [(68*a - 147, 12, 0.5730)]), (7753, [(-56*a - 131, -8, 0.2544)]), (7825, [(-20*a - 95, -8, 0.2532)]), (7849, [(28*a - 101, -16, 2.023), (-28*a - 101, -16, 1.011), (-12*a - 91, 0, 0)]), (7881, [(-44*a - 117, 16, 1.009), (44*a - 117, -48, 9.084), (-16*a - 93, 0, 0), (16*a - 93, 0, 0)]), (7921, [(-89, -4, 0.06292)]), (7953, [(32*a - 105, 0, 0), (-76*a - 159, 0, 0)]), (7969, [(40*a - 113, -8, 0.2509), (60*a - 137, 8, 0.2509)]), (7993, [(36*a - 109, 44, 7.579), (-36*a - 109, -52, 10.59)]), (8016, [(-20*a - 96, 24, 2.252)]), (8025, [(80*a - 165, 8, 0.2500)]), (8032, [(-12*a - 92, -32, 3.999), (-68*a - 148, -40, 6.248), (68*a - 148, 24, 2.249), (12*a - 92, 0, 0)]), (8052, [(-82*a - 168, -16, 0.9985), (-46*a - 120, 0, 0)]), (8089, [(8*a - 91, -40, 6.226)]), (8097, [(88*a - 177, 4, 0.06223)]), (8161, [(-64*a - 143, 4, 0.06199)]), (8209, [(-20*a - 97, 0, 0)]), (8212, [(-38*a - 112, -8, 0.2472), (38*a - 112, 24, 2.225)]), (8257, [(28*a - 103, -24, 2.219), (-28*a - 103, -32, 3.944)]), (8272, [(52*a - 128, 24, 2.217), (-52*a - 128, -24, 4.433), (76*a - 160, -24, 4.433)]), (8329, [(-68*a - 149, 32, 3.927)]), (8353, [(-44*a - 119, 24, 2.206), (44*a - 119, 24, 2.206)]), (8377, [(-32*a - 107, -12, 0.5507)]), (8404, [(58*a - 136, 16, 0.9774), (70*a - 152, -8, 0.2443)]), (8457, [(-8*a - 93, 4, 0.06089)]), (8473, [(24*a - 101, -12, 0.5475), (-72*a - 155, 12, 0.5475)]), (8529, [(-52*a - 129, -4, 0.06064)]), (8592, [(-44*a - 120, 8, 0.2417)]), (8593, [(-12*a - 95, 28, 2.960), (76*a - 161, 4, 0.06041)]), (8601, [(-4*a - 93, -4, 0.1208), (20*a - 99, -4, 0.1208)]), (8641, [(-16*a - 97, 48, 8.675)]), (8656, [(36*a - 112, 8, 0.2408), (-36*a - 112, 24, 2.167)]), (8673, [(28*a - 105, -8, 0.2405), (-28*a - 105, -40, 6.013)]), (8689, [(80*a - 167, -4, 0.06008)]), (8761, [(-84*a - 173, -12, 0.5385)]), (8800, [(20*a - 100, -56, 11.70), (-60*a - 140, 8, 0.2388)]), (8809, [(88*a - 179, -16, 0.9546), (32*a - 109, 0, 0)]), (8817, [(56*a - 135, -28, 2.922), (-56*a - 135, -28, 2.922)]), (8833, [(44*a - 121, -16, 0.9534)]), (8881, [(24*a - 103, 8, 0.2377), (-36*a - 113, 0, 0)]), (8916, [(-10*a - 96, -8, 0.2372)]), (8929, [(-68*a - 151, 12, 0.5334)]), (8977, [(4*a - 95, -8, 0.4728), (12*a - 97, -32, 7.565), (-12*a - 97, -16, 0.9457), (-4*a - 95, 0, 0)]), (9001, [(-20*a - 101, -20, 1.476), (20*a - 101, -4, 0.05903)]), (9025, [(-95, -8, 0.2358)]), (9033, [(-16*a - 99, -44, 7.130), (16*a - 99, 28, 2.887)]), (9049, [(-52*a - 131, -16, 0.9419), (52*a - 131, 0, 0)]), (9076, [(-34*a - 112, -24, 2.116)]), (9097, [(28*a - 107, 12, 0.5284), (-72*a - 157, -12, 0.5284)]), (9168, [(4*a - 96, -24, 2.105), (-4*a - 96, 32, 3.743)]), (9172, [(-74*a - 160, -48, 8.420), (74*a - 160, 32, 3.742)]), (9204, [(2*a - 96, 16, 0.9339), (-62*a - 144, 32, 3.736)]), (9217, [(8*a - 97, -12, 0.5250), (48*a - 127, -20, 1.458)]), (9232, [(-68*a - 152, 0, 0)]), (9241, [(76*a - 163, -12, 0.5243)]), (9249, [(32*a - 111, -12, 0.5241), (-32*a - 111, 12, 0.5241)]), (9312, [(-28*a - 108, 16, 0.9285), (52*a - 132, 16, 0.9285), (-52*a - 132, -48, 8.357), (28*a - 108, 0, 0)]), (9321, [(64*a - 147, -24, 2.088), (44*a - 123, 0, 0)]), (9337, [(36*a - 115, 16, 0.9273)]), (9361, [(4*a - 97, -24, 2.084), (-4*a - 97, 8, 0.2315), (80*a - 169, 48, 8.335), (-80*a - 169, -40, 5.788)]), (9364, [(22*a - 104, -8, 0.2315)]), (9409, [(-97, 48, 8.313)]), (9433, [(16*a - 101, 4, 0.05766)]), (9457, [(-84*a - 175, -56, 11.29)]), (9529, [(28*a - 109, 8, 0.2295), (88*a - 181, -16, 0.9179)]), (9537, [(68*a - 153, 8, 0.2294)]), (9556, [(-90*a - 184, 24, 2.062)]), (9568, [(12*a - 100, 64, 14.66), (-12*a - 100, -16, 0.9160), (76*a - 164, -32, 3.664), (-76*a - 164, -16, 0.9160)]), (9601, [(96*a - 193, -16, 0.9144)]), (9609, [(8*a - 99, -4, 0.05713), (-8*a - 99, 4, 0.05713)]), (9649, [(60*a - 143, 12, 0.5131), (-60*a - 143, -16, 0.9121)]), (9697, [(-32*a - 113, -24, 2.047)]), (9721, [(24*a - 107, -4, 0.05680)]), (9748, [(-54*a - 136, -8, 0.2269)]), (9753, [(4*a - 99, 36, 4.593), (-4*a - 99, -36, 4.593)]), (9769, [(12*a - 101, -8, 0.2266)]), (9808, [(84*a - 176, -24, 2.036), (-84*a - 176, 0, 0)]), (9817, [(-44*a - 125, 8, 0.2261)]), (9825, [(-20*a - 105, -16, 0.9039), (20*a - 105, 0, 0)]), (9841, [(-40*a - 121, 32, 3.613), (40*a - 121, -44, 6.831)]), (9844, [(30*a - 112, -48, 8.128), (-30*a - 112, 0, 0)]), (9913, [(-56*a - 139, 24, 2.025), (-64*a - 149, 0, 0)]), (9952, [(-4*a - 100, 24, 2.021), (92*a - 188, -8, 0.2245)]), (9969, [(-28*a - 111, 20, 1.402)])]] # map: (a |-> -1.73) -> -1, (a |-> 1.73) -> 1, Fractional ideal (4*a - 1) -> 1 [-4*a + 5, 1/2*a - 5 + (-517/2*a + 55/2)*i + (17/2*a - 1/2)*j + (-2*a - 1/2)*k, [(-12, [(2*a, 4, 2.747)]), (-23, [(4*a + 5, 4, 1.984)]), (-39, [(4*a + 3, 0, 0)]), (-44, [(10*a + 16, -4, 1.435)]), (-47, [(4*a + 1, 4, 1.388)]), (-48, [(4*a, 4, 1.374)]), (-143, [(8*a + 7, -4, 0.7958), (28*a + 47, -8, 3.183)]), (-167, [(8*a + 5, -8, 2.945)]), (-176, [(20*a + 32, -4, 0.7173)]), (-191, [(8*a - 1, -12, 6.197), (8*a + 1, 4, 0.6885)]), (-236, [(10*a + 8, 4, 0.6194), (38*a + 64, 4, 0.6194)]), (-239, [(16*a + 23, 8, 2.462), (20*a + 31, 0, 0)]), (-263, [(12*a + 13, -4, 0.5868), (32*a + 53, 8, 2.347)]), (-311, [(12*a + 11, 4, 0.5396)]), (-327, [(16*a + 21, 8, 2.105)]), (-359, [(20*a + 29, 4, 0.5022)]), (-368, [(12*a - 8, -8, 1.984)]), (-407, [(12*a + 5, 4, 0.4717), (36*a + 59, 12, 4.245)]), (-416, [(12*a + 4, 4, 0.4666), (28*a + 44, 4, 0.4666)]), (-428, [(22*a + 32, -4, 0.4600)]), (-431, [(12*a - 1, 4, 0.4584), (12*a + 1, 8, 1.833)]), (-471, [(20*a + 27, 8, 1.754), (32*a + 51, 8, 1.754)]), (-479, [(16*a + 17, 12, 3.913), (44*a + 73, 4, 0.4348)]), (-503, [(28*a + 43, 0, 0)]), (-543, [(52*a + 87, -8, 1.633)]), (-575, [(40*a + 65, 0, 0)]), (-588, [(14*a, -8, 1.570)]), (-599, [(16*a + 13, -4, 0.3888)]), (-624, [(44*a + 72, 8, 1.524)]), (-671, [(20*a + 23, -4, 0.3674), (28*a + 41, 4, 0.3674)]), (-687, [(16*a - 9, 16, 5.809)]), (-716, [(62*a + 104, 12, 3.201)]), (-743, [(16*a + 5, 8, 1.396)]), (-752, [(36*a + 56, -8, 1.388)]), (-759, [(16*a - 3, -8, 1.382), (16*a + 3, 0, 0)]), (-767, [(16*a - 1, 16, 5.498), (24*a + 31, -8, 1.374)]), (-800, [(20*a + 20, -24, 12.11), (60*a + 100, 0, 0)]), (-839, [(20*a + 19, 4, 0.3285)]), (-863, [(32*a + 47, 8, 1.296), (36*a + 55, -8, 1.296)]), (-876, [(22*a + 24, 0, 0)]), (-887, [(52*a + 85, 4, 0.3195)]), (-908, [(18*a + 8, -4, 0.3158)]), (-944, [(20*a + 16, -4, 0.3097), (76*a + 128, -12, 2.787)]), (-975, [(80*a + 135, 0, 0)]), (-983, [(48*a + 77, -24, 10.93)]), (-1031, [(20*a + 13, 0, 0)]), (-1047, [(32*a + 45, 0, 0)]), (-1056, [(20*a + 12, -8, 1.171), (52*a + 84, 16, 4.685)]), (-1079, [(20*a + 11, -4, 0.2897), (40*a + 61, 12, 2.607)]), (-1100, [(30*a + 40, -8, 1.148)]), (-1103, [(68*a + 113, -16, 4.584)]), (-1119, [(20*a + 9, 8, 1.138)]), (-1127, [(28*a + 35, 0, 0)]), (-1151, [(20*a + 7, 4, 0.2805)]), (-1184, [(20*a - 4, 20, 6.914), (20*a + 4, 4, 0.2766), (36*a + 52, -4, 0.2766), (44*a + 68, -4, 0.2766)]), (-1191, [(20*a - 3, 8, 1.103), (20*a + 3, -8, 1.103)]), (-1196, [(38*a + 56, 16, 4.403), (42*a + 64, -8, 1.101)]), (-1199, [(20*a + 1, -4, 0.2748), (20*a - 1, 0, 0)]), (-1223, [(32*a + 43, 12, 2.449), (52*a + 83, -16, 4.354)]), (-1263, [(64*a + 105, -8, 1.071)]), (-1367, [(24*a + 19, 4, 0.2574), (92*a + 155, -28, 12.61)]), (-1388, [(22*a - 8, -12, 2.299), (22*a + 8, -20, 6.385)]), (-1391, [(32*a + 41, 4, 0.2551), (60*a + 97, 8, 1.021)]), (-1439, [(100*a + 169, 0, 0)]), (-1487, [(56*a + 89, 4, 0.2468)]), (-1511, [(28*a + 29, 16, 3.917), (80*a + 133, 8, 0.9792)]), (-1551, [(68*a + 111, 8, 0.9665)]), (-1607, [(24*a - 11, 8, 0.9495), (24*a + 11, -8, 0.9495)]), (-1623, [(28*a + 27, -16, 3.779), (88*a + 147, 8, 0.9448)]), (-1676, [(30*a + 32, 12, 2.092)]), (-1679, [(64*a + 103, -8, 0.9289), (36*a + 47, 0, 0)]), (-1703, [(24*a - 5, -4, 0.2306), (76*a + 125, -4, 0.2306)]), (-1712, [(44*a + 64, -12, 2.070)]), (-1727, [(28*a + 25, -8, 0.9159), (24*a + 1, 0, 0)]), (-1772, [(26*a - 16, -12, 2.034)]), (-1775, [(60*a + 95, 16, 3.614), (40*a + 55, 0, 0)]), (-1839, [(44*a + 63, 8, 0.8876), (56*a + 87, 16, 3.550)]), (-1868, [(34*a + 40, 12, 1.982)]), (-1871, [(48*a + 71, 12, 1.980)]), (-1911, [(28*a + 21, 0, 0)]), (-1952, [(28*a + 20, -12, 1.938), (36*a + 44, 12, 1.938), (76*a + 124, -12, 1.938), (116*a + 196, 12, 1.938)]), (-1991, [(40*a + 53, 16, 3.412), (68*a + 109, 4, 0.2133)]), (-2063, [(28*a - 17, 4, 0.2095), (28*a + 17, 12, 1.886)]), (-2087, [(44*a + 61, 4, 0.2083)]), (-2111, [(100*a + 167, -8, 0.8285)]), (-2156, [(70*a + 112, 0, 0)]), (-2199, [(40*a + 51, -8, 0.8117), (76*a + 123, -16, 3.247)]), (-2207, [(36*a + 41, -4, 0.2026)]), (-2208, [(44*a + 60, 0, 0), (28*a - 12, 0, 0)]), (-2231, [(28*a + 11, -8, 0.8059), (32*a + 29, 24, 7.253)]), (-2252, [(66*a + 104, 12, 1.805)]), (-2271, [(28*a + 9, 8, 0.7987)]), (-2288, [(36*a + 40, -8, 0.7958), (92*a + 152, -32, 12.73)]), (-2303, [(28*a + 7, 8, 0.7932)]), (-2316, [(50*a + 72, 8, 0.7909)]), (-2327, [(28*a - 5, 16, 3.156), (28*a + 5, -20, 4.932)]), (-2336, [(28*a - 4, -8, 0.7875), (52*a + 76, 0, 0)]), (-2343, [(28*a - 3, 8, 0.7864), (116*a + 195, -8, 0.7864)]), (-2348, [(58*a + 88, -4, 0.1964)]), (-2351, [(28*a - 1, -16, 3.140), (28*a + 1, -4, 0.1963)]), (-2352, [(28*a, -24, 7.064)]), (-2399, [(40*a + 49, 12, 1.749), (84*a + 137, 0, 0)]), (-2423, [(48*a + 67, -8, 0.7733)]), (-2444, [(34*a + 32, 24, 6.929)]), (-2487, [(64*a + 99, 0, 0)]), (-2519, [(56*a + 83, -16, 3.034), (60*a + 91, 20, 4.740)]), (-2543, [(132*a + 223, -8, 0.7548)]), (-2559, [(44*a + 57, -24, 6.772), (80*a + 129, 8, 0.7524)]), (-2631, [(32*a - 21, -16, 2.968)]), (-2663, [(112*a + 187, -8, 0.7376)]), (-2672, [(84*a + 136, -8, 0.7364)]), (-2711, [(32*a - 19, 4, 0.1828), (32*a + 19, 0, 0)]), (-2775, [(40*a + 45, 0, 0), (100*a + 165, 0, 0)]), (-2783, [(88*a + 143, -16, 2.886)]), (-2847, [(68*a + 105, 24, 6.420), (56*a + 81, 0, 0)]), (-2864, [(124*a + 208, 4, 0.1778)]), (-2892, [(34*a + 24, -16, 2.831), (142*a + 240, 24, 6.370)]), (-2903, [(32*a - 13, -8, 0.7065), (32*a + 13, -4, 0.1766)]), (-2927, [(128*a + 215, -8, 0.7036)]), (-2951, [(40*a + 43, -8, 0.7007), (108*a + 179, 28, 8.583)]), (-2991, [(32*a + 9, 0, 0)]), (-2999, [(44*a + 53, 0, 0)]), (-3023, [(32*a - 7, -24, 6.231)]), (-3047, [(32*a - 5, 4, 0.1724), (136*a + 229, 4, 0.1724)]), (-3056, [(60*a + 88, -8, 0.6885), (68*a + 104, 16, 2.754)]), (-3071, [(32*a - 1, -12, 1.545), (32*a + 1, -4, 0.1717), (52*a + 71, 12, 1.545), (80*a + 127, 20, 4.293)]), (-3104, [(44*a + 52, 8, 0.6832), (140*a + 236, -8, 0.6832), (36*a + 28, 0, 0), (100*a + 164, 0, 0)]), (-3119, [(40*a + 41, -24, 6.134), (116*a + 193, 12, 1.533)]), (-3207, [(104*a + 171, 0, 0)]), (-3212, [(34*a - 16, -24, 6.045), (34*a + 16, -8, 0.6716)]), (-3263, [(36*a + 25, -12, 1.499), (64*a + 95, 12, 1.499)]), (-3279, [(40*a + 39, 8, 0.6647), (124*a + 207, -8, 0.6647)]), (-3308, [(38*a + 32, 20, 4.136), (138*a + 232, -4, 0.1655)]), (-3359, [(36*a + 23, 8, 0.6568)]), (-3404, [(34*a - 8, -8, 0.6524), (50*a + 64, 0, 0)]), (-3407, [(112*a + 185, 8, 0.6521)]), (-3431, [(48*a + 59, 8, 0.6498)]), (-3468, [(34*a, 0, 0)]), (-3488, [(36*a - 20, -12, 1.450), (52*a + 68, 4, 0.1611)]), (-3504, [(44*a + 48, 16, 2.572)]), (-3527, [(36*a - 19, 8, 0.6409), (36*a + 19, -8, 0.6409)]), (-3575, [(60*a + 85, 8, 0.6366), (80*a + 125, 8, 0.6366)]), (-3632, [(36*a + 16, 12, 1.421)]), (-3639, [(76*a + 117, 8, 0.6310)]), (-3671, [(68*a + 101, -8, 0.6282)]), (-3692, [(58*a + 80, 8, 0.6264), (42*a + 40, 0, 0)]), (-3711, [(148*a + 249, -8, 0.6248)]), (-3756, [(38*a - 24, 0, 0)]), (-3783, [(56*a + 75, -16, 2.475), (44*a + 45, 0, 0)]), (-3824, [(36*a - 8, -16, 2.462), (36*a + 8, 32, 9.849)]), (-3839, [(36*a - 7, -20, 3.840), (36*a + 7, 0, 0)]), (-3863, [(36*a - 5, 24, 5.512), (36*a + 5, 0, 0)]), (-3872, [(44*a + 44, -24, 5.505), (132*a + 220, -16, 2.447)]), (-3884, [(70*a + 104, 4, 0.1527)]), (-3887, [(104*a + 169, 8, 0.6105)]), (-3911, [(60*a + 83, -20, 3.804)]), (-3959, [(44*a + 43, 4, 0.1512), (164*a + 277, -12, 1.361)]), (-4044, [(46*a + 48, 8, 0.5986), (130*a + 216, 32, 9.577)]), (-4071, [(40*a + 27, 8, 0.5966), (80*a + 123, -8, 0.5966)]), (-4076, [(38*a - 16, 20, 3.726), (38*a + 16, -20, 3.726)]), (-4103, [(48*a + 53, -28, 7.279), (124*a + 205, -8, 0.5942)]), (-4127, [(144*a + 241, -4, 0.1481)]), (-4175, [(40*a - 25, 16, 2.356)]), (-4208, [(44*a + 40, -8, 0.5868), (148*a + 248, -8, 0.5868)]), (-4268, [(38*a - 8, -8, 0.5826), (166*a + 280, -8, 0.5826)]), (-4271, [(40*a - 23, 4, 0.1456)]), (-4287, [(44*a + 39, -16, 2.325)]), (-4359, [(40*a - 21, 0, 0)]), (-4364, [(126*a + 208, 4, 0.1440)]), (-4367, [(92*a + 145, -16, 2.304), (108*a + 175, 8, 0.5760)]), (-4391, [(52*a + 61, 4, 0.1436)]), (-4400, [(60*a + 80, -24, 5.164)]), (-4439, [(44*a + 37, 8, 0.5713), (160*a + 269, 8, 0.5713)]), (-4463, [(88*a + 137, 20, 3.561)]), (-4511, [(40*a + 17, -8, 0.5667), (48*a + 49, 8, 0.5667)]), (-4575, [(40*a - 15, 16, 2.251), (40*a + 15, 32, 9.004)]), (-4631, [(52*a + 59, -8, 0.5593), (128*a + 211, 12, 1.258)]), (-4647, [(56*a + 69, -8, 0.5584)]), (-4652, [(54*a + 64, 4, 0.1395)]), (-4679, [(40*a + 11, 0, 0)]), (-4703, [(48*a + 47, -32, 8.881), (148*a + 247, 4, 0.1388)]), (-4719, [(176*a + 297, -8, 0.5541)]), (-4748, [(46*a + 40, -12, 1.243), (162*a + 272, -12, 1.243)]), (-4751, [(40*a + 7, 12, 1.243), (40*a - 7, 0, 0)]), (-4784, [(76*a + 112, 16, 2.201), (84*a + 128, -8, 0.5503)]), (-4791, [(40*a - 3, 24, 4.949)]), (-4799, [(40*a - 1, 8, 0.5495)]), (-4847, [(44*a + 31, 4, 0.1367), (68*a + 95, -28, 6.697), (96*a + 151, -4, 0.1367), (184*a + 311, 12, 1.230)]), (-4863, [(136*a + 225, -16, 2.183)]), (-4871, [(112*a + 181, -8, 0.5454)]), (-4908, [(58*a + 72, -8, 0.5433)]), (-4919, [(56*a + 67, -8, 0.5427)]), (-4943, [(72*a + 103, -4, 0.1353), (92*a + 143, -12, 1.218)]), (-4976, [(140*a + 232, 0, 0)]), (-5007, [(76*a + 111, -24, 4.841), (88*a + 135, -16, 2.152)]), (-5036, [(42*a - 16, -12, 1.207), (42*a + 16, -4, 0.1341)]), (-5039, [(84*a + 127, -4, 0.1341)]), (-5063, [(48*a + 43, 20, 3.343), (64*a + 85, -12, 1.204), (108*a + 173, -12, 1.204), (164*a + 275, 12, 1.204)]), (-5087, [(52*a + 55, -4, 0.1334)]), (-5132, [(62*a + 80, 4, 0.1328), (114*a + 184, 4, 0.1328)]), (-5183, [(44*a + 25, 16, 2.115), (56*a + 65, -8, 0.5287)]), (-5196, [(50*a + 48, 0, 0)]), (-5223, [(68*a + 93, -16, 2.107), (104*a + 165, -16, 2.107)]), (-5228, [(42*a + 8, -12, 1.184)]), (-5231, [(48*a + 41, -4, 0.1316), (172*a + 289, -8, 0.5263)]), (-5232, [(44*a - 24, -8, 0.5262)]), (-5279, [(44*a + 23, -8, 0.5239)]), (-5303, [(152*a + 253, 8, 0.5227)]), (-5351, [(72*a + 101, -16, 2.081)]), (-5367, [(44*a - 21, 16, 2.078), (44*a + 21, 16, 2.078)]), (-5399, [(116*a + 187, -4, 0.1295)]), (-5408, [(52*a + 52, 16, 2.070), (156*a + 260, 8, 0.5176)]), (-5447, [(76*a + 109, 8, 0.5157), (96*a + 149, -20, 3.223)]), (-5471, [(128*a + 209, 12, 1.158)]), (-5511, [(52*a + 51, 8, 0.5127), (160*a + 267, 0, 0)]), (-5519, [(44*a + 17, -4, 0.1281)]), (-5543, [(48*a + 37, -8, 0.5113), (88*a + 133, -8, 0.5113)]), (-5552, [(44*a - 16, -20, 3.193), (44*a + 16, 4, 0.1277)]), (-5591, [(68*a + 91, 0, 0)]), (-5612, [(102*a + 160, -8, 0.5081), (154*a + 256, 0, 0)]), (-5639, [(44*a + 13, -16, 2.028)]), (-5708, [(78*a + 112, 12, 1.134), (98*a + 152, -12, 1.134)]), (-5727, [(44*a - 9, -16, 2.012), (64*a + 81, 16, 2.012)]), (-5744, [(44*a - 8, -8, 0.5022)]), (-5759, [(44*a - 7, -4, 0.1254), (44*a + 7, 0, 0)]), (-5772, [(46*a + 24, -8, 0.5010), (94*a + 144, 8, 0.5010)]), (-5783, [(44*a - 5, -8, 0.5005), (44*a + 5, -4, 0.1251)]), (-5792, [(44*a - 4, 36, 10.13), (84*a + 124, -4, 0.1250)]), (-5799, [(44*a - 3, -8, 0.4998), (44*a + 3, 0, 0)]), (-5804, [(86*a + 128, 20, 3.123)]), (-5807, [(44*a + 1, 24, 4.495)]), (-5879, [(76*a + 107, -20, 3.103), (104*a + 163, 0, 0)]), (-5927, [(156*a + 259, -12, 1.112)]), (-5951, [(48*a - 31, 16, 1.974), (68*a + 89, 0, 0)]), (-5996, [(58*a + 64, 12, 1.106), (150*a + 248, 20, 3.072)]), (-6047, [(64*a + 79, 12, 1.101)]), (-6071, [(88*a + 131, 16, 1.954), (92*a + 139, -12, 1.099)]), (-6092, [(46*a + 16, -4, 0.1219)]), (-6143, [(72*a + 97, -4, 0.1214)]), (-6159, [(164*a + 273, 32, 7.760), (56*a + 57, 0, 0)]), (-6176, [(60*a + 68, 16, 1.937), (188*a + 316, 16, 1.937)]), (-6263, [(52*a + 43, -8, 0.4810), (192*a + 323, -16, 1.924)]), (-6284, [(46*a - 8, -4, 0.1200)]), (-6287, [(48*a - 25, 16, 1.920), (48*a + 25, -12, 1.080)]), (-6303, [(112*a + 177, 8, 0.4794), (128*a + 207, 8, 0.4794)]), (-6311, [(152*a + 251, 16, 1.917)]), (-6383, [(48*a - 23, -12, 1.072), (172*a + 287, 20, 2.978)]), (-6431, [(52*a + 41, 16, 1.899), (108*a + 169, 8, 0.4746)]), (-6476, [(50*a - 32, -20, 2.956), (50*a + 32, 28, 5.794)]), (-6512, [(116*a + 184, 8, 0.4717), (52*a + 40, 0, 0)]), (-6527, [(84*a + 121, 12, 1.060), (124*a + 199, 12, 1.060)]), (-6599, [(180*a + 301, -8, 0.4686)]), (-6623, [(48*a - 17, 12, 1.052), (96*a + 145, -4, 0.1169)]), (-6647, [(68*a + 85, 8, 0.4669)]), (-6668, [(142*a + 232, -28, 5.710)]), (-6704, [(60*a + 64, 12, 1.046)]), (-6719, [(76*a + 103, 4, 0.1161)]), (-6743, [(52*a + 37, 0, 0), (48*a + 13, 0, 0)]), (-6791, [(48*a - 11, -4, 0.1155)]), (-6807, [(56*a + 51, 0, 0)]), (-6816, [(52*a + 36, -8, 0.4610), (68*a + 84, 8, 0.4610), (140*a + 228, 8, 0.4610), (220*a + 372, -24, 4.149)]), (-6879, [(80*a + 111, 8, 0.4589), (116*a + 183, 0, 0)]), (-6887, [(48*a - 5, 8, 0.4587), (48*a + 5, -40, 11.47), (52*a + 35, -8, 0.4587), (224*a + 379, -8, 0.4587)]), (-6896, [(100*a + 152, -16, 1.833), (92*a + 136, 0, 0)]), (-6924, [(50*a - 24, 0, 0)]), (-6959, [(64*a + 73, 4, 0.1141), (156*a + 257, 20, 2.852)]), (-6983, [(68*a + 83, -12, 1.025), (144*a + 235, 0, 0)]), (-7007, [(56*a + 49, -8, 0.4547), (196*a + 329, -16, 1.819)]), (-7023, [(52*a - 33, 0, 0)]), (-7079, [(176*a + 293, -24, 4.072)]), (-7088, [(52*a - 32, -20, 2.826)]), (-7103, [(88*a + 127, -8, 0.4516), (108*a + 167, -16, 1.807)]), (-7127, [(128*a + 205, 4, 0.1127)]), (-7167, [(92*a + 135, 0, 0)]), (-7199, [(56*a + 47, 16, 1.794), (204*a + 343, -16, 1.794)]), (-7271, [(52*a + 29, 4, 0.1116), (140*a + 227, 12, 1.004)]), (-7311, [(68*a + 81, 0, 0)]), (-7319, [(60*a + 59, -4, 0.1112), (184*a + 307, 0, 0)]), (-7328, [(52*a - 28, -20, 2.779), (76*a + 100, 20, 2.779)]), (-7383, [(212*a + 357, -8, 0.4430), (56*a + 45, 0, 0)]), (-7436, [(78*a + 104, 16, 1.766)]), (-7472, [(68*a + 80, -4, 0.1101)]), (-7527, [(76*a + 99, -16, 1.755), (136*a + 219, 16, 1.755)]), (-7536, [(52*a - 24, 8, 0.4385), (52*a + 24, 24, 3.946)]), (-7559, [(220*a + 371, -4, 0.1095)]), (-7583, [(52*a + 23, -8, 0.4371), (52*a - 23, 0, 0)]), (-7607, [(88*a + 125, -8, 0.4364)]), (-7631, [(68*a + 79, -4, 0.1089), (160*a + 263, 0, 0)]), (-7664, [(60*a + 56, -24, 3.913), (196*a + 328, 0, 0)]), (-7671, [(52*a + 21, 0, 0)]), (-7727, [(56*a + 41, -12, 0.9743)]), (-7751, [(52*a + 19, -16, 1.729), (132*a + 211, 0, 0)]), (-7775, [(200*a + 335, -8, 0.4317)]), (-7788, [(86*a + 120, 8, 0.4313), (214*a + 360, -8, 0.4313)]), (-7799, [(64*a + 67, 4, 0.1078), (104*a + 157, 20, 2.694)]), (-7887, [(52*a + 15, 16, 1.714), (56*a + 39, 0, 0)]), (-7916, [(118*a + 184, -12, 0.9626)]), (-7919, [(144*a + 233, 8, 0.4277)]), (-7968, [(52*a + 12, -8, 0.4264), (92*a + 132, 40, 10.66), (116*a + 180, 0, 0), (52*a - 12, 0, 0)]), (-7991, [(52*a - 11, 12, 0.9581), (52*a + 11, -20, 2.661), (60*a + 53, 4, 0.1065), (208*a + 349, -20, 2.661)]), (-8012, [(94*a + 136, -12, 0.9568)]), (-8031, [(52*a - 9, -8, 0.4247)]), (-8039, [(56*a + 37, 20, 2.653), (56*a - 37, 0, 0)]), (-8048, [(52*a + 8, -24, 3.819)]), (-8063, [(52*a - 7, 8, 0.4239), (64*a + 65, 8, 0.4239)]), (-8076, [(98*a + 144, 8, 0.4236)]), (-8087, [(52*a - 5, -32, 6.772), (52*a + 5, 28, 5.185)]), (-8096, [(52*a - 4, 8, 0.4230), (52*a + 4, -16, 1.692), (100*a + 148, 8, 0.4230), (108*a + 164, -32, 6.768)]), (-8103, [(52*a + 3, 8, 0.4229), (88*a + 123, 8, 0.4229)]), (-8111, [(52*a - 1, -12, 0.9509), (52*a + 1, 8, 0.4226)]), (-8175, [(140*a + 225, 0, 0)]), (-8183, [(56*a + 35, -32, 6.732)]), (-8247, [(176*a + 291, 0, 0)]), (-8300, [(70*a + 80, 32, 6.685), (170*a + 280, 0, 0)]), (-8303, [(152*a + 247, 8, 0.4177)]), (-8319, [(56*a - 33, 8, 0.4173), (64*a + 63, -24, 3.756)]), (-8327, [(72*a + 85, -28, 5.110), (164*a + 269, 8, 0.4171)]), (-8396, [(62*a + 56, -4, 0.1039)]), (-8399, [(60*a + 49, 4, 0.1038), (136*a + 217, -12, 0.9345)]), (-8423, [(108*a + 163, 8, 0.4147)]), (-8492, [(54*a - 16, -32, 6.609), (54*a + 16, -16, 1.652)]), (-8567, [(56*a - 29, -4, 0.1028), (204*a + 341, 4, 0.1028)]), (-8591, [(88*a + 121, 8, 0.4107), (132*a + 209, 32, 6.571)]), (-8624, [(140*a + 224, 0, 0)]), (-8663, [(72*a + 83, 8, 0.4090)]), (-8679, [(56*a - 27, 8, 0.4086), (76*a + 93, 0, 0)]), (-8684, [(166*a + 272, 24, 3.676), (74*a + 88, 0, 0)]), (-8688, [(68*a + 72, -24, 3.675)]), (-8783, [(56*a - 25, 12, 0.9138)]), (-8807, [(64*a + 59, 28, 4.969), (212*a + 355, 16, 1.622)]), (-8864, [(60*a + 44, 4, 0.1011), (76*a + 92, -12, 0.9096), (164*a + 268, 12, 0.9096), (244*a + 412, -4, 0.1011)]), (-8879, [(56*a + 23, -4, 0.1010), (124*a + 193, -4, 0.1010)]), (-8975, [(120*a + 185, 8, 0.4018)]), (-8999, [(80*a + 101, -32, 6.420)]), (-9008, [(132*a + 208, 4, 0.1003)]), (-9039, [(116*a + 177, 16, 1.601), (220*a + 369, -16, 1.601)]), (-9047, [(56*a - 19, 28, 4.902), (76*a + 91, 4, 0.1000)]), (-9068, [(58*a - 32, 4, 0.09993)]), (-9071, [(112*a + 169, 8, 0.3997)]), (-9111, [(200*a + 333, -8, 0.3988)]), (-9119, [(60*a + 41, -8, 0.3986), (256*a + 433, 20, 2.491)]), (-9200, [(60*a + 40, 0, 0)]), (-9239, [(56*a - 13, 12, 0.8910), (56*a + 13, 16, 1.584)]), (-9263, [(64*a + 55, 16, 1.582), (92*a + 127, -8, 0.3955), (136*a + 215, -24, 3.559), (228*a + 383, 16, 1.582)]), (-9264, [(100*a + 144, 8, 0.3955)]), (-9287, [(56*a - 11, -12, 0.8887), (56*a + 11, 12, 0.8887), (84*a + 109, -12, 0.8887), (152*a + 245, 28, 4.839)]), (-9311, [(72*a + 79, 0, 0)]), (-9356, [(82*a + 104, -4, 0.09838), (158*a + 256, 4, 0.09838)]), (-9359, [(56*a - 7, -16, 1.574), (56*a + 7, 0, 0)]), (-9383, [(56*a - 5, -16, 1.572), (68*a + 67, 0, 0)]), (-9392, [(116*a + 176, -44, 11.88)]), (-9399, [(80*a + 99, 0, 0), (56*a + 3, 0, 0)]), (-9407, [(76*a + 89, -48, 14.13), (176*a + 289, 8, 0.3924)]), (-9431, [(60*a - 37, 12, 0.8819)]), (-9516, [(58*a - 24, -8, 0.3902), (202*a + 336, 8, 0.3902)]), (-9551, [(100*a + 143, -16, 1.558)]), (-9575, [(60*a - 35, 16, 1.556), (60*a + 35, 24, 3.501)]), (-9584, [(180*a + 296, 0, 0)]), (-9623, [(72*a + 77, -4, 0.09701)]), (-9644, [(86*a + 112, 4, 0.09690), (154*a + 248, 20, 2.422)]), (-9647, [(104*a + 151, -8, 0.3875), (124*a + 191, -4, 0.09688)]), (-9687, [(244*a + 411, 16, 1.547)]), (-9719, [(84*a + 107, 48, 13.90), (160*a + 259, -16, 1.544)]), (-9743, [(112*a + 167, 12, 0.8676), (116*a + 175, -16, 1.542)]), (-9759, [(76*a + 87, 8, 0.3853)]), (-9767, [(92*a + 125, 0, 0)]), (-9776, [(68*a + 64, -8, 0.3850)]), (-9791, [(172*a + 281, -8, 0.3847)]), (-9836, [(58*a + 16, -12, 0.8635)]), (-9887, [(64*a + 49, -8, 0.3828), (252*a + 425, -36, 7.752)]), (-9903, [(224*a + 375, 8, 0.3825)]), (-9932, [(62*a + 40, 8, 0.3819), (66*a + 56, 8, 0.3819)]), (-9959, [(96*a + 133, 0, 0), (140*a + 221, 0, 0)])]] # map: (a |-> -1.73) -> 1, (a |-> 1.73) -> -1, Fractional ideal (4*a - 1) -> 1 [4*a + 5, -3/2*a - 1 + (21*a - 49/2)*i + (-1/2*a)*j + (2*a + 1/2)*k, [(-23, [(-4*a + 5, -4, 2.807)]), (-32, [(-4*a + 4, -4, 2.380), (-12*a + 20, 4, 2.380)]), (-39, [(-4*a + 3, 4, 2.156)]), (-44, [(-10*a + 16, 0, 0)]), (-71, [(-12*a + 19, 4, 1.598), (-8*a + 11, 0, 0)]), (-111, [(-8*a + 9, 4, 1.278), (-20*a + 33, 4, 1.278)]), (-143, [(-12*a + 17, -8, 4.504), (-16*a + 25, 4, 1.126)]), (-167, [(-8*a + 5, 0, 0)]), (-176, [(-20*a + 32, -8, 4.060)]), (-183, [(-8*a - 3, -4, 0.9953), (-8*a + 3, 4, 0.9953)]), (-300, [(-10*a, -8, 3.109)]), (-311, [(-12*a + 11, 8, 3.054)]), (-327, [(-16*a + 21, -4, 0.7446)]), (-332, [(-14*a + 16, 8, 2.956), (-34*a + 56, -8, 2.956)]), (-359, [(-20*a + 29, 0, 0)]), (-368, [(-12*a - 8, 0, 0)]), (-383, [(-12*a - 7, 12, 6.192), (-12*a + 7, -4, 0.6880)]), (-407, [(-12*a + 5, 4, 0.6674), (-36*a + 59, -12, 6.007)]), (-416, [(-28*a + 44, -8, 2.641), (-12*a + 4, 0, 0)]), (-428, [(-22*a + 32, -8, 2.603)]), (-503, [(-28*a + 43, 0, 0)]), (-524, [(-14*a + 8, 0, 0), (-14*a - 8, 0, 0)]), (-543, [(-52*a + 87, -4, 0.5778)]), (-575, [(-40*a + 65, 0, 0)]), (-599, [(-16*a + 13, 4, 0.5501)]), (-624, [(-44*a + 72, 8, 2.156)]), (-647, [(-16*a + 11, 8, 2.117), (-68*a + 115, 4, 0.5293)]), (-671, [(-20*a + 23, 4, 0.5198), (-28*a + 41, -4, 0.5198)]), (-687, [(-16*a - 9, -12, 4.623)]), (-716, [(-62*a + 104, 8, 2.013)]), (-719, [(-16*a - 7, 12, 4.519), (-16*a + 7, 4, 0.5021)]), (-743, [(-16*a + 5, -4, 0.4940)]), (-759, [(-20*a + 21, -8, 1.955), (-56*a + 93, -8, 1.955)]), (-767, [(-16*a - 1, -12, 4.375), (-24*a + 31, 4, 0.4862)]), (-831, [(-28*a + 39, 4, 0.4671), (-40*a + 63, -12, 4.204)]), (-839, [(-20*a + 19, -8, 1.859)]), (-876, [(-22*a + 24, -8, 1.820)]), (-887, [(-52*a + 85, -4, 0.4521)]), (-908, [(-18*a + 8, -16, 7.149)]), (-911, [(-20*a + 17, 8, 1.784), (-72*a + 121, 4, 0.4461)]), (-975, [(-80*a + 135, -8, 1.725)]), (-983, [(-48*a + 77, 0, 0)]), (-1004, [(-54*a + 88, -8, 1.700), (-26*a + 32, 0, 0)]), (-1031, [(-20*a + 13, 0, 0)]), (-1047, [(-32*a + 45, -4, 0.4161)]), (-1056, [(-20*a + 12, 0, 0), (-52*a + 84, 0, 0)]), (-1079, [(-40*a + 61, -8, 1.640), (-20*a + 11, 0, 0)]), (-1100, [(-30*a + 40, 8, 1.624)]), (-1103, [(-68*a + 113, -16, 6.487)]), (-1119, [(-20*a + 9, 12, 3.622)]), (-1127, [(-28*a + 35, 8, 1.604)]), (-1136, [(-20*a + 8, 8, 1.598), (-20*a - 8, 0, 0)]), (-1151, [(-20*a + 7, -4, 0.3969)]), (-1164, [(-34*a + 48, -16, 6.314), (-46*a + 72, 0, 0)]), (-1175, [(-20*a - 5, 0, 0)]), (-1196, [(-90*a + 152, 16, 6.229), (-22*a + 16, 0, 0)]), (-1199, [(-24*a + 23, -8, 1.555), (-76*a + 127, -4, 0.3888)]), (-1200, [(-20*a, -8, 1.555)]), (-1263, [(-64*a + 105, -4, 0.3789)]), (-1319, [(-40*a + 59, 12, 3.337), (-44*a + 67, 4, 0.3707)]), (-1328, [(-28*a + 32, 16, 5.912), (-68*a + 112, 0, 0)]), (-1391, [(-72*a + 119, 4, 0.3610), (-28*a + 31, 0, 0)]), (-1439, [(-100*a + 169, 8, 1.420)]), (-1452, [(-22*a, 0, 0)]), (-1487, [(-56*a + 89, -4, 0.3492)]), (-1551, [(-52*a + 81, 0, 0)]), (-1559, [(-24*a - 13, -12, 3.069), (-24*a + 13, 8, 1.364)]), (-1568, [(-28*a + 28, 8, 1.360), (-84*a + 140, -8, 1.360)]), (-1583, [(-44*a + 65, -16, 5.415), (-48*a + 73, 4, 0.3384)]), (-1676, [(-30*a + 32, 0, 0)]), (-1679, [(-24*a - 7, 8, 1.314), (-24*a + 7, 8, 1.314)]), (-1703, [(-24*a - 5, 8, 1.305), (-76*a + 125, 0, 0)]), (-1712, [(-44*a + 64, 0, 0)]), (-1727, [(-24*a + 1, 8, 1.296), (-28*a + 25, -8, 1.296)]), (-1772, [(-26*a - 16, 0, 0)]), (-1776, [(-28*a + 24, -8, 1.278), (-100*a + 168, 0, 0)]), (-1823, [(-104*a + 175, 16, 5.046), (-28*a + 23, 0, 0)]), (-1847, [(-84*a + 139, 8, 1.253), (-32*a + 35, 0, 0)]), (-1868, [(-34*a + 40, 8, 1.246)]), (-1871, [(-48*a + 71, 12, 2.801)]), (-1911, [(-28*a + 21, 0, 0)]), (-1964, [(-26*a - 8, -8, 1.215), (-26*a + 8, 16, 4.861)]), (-1983, [(-32*a + 33, 12, 2.721), (-92*a + 153, 12, 2.721)]), (-1991, [(-28*a + 19, 4, 0.3018), (-120*a + 203, -16, 4.828)]), (-2028, [(-26*a, -16, 4.784)]), (-2039, [(-36*a + 43, 4, 0.2982), (-80*a + 131, 0, 0)]), (-2087, [(-44*a + 61, -4, 0.2947)]), (-2096, [(-28*a - 16, 8, 1.176), (-28*a + 16, -8, 1.176)]), (-2111, [(-100*a + 167, -12, 2.637)]), (-2127, [(-28*a - 15, -20, 7.299), (-28*a + 15, 4, 0.2919)]), (-2156, [(-70*a + 112, 0, 0)]), (-2183, [(-28*a - 13, -20, 7.204), (-28*a + 13, -4, 0.2882), (-52*a + 77, -4, 0.2882), (-56*a + 85, -12, 2.594)]), (-2207, [(-36*a + 41, 8, 1.146)]), (-2208, [(-44*a + 60, 16, 4.585), (-28*a - 12, 0, 0)]), (-2231, [(-32*a + 29, 0, 0), (-28*a + 11, 0, 0)]), (-2252, [(-66*a + 104, -8, 1.135)]), (-2271, [(-28*a + 9, 4, 0.2825)]), (-2288, [(-28*a + 8, 16, 4.504), (-28*a - 8, 0, 0)]), (-2316, [(-50*a + 72, -8, 1.119)]), (-2327, [(-44*a + 59, 4, 0.2791), (-72*a + 115, -8, 1.116)]), (-2336, [(-28*a - 4, 8, 1.114), (-52*a + 76, 8, 1.114)]), (-2343, [(-28*a - 3, -8, 1.113), (-116*a + 195, -8, 1.113)]), (-2348, [(-58*a + 88, 8, 1.111)]), (-2423, [(-48*a + 67, -4, 0.2735)]), (-2444, [(-30*a + 16, -8, 1.089)]), (-2447, [(-124*a + 209, 12, 2.450), (-32*a + 25, 0, 0)]), (-2487, [(-64*a + 99, 4, 0.2700)]), (-2519, [(-36*a + 37, -4, 0.2683), (-104*a + 173, 0, 0)]), (-2543, [(-132*a + 223, -4, 0.2670)]), (-2591, [(-40*a + 47, 20, 6.613), (-92*a + 151, 4, 0.2645)]), (-2631, [(-32*a - 21, -4, 0.2625)]), (-2636, [(-30*a - 8, -16, 4.196), (-30*a + 8, 24, 9.441)]), (-2663, [(-112*a + 187, -4, 0.2609)]), (-2672, [(-84*a + 136, 0, 0)]), (-2687, [(-48*a + 65, 8, 1.039), (-76*a + 121, -4, 0.2597)]), (-2732, [(-38*a + 40, -8, 1.030), (-106*a + 176, -16, 4.122)]), (-2783, [(-88*a + 143, -8, 1.021)]), (-2847, [(-32*a + 15, -16, 4.037), (-32*a - 15, 0, 0)]), (-2864, [(-124*a + 208, -16, 4.025)]), (-2879, [(-60*a + 89, 8, 1.004), (-64*a + 97, 0, 0)]), (-2927, [(-128*a + 215, -4, 0.2489)]), (-2928, [(-52*a + 72, 24, 8.958), (-76*a + 120, 16, 3.981)]), (-2951, [(-32*a + 11, -4, 0.2479), (-32*a - 11, 0, 0)]), (-2991, [(-32*a + 9, 4, 0.2462)]), (-2999, [(-44*a + 53, -12, 2.213)]), (-3023, [(-32*a - 7, -12, 2.204)]), (-3047, [(-32*a - 5, -4, 0.2439), (-136*a + 229, -12, 2.195)]), (-3063, [(-32*a - 3, -12, 2.190), (-32*a + 3, -4, 0.2433)]), (-3167, [(-56*a + 79, -8, 0.9570), (-76*a + 119, 20, 5.981)]), (-3191, [(-48*a + 61, 8, 0.9534), (-92*a + 149, -8, 0.9534)]), (-3207, [(-104*a + 171, 12, 2.140)]), (-3212, [(-46*a + 56, 32, 15.20), (-98*a + 160, 8, 0.9503)]), (-3263, [(-36*a + 25, 8, 0.9428), (-64*a + 95, 24, 8.485)]), (-3351, [(-52*a + 69, 4, 0.2326), (-88*a + 141, 4, 0.2326)]), (-3359, [(-36*a + 23, 4, 0.2323)]), (-3404, [(-50*a + 64, 0, 0), (-34*a - 8, 0, 0)]), (-3407, [(-112*a + 185, -4, 0.2307)]), (-3431, [(-40*a + 37, -8, 0.9195)]), (-3479, [(-56*a + 77, 24, 8.218), (-84*a + 133, 8, 0.9131)]), (-3488, [(-36*a - 20, 8, 0.9119), (-52*a + 68, -16, 3.648)]), (-3504, [(-44*a + 48, 8, 0.9098)]), (-3575, [(-40*a + 35, 8, 0.9007), (-140*a + 235, -16, 3.603)]), (-3599, [(-36*a - 17, -4, 0.2244), (-36*a + 17, 4, 0.2244), (-44*a + 47, 4, 0.2244), (-120*a + 199, -4, 0.2244)]), (-3623, [(-96*a + 155, -8, 0.8948), (-52*a + 67, 0, 0)]), (-3632, [(-36*a + 16, 8, 0.8937)]), (-3639, [(-76*a + 117, 12, 2.009)]), (-3671, [(-68*a + 101, -8, 0.8889)]), (-3692, [(-42*a + 40, -16, 3.545), (-58*a + 80, -16, 3.545)]), (-3711, [(-148*a + 249, 4, 0.2210)]), (-3719, [(-36*a - 13, -20, 5.520), (-36*a + 13, 4, 0.2208)]), (-3756, [(-38*a - 24, -8, 0.8788)]), (-3767, [(-36*a + 11, -16, 3.510), (-36*a - 11, 0, 0)]), (-3783, [(-56*a + 75, 8, 0.8756), (-44*a + 45, 0, 0)]), (-3788, [(-82*a + 128, 16, 3.500), (-62*a + 88, 0, 0)]), (-3839, [(-40*a + 31, 8, 0.8692), (-156*a + 263, -12, 1.956)]), (-3884, [(-70*a + 104, 16, 3.457)]), (-3887, [(-104*a + 169, 8, 0.8638)]), (-3911, [(-60*a + 83, 12, 1.938)]), (-3959, [(-44*a + 43, -4, 0.2140), (-164*a + 277, -4, 0.2140)]), (-4007, [(-64*a + 91, 12, 1.914), (-84*a + 131, 12, 1.914)]), (-4016, [(-52*a + 64, -8, 0.8499), (-108*a + 176, 0, 0)]), (-4071, [(-40*a + 27, 0, 0), (-80*a + 123, 0, 0)]), (-4079, [(-56*a + 73, -4, 0.2108), (-100*a + 161, 0, 0)]), (-4103, [(-72*a + 107, -20, 5.255), (-76*a + 115, -16, 3.363)]), (-4127, [(-144*a + 241, -4, 0.2096)]), (-4143, [(-52*a + 63, 20, 5.230), (-112*a + 183, 28, 10.25)]), (-4175, [(-40*a - 25, -24, 7.502)]), (-4268, [(-166*a + 280, -16, 3.298), (-38*a - 8, 0, 0)]), (-4271, [(-40*a - 23, 12, 1.854)]), (-4287, [(-44*a + 39, -12, 1.851)]), (-4332, [(-38*a, -16, 3.273)]), (-4359, [(-40*a - 21, -4, 0.2039)]), (-4364, [(-126*a + 208, -8, 0.8153)]), (-4367, [(-92*a + 145, -8, 0.8150), (-108*a + 175, -8, 0.8150)]), (-4391, [(-52*a + 61, -4, 0.2032)]), (-4400, [(-60*a + 80, 8, 0.8119)]), (-4439, [(-40*a - 19, -8, 0.8083), (-40*a + 19, 0, 0)]), (-4463, [(-88*a + 137, -4, 0.2015)]), (-4511, [(-40*a + 17, 4, 0.2005), (-48*a + 49, -4, 0.2005)]), (-4512, [(-44*a + 36, -8, 0.8018), (-124*a + 204, -8, 0.8018)]), (-4559, [(-60*a + 79, -8, 0.7976), (-80*a + 121, -8, 0.7976)]), (-4583, [(-168*a + 283, -8, 0.7955), (-44*a + 35, 0, 0)]), (-4631, [(-40*a - 13, 8, 0.7914), (-40*a + 13, -4, 0.1979)]), (-4647, [(-56*a + 69, 20, 4.938)]), (-4652, [(-54*a + 64, 8, 0.7896)]), (-4656, [(-68*a + 96, 0, 0), (-92*a + 144, 0, 0)]), (-4679, [(-40*a + 11, -8, 0.7873)]), (-4719, [(-176*a + 297, 0, 0)]), (-4775, [(-40*a - 5, -8, 0.7794), (-40*a + 5, 0, 0)]), (-4784, [(-44*a + 32, -16, 3.115), (-180*a + 304, 0, 0)]), (-4791, [(-40*a - 3, 4, 0.1945)]), (-4799, [(-40*a - 1, 0, 0)]), (-4863, [(-136*a + 225, -4, 0.1931)]), (-4871, [(-112*a + 181, 0, 0)]), (-4908, [(-58*a + 72, 16, 3.075)]), (-4919, [(-56*a + 67, 0, 0)]), (-4967, [(-44*a - 29, 8, 0.7642), (-44*a + 29, 16, 3.057)]), (-4976, [(-140*a + 232, 0, 0)]), (-5024, [(-44*a - 28, -24, 6.838), (-44*a + 28, 8, 0.7598), (-60*a + 76, 0, 0), (-116*a + 188, 0, 0)]), (-5039, [(-84*a + 127, -8, 0.7587)]), (-5079, [(-44*a - 27, 20, 4.723), (-44*a + 27, -20, 4.723)]), (-5087, [(-52*a + 55, 0, 0)]), (-5183, [(-44*a + 25, 8, 0.7481), (-56*a + 65, -8, 0.7481)]), (-5196, [(-50*a + 48, 16, 2.989)]), (-5228, [(-42*a + 8, 0, 0)]), (-5232, [(-44*a - 24, -8, 0.7446)]), (-5279, [(-44*a + 23, 0, 0)]), (-5303, [(-152*a + 253, 4, 0.1849)]), (-5351, [(-72*a + 101, -4, 0.1841)]), (-5399, [(-116*a + 187, 0, 0)]), (-5439, [(-56*a + 63, -8, 0.7303), (-140*a + 231, -8, 0.7303)]), (-5447, [(-44*a - 19, -12, 1.642), (-44*a + 19, -16, 2.919)]), (-5471, [(-128*a + 209, -4, 0.1820)]), (-5484, [(-70*a + 96, -16, 2.909), (-106*a + 168, 16, 2.909)]), (-5511, [(-80*a + 117, -16, 2.902), (-92*a + 141, -8, 0.7255)]), (-5519, [(-44*a + 17, 28, 8.881)]), (-5543, [(-48*a + 37, 8, 0.7234), (-88*a + 133, 0, 0)]), (-5583, [(-44*a - 15, -12, 1.622), (-44*a + 15, 4, 0.1802)]), (-5591, [(-68*a + 91, 4, 0.1801)]), (-5612, [(-102*a + 160, 0, 0), (-154*a + 256, 0, 0)]), (-5639, [(-44*a + 13, 4, 0.1793)]), (-5664, [(-44*a - 12, 24, 6.441), (-44*a + 12, -8, 0.7156), (-76*a + 108, 8, 0.7156), (-100*a + 156, -8, 0.7156)]), (-5687, [(-44*a - 11, 0, 0)]), (-5711, [(-52*a + 49, -4, 0.1782), (-168*a + 281, 8, 0.7127)]), (-5727, [(-44*a - 9, 8, 0.7117), (-64*a + 81, 0, 0)]), (-5744, [(-44*a - 8, 0, 0)]), (-5759, [(-60*a + 71, 4, 0.1774), (-136*a + 223, 0, 0)]), (-5772, [(-46*a + 24, -16, 2.836), (-94*a + 144, 0, 0)]), (-5792, [(-44*a - 4, -8, 0.7077), (-84*a + 124, 16, 2.831)]), (-5804, [(-86*a + 128, 8, 0.7069)]), (-5807, [(-44*a + 1, 0, 0)]), (-5808, [(-44*a, -32, 11.31)]), (-5900, [(-50*a + 40, 8, 0.7012), (-190*a + 320, 8, 0.7012)]), (-5903, [(-52*a + 47, 16, 2.804), (-176*a + 295, 12, 1.577)]), (-5927, [(-156*a + 259, 8, 0.6996)]), (-5951, [(-68*a + 89, 8, 0.6981), (-48*a - 31, 0, 0)]), (-5975, [(-80*a + 115, -8, 0.6967), (-100*a + 155, 16, 2.787)]), (-6047, [(-64*a + 79, -8, 0.6926)]), (-6071, [(-48*a - 29, -4, 0.1728), (-48*a + 29, 8, 0.6912)]), (-6087, [(-52*a + 45, 20, 4.314), (-184*a + 309, 20, 4.314)]), (-6092, [(-46*a + 16, 16, 2.760)]), (-6128, [(-68*a + 88, -8, 0.6880), (-124*a + 200, -32, 11.01)]), (-6143, [(-72*a + 97, -8, 0.6871)]), (-6176, [(-60*a + 68, 8, 0.6853), (-188*a + 316, 8, 0.6853)]), (-6284, [(-46*a - 8, -16, 2.718)]), (-6303, [(-112*a + 177, -16, 2.714), (-128*a + 207, -16, 2.714)]), (-6311, [(-152*a + 251, 0, 0)]), (-6348, [(-46*a, -16, 2.704)]), (-6359, [(-64*a + 77, 32, 10.81), (-140*a + 229, 4, 0.1688)]), (-6383, [(-48*a - 23, -8, 0.6741), (-172*a + 287, 0, 0)]), (-6431, [(-52*a + 41, 12, 1.511), (-108*a + 169, -4, 0.1679)]), (-6512, [(-52*a + 40, -8, 0.6674), (-116*a + 184, -16, 2.670)]), (-6527, [(-84*a + 121, -4, 0.1667), (-124*a + 199, -4, 0.1667)]), (-6551, [(-48*a - 19, -12, 1.497), (-48*a + 19, -8, 0.6654)]), (-6575, [(-60*a + 65, -24, 5.978), (-160*a + 265, 8, 0.6642)]), (-6599, [(-180*a + 301, 0, 0)]), (-6623, [(-48*a - 17, -4, 0.1654), (-96*a + 145, -4, 0.1654)]), (-6647, [(-68*a + 85, 8, 0.6606)]), (-6663, [(-64*a + 75, 12, 1.485), (-148*a + 243, -4, 0.1649)]), (-6668, [(-142*a + 232, 0, 0)]), (-6704, [(-60*a + 64, -8, 0.6578)]), (-6719, [(-76*a + 103, 0, 0)]), (-6743, [(-52*a + 37, 8, 0.6559), (-48*a + 13, 0, 0)]), (-6791, [(-48*a - 11, -8, 0.6535)]), (-6807, [(-56*a + 51, -12, 1.469)]), (-6863, [(-48*a - 7, -16, 2.600), (-48*a + 7, 4, 0.1625)]), (-6911, [(-48*a + 1, 8, 0.6478), (-48*a - 1, 0, 0)]), (-6924, [(-50*a - 24, -8, 0.6472)]), (-6956, [(-58*a + 56, 24, 5.812), (-138*a + 224, -8, 0.6457)]), (-7007, [(-84*a + 119, -16, 2.574), (-112*a + 175, 8, 0.6434)]), (-7023, [(-52*a - 33, 12, 1.446)]), (-7079, [(-176*a + 293, 0, 0)]), (-7088, [(-52*a - 32, -8, 0.6397)]), (-7127, [(-128*a + 205, 24, 5.742)]), (-7148, [(-218*a + 368, -8, 0.6370), (-54*a + 40, 0, 0)]), (-7151, [(-52*a - 31, 28, 7.802), (-52*a + 31, 4, 0.1592)]), (-7167, [(-92*a + 135, -4, 0.1590)]), (-7199, [(-96*a + 143, 8, 0.6348), (-100*a + 151, 0, 0)]), (-7212, [(-74*a + 96, 24, 5.708), (-134*a + 216, -24, 5.708)]), (-7244, [(-50*a - 16, 8, 0.6328), (-50*a + 16, 8, 0.6328)]), (-7247, [(-64*a + 71, -36, 12.81), (-164*a + 271, 12, 1.423)]), (-7271, [(-52*a + 29, -4, 0.1579), (-140*a + 227, -4, 0.1579)]), (-7311, [(-68*a + 81, -20, 3.937)]), (-7319, [(-80*a + 109, 8, 0.6295), (-124*a + 197, 12, 1.416)]), (-7328, [(-76*a + 100, 8, 0.6291), (-52*a - 28, 0, 0)]), (-7383, [(-52*a + 27, -16, 2.507), (-52*a - 27, 0, 0)]), (-7436, [(-78*a + 104, 0, 0)]), (-7472, [(-68*a + 80, -16, 2.492)]), (-7487, [(-52*a - 25, -4, 0.1556), (-52*a + 25, -4, 0.1556)]), (-7527, [(-64*a + 69, -8, 0.6208), (-172*a + 285, 16, 2.483)]), (-7559, [(-220*a + 371, 20, 3.872)]), (-7607, [(-88*a + 125, -4, 0.1544)]), (-7628, [(-82*a + 112, 16, 2.467), (-126*a + 200, -24, 5.550)]), (-7631, [(-72*a + 89, -16, 2.466), (-148*a + 241, -4, 0.1541)]), (-7671, [(-52*a + 21, 4, 0.1537)]), (-7703, [(-92*a + 133, 8, 0.6136), (-112*a + 173, 20, 3.835)]), (-7712, [(-52*a - 20, 24, 5.519), (-52*a + 20, -24, 5.519), (-84*a + 116, -8, 0.6133), (-124*a + 196, 8, 0.6133)]), (-7724, [(-54*a - 32, 8, 0.6128), (-54*a + 32, 24, 5.515)]), (-7727, [(-56*a + 41, 12, 1.379)]), (-7751, [(-52*a + 19, 8, 0.6117), (-132*a + 211, -8, 0.6117)]), (-7775, [(-200*a + 335, 8, 0.6108)]), (-7788, [(-86*a + 120, 16, 2.441), (-214*a + 360, -16, 2.441)]), (-7799, [(-64*a + 67, -4, 0.1525), (-104*a + 157, 4, 0.1525)]), (-7823, [(-52*a - 17, 4, 0.1522), (-52*a + 17, -24, 5.480)]), (-7856, [(-52*a - 16, 16, 2.431), (-52*a + 16, 8, 0.6076)]), (-7887, [(-52*a + 15, 8, 0.6064), (-56*a + 39, -16, 2.426)]), (-7916, [(-118*a + 184, -8, 0.6053)]), (-7919, [(-144*a + 233, -16, 2.421)]), (-7943, [(-52*a - 13, -8, 0.6043)]), (-8012, [(-94*a + 136, 0, 0)]), (-8031, [(-52*a - 9, 4, 0.1502)]), (-8048, [(-52*a + 8, 16, 2.401)]), (-8063, [(-52*a - 7, 8, 0.5998), (-64*a + 65, 0, 0)]), (-8076, [(-98*a + 144, 0, 0)]), (-8096, [(-60*a + 52, -16, 2.394), (-68*a + 76, -16, 2.394), (-172*a + 284, 16, 2.394), (-212*a + 356, -32, 9.577)]), (-8103, [(-88*a + 123, 0, 0), (-52*a + 3, 0, 0)]), (-8108, [(-102*a + 152, -8, 0.5981), (-106*a + 160, 8, 0.5981)]), (-8112, [(-52*a, 0, 0)]), (-8175, [(-140*a + 225, 0, 0)]), (-8183, [(-56*a + 35, -16, 2.381)]), (-8231, [(-92*a + 131, -8, 0.5936), (-120*a + 187, -8, 0.5936)]), (-8247, [(-176*a + 291, 12, 1.334)]), (-8303, [(-152*a + 247, -8, 0.5910)]), (-8327, [(-96*a + 139, -4, 0.1476), (-116*a + 179, 16, 2.361)]), (-8391, [(-100*a + 147, 12, 1.323), (-112*a + 171, 12, 1.323)]), (-8396, [(-62*a + 56, 16, 2.351)]), (-8399, [(-60*a + 49, -12, 1.322), (-136*a + 217, -4, 0.1469)]), (-8423, [(-108*a + 163, 0, 0)]), (-8447, [(-56*a - 31, -12, 1.318), (-56*a + 31, 16, 2.344)]), (-8492, [(-58*a + 40, -16, 2.338), (-246*a + 416, -24, 5.260)]), (-8543, [(-68*a + 73, -8, 0.5827), (-184*a + 305, 4, 0.1457)]), (-8567, [(-204*a + 341, -16, 2.328), (-56*a - 29, 0, 0)]), (-8624, [(-140*a + 224, -16, 2.320)]), (-8663, [(-72*a + 83, 12, 1.302)]), (-8679, [(-76*a + 93, 8, 0.5781), (-56*a - 27, 0, 0)]), (-8684, [(-54*a - 8, -16, 2.312), (-54*a + 8, -8, 0.5779)]), (-8688, [(-68*a + 72, 0, 0)]), (-8751, [(-92*a + 129, -12, 1.295), (-128*a + 201, -4, 0.1439)]), (-8783, [(-56*a - 25, -16, 2.299)]), (-8831, [(-68*a + 71, -8, 0.5731), (-192*a + 319, -24, 5.158)]), (-8879, [(-56*a + 23, 8, 0.5716), (-124*a + 193, -8, 0.5716)]), (-8951, [(-60*a + 43, -12, 1.281), (-248*a + 419, 24, 5.123)]), (-8967, [(-56*a - 21, -16, 2.275), (-56*a + 21, -32, 9.100)]), (-8972, [(-66*a + 64, 8, 0.5686), (-206*a + 344, 0, 0)]), (-8975, [(-120*a + 185, -8, 0.5685)]), (-8999, [(-80*a + 101, 4, 0.1419)]), (-9008, [(-132*a + 208, -16, 2.270)]), (-9039, [(-116*a + 177, 8, 0.5665), (-220*a + 369, -8, 0.5665)]), (-9047, [(-56*a - 19, -8, 0.5662), (-76*a + 91, 0, 0)]), (-9068, [(-58*a - 32, -8, 0.5656)]), (-9071, [(-88*a + 119, -8, 0.5655)]), (-9111, [(-200*a + 333, -4, 0.1411)]), (-9119, [(-56*a - 17, 12, 1.269), (-56*a + 17, -16, 2.256)]), (-9183, [(-56*a - 15, -12, 1.265), (-56*a + 15, -36, 11.38)]), (-9200, [(-60*a + 40, 16, 2.246)]), (-9228, [(-62*a + 48, 24, 5.046), (-242*a + 408, -8, 0.5606)]), (-9248, [(-68*a + 68, -24, 5.040), (-204*a + 340, -8, 0.5600)]), (-9264, [(-100*a + 144, 8, 0.5596)]), (-9311, [(-72*a + 79, 4, 0.1395)]), (-9327, [(-56*a - 9, 20, 3.485), (-56*a + 9, 4, 0.1394)]), (-9383, [(-56*a - 5, -8, 0.5560), (-68*a + 67, 0, 0)]), (-9392, [(-116*a + 176, 0, 0)]), (-9399, [(-56*a + 3, -8, 0.5555), (-80*a + 99, 8, 0.5555)]), (-9407, [(-56*a - 1, 24, 4.998), (-56*a + 1, 8, 0.5553)]), (-9431, [(-60*a - 37, -12, 1.248)]), (-9479, [(-64*a + 53, -8, 0.5532), (-236*a + 397, -12, 1.245)]), (-9516, [(-58*a - 24, 16, 2.208), (-202*a + 336, 0, 0)]), (-9543, [(-88*a + 117, -12, 1.240), (-148*a + 237, 4, 0.1378)]), (-9551, [(-100*a + 143, -8, 0.5511)]), (-9584, [(-180*a + 296, 24, 4.951)]), (-9623, [(-72*a + 77, 0, 0)]), (-9647, [(-68*a + 65, 20, 3.427), (-216*a + 361, 8, 0.5483)]), (-9687, [(-244*a + 411, 4, 0.1368)]), (-9759, [(-76*a + 87, -4, 0.1363)]), (-9767, [(-92*a + 125, 8, 0.5450)]), (-9776, [(-60*a + 32, -8, 0.5447)]), (-9791, [(-172*a + 281, 32, 8.709)]), (-9836, [(-58*a + 16, 0, 0)]), (-9839, [(-60*a - 31, -20, 3.393), (-60*a + 31, -8, 0.5430)]), (-9903, [(-224*a + 375, -4, 0.1353)]), (-9932, [(-66*a + 56, -8, 0.5404), (-62*a + 40, 0, 0)]), (-9959, [(-60*a - 29, 8, 0.5397), (-60*a + 29, 0, 0)])]] # map: (a |-> -1.73) -> 1, (a |-> 1.73) -> 1, Fractional ideal (4*a - 1) -> -1 [-1, None, [(25, [(5, -2, 4.574)]), (33, [(4*a + 9, 2, 3.981)]), (52, [(-2*a + 8, 2, 3.172)]), (73, [(-4*a + 11, 0, 0)]), (96, [(4*a + 12, -2, 2.334), (-4*a + 12, 2, 2.334)]), (97, [(8*a + 17, -2, 2.322), (-8*a + 17, 2, 2.322)]), (121, [(11, -2, 2.079)]), (148, [(6*a + 16, -2, 1.880), (-6*a + 16, -2, 1.880)]), (169, [(13, 0, 0)]), (193, [(-12*a + 25, 0, 0)]), (208, [(-4*a + 16, 2, 1.586)]), (244, [(2*a + 16, 2, 1.464), (-2*a + 16, -2, 1.464)]), (249, [(8*a + 21, 2, 1.449), (-8*a + 21, -2, 1.449)]), (276, [(-10*a + 24, 0, 0)]), (313, [(4*a + 19, -2, 1.293)]), (321, [(-16*a + 33, -2, 1.276)]), (352, [(-4*a + 20, -2, 1.219), (12*a + 28, -2, 1.219)]), (361, [(19, 2, 1.204)]), (393, [(4*a + 21, -2, 1.154), (-4*a + 21, 2, 1.154)]), (400, [(20*a + 40, 0, 0)]), (409, [(-12*a + 29, 0, 0)]), (433, [(-8*a + 25, 2, 1.099)]), (436, [(-14*a + 32, 2, 1.095)]), (457, [(-16*a + 35, 4, 4.279), (16*a + 35, 0, 0)]), (481, [(-4*a + 23, 0, 0), (20*a + 41, 0, 0)]), (528, [(-4*a + 24, 0, 0)]), (529, [(23, 0, 0)]), (537, [(8*a + 27, 2, 0.9869)]), (564, [(-2*a + 24, 2, 1.926)]), (577, [(4*a + 25, 2, 0.9521)]), (592, [(12*a + 32, 2, 0.9400), (-12*a + 32, -6, 8.460)]), (601, [(16*a + 37, 0, 0), (-16*a + 37, 0, 0)]), (649, [(8*a + 29, 2, 0.8977), (-20*a + 43, -2, 0.8977)]), (673, [(-24*a + 49, 2, 0.8816)]), (681, [(-4*a + 27, -2, 0.8764)]), (724, [(10*a + 32, -2, 0.8500)]), (736, [(-20*a + 44, 4, 3.372), (4*a + 28, 0, 0)]), (753, [(-16*a + 39, -2, 0.8334), (16*a + 39, -2, 0.8334)]), (769, [(-8*a + 31, 4, 3.299), (8*a + 31, 0, 0)]), (793, [(12*a + 35, 4, 3.249), (4*a + 29, 0, 0)]), (825, [(-20*a + 45, 0, 0)]), (841, [(29, -2, 0.7886)]), (852, [(-22*a + 48, 4, 3.134), (22*a + 48, 0, 0)]), (897, [(-8*a + 33, -4, 3.054), (8*a + 33, 0, 0)]), (913, [(-4*a + 31, 2, 0.7569), (16*a + 41, 2, 0.7569)]), (916, [(6*a + 32, -6, 6.801)]), (937, [(12*a + 37, -2, 0.7471)]), (961, [(31, 2, 0.7377)]), (976, [(4*a + 32, -6, 6.588), (-4*a + 32, -2, 0.7321)]), (1009, [(20*a + 47, 2, 0.7200)]), (1012, [(-14*a + 40, 4, 2.876), (14*a + 40, 0, 0)]), (1033, [(-8*a + 35, 2, 0.7116)]), (1081, [(16*a + 43, 2, 1.391), (-24*a + 53, -2, 1.391), (-16*a + 43, 0, 0)]), (1104, [(-20*a + 48, 0, 0)]), (1108, [(26*a + 56, 2, 0.6871), (-26*a + 56, -2, 0.6871)]), (1129, [(28*a + 59, 2, 0.6806), (-28*a + 59, 6, 6.126)]), (1153, [(32*a + 65, -4, 2.694), (-32*a + 65, -4, 2.694)]), (1168, [(12*a + 40, -4, 2.677)]), (1177, [(8*a + 37, 2, 0.6666), (-8*a + 37, 2, 0.6666)]), (1201, [(-20*a + 49, -2, 0.6599)]), (1225, [(35, -4, 2.614)]), (1248, [(-4*a + 36, 4, 2.590), (28*a + 60, 0, 0)]), (1249, [(12*a + 41, -2, 0.6471), (-12*a + 41, 6, 5.824)]), (1257, [(-16*a + 45, -2, 0.6451)]), (1300, [(10*a + 40, 4, 2.537)]), (1321, [(4*a + 37, 0, 0)]), (1329, [(8*a + 39, -2, 0.6273)]), (1396, [(-30*a + 64, 2, 0.6121)]), (1401, [(-20*a + 51, 2, 0.6110)]), (1417, [(12*a + 43, -4, 2.430), (-12*a + 43, 4, 2.430)]), (1441, [(-16*a + 47, -2, 0.6025), (36*a + 73, -2, 0.6025)]), (1473, [(4*a + 39, 2, 0.5959), (-4*a + 39, -2, 0.5959)]), (1489, [(8*a + 41, 2, 0.5927), (-8*a + 41, -2, 0.5927)]), (1492, [(-6*a + 40, -2, 0.5921)]), (1504, [(12*a + 44, 2, 1.179), (-20*a + 52, -2, 1.179), (-12*a + 44, 0, 0), (20*a + 52, 0, 0)]), (1552, [(4*a + 40, 0, 0), (-4*a + 40, 0, 0)]), (1609, [(20*a + 53, 2, 0.5702)]), (1617, [(28*a + 63, 0, 0)]), (1633, [(-4*a + 41, -8, 9.055), (-16*a + 49, 0, 0)]), (1657, [(8*a + 43, -4, 2.247), (-8*a + 43, 0, 0)]), (1681, [(41, 4, 2.231)]), (1684, [(22*a + 56, -2, 0.5573)]), (1689, [(32*a + 69, -6, 5.008)]), (1716, [(34*a + 72, 4, 2.208), (-34*a + 72, 0, 0)]), (1744, [(-28*a + 64, 2, 0.5476)]), (1761, [(40*a + 81, 2, 0.5450)]), (1777, [(-12*a + 47, 0, 0)]), (1801, [(4*a + 43, 0, 0)]), (1825, [(20*a + 55, 0, 0)]), (1833, [(8*a + 45, -4, 4.273), (-8*a + 45, 4, 2.137), (-16*a + 51, -2, 1.068)]), (1849, [(43, -2, 0.5319)]), (1873, [(-28*a + 65, 8, 8.455)]), (1888, [(4*a + 44, 2, 0.5263), (-4*a + 44, 10, 13.16), (36*a + 76, 2, 0.5263), (-36*a + 76, 2, 0.5263)]), (1936, [(-44*a + 88, 4, 2.079)]), (1969, [(12*a + 49, 2, 0.5154), (-12*a + 49, -6, 4.639)]), (1977, [(4*a + 45, 2, 0.5144), (-4*a + 45, -2, 0.5144)]), (1993, [(24*a + 61, -2, 0.5123)]), (2004, [(-10*a + 48, 0, 0)]), (2017, [(-8*a + 47, -4, 2.037)]), (2041, [(16*a + 53, 0, 0), (36*a + 77, 0, 0)]), (2049, [(-20*a + 57, 2, 0.5052), (20*a + 57, 2, 0.5052)]), (2068, [(-38*a + 80, -6, 9.052), (38*a + 80, -4, 2.012), (26*a + 64, 0, 0)]), (2089, [(-40*a + 83, 2, 0.5004), (40*a + 83, 2, 0.5004)]), (2113, [(-44*a + 89, -6, 4.478)]), (2137, [(-28*a + 67, -2, 0.4947)]), (2161, [(-4*a + 47, 2, 0.4920)]), (2209, [(47, 2, 0.9732)]), (2256, [(-4*a + 48, -2, 0.9630)]), (2353, [(-36*a + 79, -4, 1.886), (36*a + 79, 0, 0)]), (2409, [(-28*a + 69, 4, 1.864), (28*a + 69, 0, 0)]), (2473, [(-44*a + 91, -4, 1.840)]), (2497, [(-48*a + 97, -2, 0.4577), (48*a + 97, -2, 0.4577)]), (2521, [(20*a + 61, 0, 0)]), (2548, [(-14*a + 56, 8, 7.249)]), (2553, [(4*a + 51, -4, 1.811), (-32*a + 75, 0, 0)]), (2593, [(-12*a + 55, -4, 1.796), (12*a + 55, 0, 0)]), (2644, [(-22*a + 64, -2, 0.4448), (22*a + 64, -2, 0.4448)]), (2689, [(28*a + 71, -4, 1.764)]), (2704, [(52*a + 104, -4, 1.759)]), (2761, [(-4*a + 53, 2, 0.4352), (24*a + 67, -2, 0.4352)]), (2769, [(-40*a + 87, 4, 1.738), (-20*a + 63, 0, 0)]), (2833, [(8*a + 55, 2, 0.4297)]), (2836, [(10*a + 56, 2, 0.4295), (-10*a + 56, 10, 10.74)]), (2841, [(-44*a + 93, -2, 0.4291), (44*a + 93, -6, 3.862)]), (2857, [(32*a + 77, -4, 1.711), (-32*a + 77, 0, 0)]), (2896, [(20*a + 64, 2, 0.4250)]), (2913, [(-52*a + 105, -6, 3.814)]), (2953, [(-16*a + 61, 2, 0.4209)]), (2977, [(28*a + 73, 4, 1.677), (-28*a + 73, 4, 1.677)]), (3001, [(36*a + 83, 2, 0.4175)]), (3028, [(-6*a + 56, -6, 3.741)]), (3049, [(12*a + 59, 0, 0)]), (3088, [(4*a + 56, 8, 6.585)]), (3121, [(40*a + 89, -4, 1.637)]), (3124, [(2*a + 56, 0, 0), (18*a + 64, 0, 0)]), (3169, [(32*a + 79, 0, 0)]), (3201, [(4*a + 57, -4, 1.617), (16*a + 63, 4, 1.617)]), (3273, [(28*a + 75, 6, 3.598)]), (3289, [(-8*a + 59, -4, 1.595), (48*a + 101, 4, 1.595), (-12*a + 61, 0, 0), (-20*a + 67, 0, 0)]), (3313, [(24*a + 71, -6, 3.576)]), (3316, [(50*a + 104, 6, 3.574)]), (3337, [(36*a + 85, -2, 0.7918), (-36*a + 85, -4, 1.584), (52*a + 107, -4, 1.584), (-52*a + 107, 4, 3.167)]), (3361, [(56*a + 113, 8, 6.312), (-56*a + 113, -4, 1.578)]), (3408, [(-44*a + 96, 4, 1.567), (44*a + 96, 8, 6.268)]), (3424, [(20*a + 68, -2, 0.3908), (-28*a + 76, -2, 0.3908)]), (3433, [(4*a + 59, 2, 0.3903), (-4*a + 59, -2, 0.3903)]), (3457, [(16*a + 65, 2, 0.3890)]), (3489, [(-32*a + 81, 2, 0.3872)]), (3508, [(14*a + 64, -2, 0.3861)]), (3577, [(-28*a + 77, -4, 1.530)]), (3601, [(-24*a + 73, 4, 1.524), (-44*a + 97, -4, 1.524)]), (3664, [(12*a + 64, -2, 0.3778)]), (3673, [(4*a + 61, -2, 0.3774), (-4*a + 61, -2, 0.3774)]), (3697, [(-48*a + 103, 0, 0)]), (3732, [(-22*a + 72, 0, 0)]), (3793, [(-12*a + 65, 0, 0)]), (3796, [(10*a + 64, -4, 1.485), (-10*a + 64, 0, 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