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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 1, -16, 97, -223, 215, 28, -291, 299, -89, -91, 114, -52, 3, 9, -5, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 52401279790283203125, 'disc_rad': 2741385, 'disc_sign': 1, 'frobs': [[2, [[16, 1]]], [3, [0]], [5, [0]], [7, [[16, 1]]], [11, [[8, 1], [4, 1], [2, 2]]], [13, [[8, 1], [4, 2]]], [17, [[8, 2]]], [19, [[8, 1], [4, 2]]], [23, [[8, 2]]], [29, [[4, 2], [2, 4]]], [31, [[2, 7], [1, 2]]], [37, [[16, 1]]], [41, [[4, 4]]], [43, [[8, 1], [4, 2]]], [47, [[8, 2]]], [53, [[16, 1]]], [59, [[4, 1], [2, 4], [1, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [8192, 12288, 8192, 8192], 'galois_label': '16T1771', 'galt': 1771, 'grd': 2475.868173489506, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '16.4.52401279790283203125.2', 'local_algs': ['3.4.2.2', '3.4.2.2', '3.8.4.1', '5.16.12.1', '179.1.0.1', '179.1.0.1', '179.2.0.1', '179.2.0.1', '179.2.0.1', '179.4.0.1', '179.4.2.1', 'm1021.1.1.0', 'm1021.1.1.0', 'm1021.1.2.0', 'm1021.1.2.0', 'm1021.1.2.0', 'm1021.1.2.0', 'm1021.2.1.1', 'm1021.1.4.0'], 'monogenic': 0, 'num_ram': 4, 'r2': 6, 'ramps': [3, 5, 179, 1021], 'rd': 17.0788596007, 'regulator': {'__RealLiteral__': 0, 'data': '3051.12459213', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-1.-1.1', '1.4.-4.-1.1', '1.-1.-6.8.-1.1.1.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{115825}{922111} a^{15} - 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\\frac{2206207207}{386364509} a^{8} + \\frac{17174516798}{386364509} a^{7} - \\frac{19875816256}{386364509} a^{6} + \\frac{3679371885}{386364509} a^{5} + \\frac{12963210066}{386364509} a^{4} - \\frac{13697145543}{386364509} a^{3} + \\frac{5097720391}{386364509} a^{2} - \\frac{686113546}{386364509} a - \\frac{87344117}{386364509} \\)', '\\( \\frac{144225693}{386364509} a^{15} - \\frac{633877692}{386364509} a^{14} + \\frac{820697113}{386364509} a^{13} + \\frac{1209321694}{386364509} a^{12} - \\frac{6872398289}{386364509} a^{11} + \\frac{11226111710}{386364509} a^{10} - \\frac{3290667237}{386364509} a^{9} - \\frac{17328444649}{386364509} a^{8} + \\frac{29705885098}{386364509} a^{7} - \\frac{15434234849}{386364509} a^{6} - \\frac{10768657410}{386364509} a^{5} + \\frac{20694977836}{386364509} a^{4} - \\frac{12207684851}{386364509} a^{3} + \\frac{4209547456}{386364509} a^{2} - \\frac{1379839950}{386364509} a - \\frac{73565624}{386364509} \\)', '\\( \\frac{9664897}{386364509} a^{15} - \\frac{37221984}{386364509} a^{14} + \\frac{48597691}{386364509} a^{13} + \\frac{55976993}{386364509} a^{12} - \\frac{450753085}{386364509} a^{11} + \\frac{909990659}{386364509} a^{10} - \\frac{627815277}{386364509} a^{9} - \\frac{1120327756}{386364509} a^{8} + \\frac{3873780806}{386364509} a^{7} - \\frac{4701096724}{386364509} a^{6} + \\frac{1391792692}{386364509} a^{5} + \\frac{3885185023}{386364509} a^{4} - \\frac{5920158836}{386364509} a^{3} + \\frac{3303622158}{386364509} a^{2} - \\frac{340773934}{386364509} a - \\frac{31285278}{386364509} \\)', '\\( \\frac{159211345}{386364509} a^{15} - \\frac{727019525}{386364509} a^{14} + \\frac{1127186011}{386364509} a^{13} + \\frac{925331150}{386364509} a^{12} - \\frac{7814838357}{386364509} a^{11} + \\frac{14848952323}{386364509} a^{10} - \\frac{8641011923}{386364509} a^{9} - \\frac{16886755029}{386364509} a^{8} + \\frac{39983526062}{386364509} a^{7} - \\frac{31262156364}{386364509} a^{6} - \\frac{4481204597}{386364509} a^{5} + \\frac{29087813597}{386364509} a^{4} - \\frac{24655627152}{386364509} a^{3} + \\frac{9676124856}{386364509} a^{2} - \\frac{1992712977}{386364509} a + \\frac{173622775}{386364509} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', 'a^14', '1/386364509*a^15 - 39474325/386364509*a^14 + 162914685/386364509*a^13 + 48256188/386364509*a^12 - 18398309/386364509*a^11 + 164786933/386364509*a^10 + 66688799/386364509*a^9 - 23705760/386364509*a^8 + 97117643/386364509*a^7 - 145168194/386364509*a^6 - 85206071/386364509*a^5 - 88584030/386364509*a^4 + 40217823/386364509*a^3 + 166311228/386364509*a^2 + 34893589/386364509*a - 18978718/386364509']}