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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -7, 19, -27, 19, 6, -38, 66, -77, 66, -38, 6, 19, -27, 19, -7, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 847267028262109375, 'disc_rad': 90487505, 'disc_sign': -1, 'frobs': [[2, [[8, 2]]], [3, [[16, 1]]], [5, [0]], [7, [[16, 1]]], [11, [[4, 4]]], [13, [[6, 2], [4, 1]]], [17, [[12, 1], [4, 1]]], [19, [[6, 2], [2, 2]]], [23, [[6, 2], [4, 1]]], [29, [[8, 2]]], [31, [[8, 1], [3, 2], [2, 1]]], [37, [[8, 2]]], [41, [[4, 1], [2, 4], [1, 4]]], [43, [[4, 2], [2, 4]]], [47, [[4, 2], [2, 4]]], [53, [[16, 1]]], [59, [[6, 1], [4, 1], [1, 6]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [147456, 147456, 147456], 'galois_label': '16T1905', 'galt': 1905, 'grd': 9512.492049930976, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '16.6.847267028262109375.1', 'local_algs': ['5.16.8.1', '151.1.0.1', '151.1.0.1', '151.2.1.1', '151.2.0.1', '151.2.0.1', '151.2.0.1', '151.2.0.1', '151.4.0.1', 'm119851.1.1.0', 'm119851.1.1.0', 'm119851.1.1.0', 'm119851.1.1.0', 'm119851.1.1.0', 'm119851.1.1.0', 'm119851.1.2.0', 'm119851.1.2.0', 'm119851.1.2.0', 'm119851.2.2.2'], 'monogenic': 0, 'num_ram': 3, 'r2': 5, 'ramps': [5, 151, 119851], 'rd': 13.1977916845, 'regulator': {'__RealLiteral__': 0, 'data': '448.860326258', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '1.-3.-2.7.3.-3.-3.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{56}{59} a^{15} - \\frac{366}{59} a^{14} + \\frac{831}{59} a^{13} - \\frac{808}{59} a^{12} + \\frac{211}{59} a^{11} + \\frac{682}{59} a^{10} - \\frac{1649}{59} a^{9} + \\frac{2252}{59} a^{8} - \\frac{2264}{59} a^{7} + \\frac{1506}{59} a^{6} - \\frac{675}{59} a^{5} - \\frac{365}{59} a^{4} + \\frac{764}{59} a^{3} - \\frac{747}{59} a^{2} + \\frac{233}{59} a - \\frac{71}{59} \\)', '\\( \\frac{3}{59} a^{15} - \\frac{47}{59} a^{14} + \\frac{290}{59} a^{13} - \\frac{785}{59} a^{12} + \\frac{910}{59} a^{11} - \\frac{328}{59} a^{10} - \\frac{593}{59} a^{9} + \\frac{1642}{59} a^{8} - \\frac{2279}{59} a^{7} + \\frac{2388}{59} a^{6} - \\frac{1567}{59} a^{5} + \\frac{719}{59} a^{4} + \\frac{357}{59} a^{3} - \\frac{846}{59} a^{2} + \\frac{829}{59} a - \\frac{283}{59} \\)', '\\( \\frac{50}{59} a^{15} - \\frac{213}{59} a^{14} + \\frac{133}{59} a^{13} + \\frac{349}{59} a^{12} - \\frac{665}{59} a^{11} + \\frac{630}{59} a^{10} - \\frac{286}{59} a^{9} - \\frac{206}{59} a^{8} + \\frac{937}{59} a^{7} - \\frac{1087}{59} a^{6} + \\frac{1043}{59} a^{5} - \\frac{564}{59} a^{4} + \\frac{50}{59} a^{3} + \\frac{532}{59} a^{2} - \\frac{481}{59} a + \\frac{141}{59} \\)', '\\( \\frac{79}{59} a^{15} - \\frac{516}{59} a^{14} + \\frac{1304}{59} a^{13} - \\frac{1762}{59} a^{12} + \\frac{1087}{59} a^{11} + \\frac{690}{59} a^{10} - \\frac{2709}{59} a^{9} + \\frac{4461}{59} a^{8} - \\frac{4905}{59} a^{7} + \\frac{3967}{59} a^{6} - \\frac{1965}{59} a^{5} + a^{4} + \\frac{1491}{59} a^{3} - \\frac{1795}{59} a^{2} + \\frac{1141}{59} a - \\frac{280}{59} \\)', '\\( a \\)', '\\( a - 1 \\)', '\\( \\frac{30}{59} a^{15} - \\frac{133}{59} a^{14} + \\frac{127}{59} a^{13} + \\frac{45}{59} a^{12} - \\frac{135}{59} a^{11} + \\frac{203}{59} a^{10} - \\frac{205}{59} a^{9} + \\frac{204}{59} a^{8} - \\frac{74}{59} a^{7} + \\frac{53}{59} a^{6} + \\frac{26}{59} a^{5} - \\frac{65}{59} a^{4} - \\frac{1}{59} a^{3} + \\frac{25}{59} a^{2} + \\frac{30}{59} a - \\frac{74}{59} \\)', '\\( \\frac{102}{59} a^{15} - \\frac{829}{59} a^{14} + \\frac{2544}{59} a^{13} - \\frac{3703}{59} a^{12} + \\frac{2346}{59} a^{11} + \\frac{1092}{59} a^{10} - \\frac{5263}{59} a^{9} + \\frac{8679}{59} a^{8} - \\frac{9886}{59} a^{7} + 136 a^{6} - \\frac{4159}{59} a^{5} + \\frac{110}{59} a^{4} + \\frac{2955}{59} a^{3} - \\frac{3653}{59} a^{2} + \\frac{2226}{59} a - \\frac{475}{59} \\)', '\\( \\frac{66}{59} a^{15} - \\frac{399}{59} a^{14} + \\frac{952}{59} a^{13} - \\frac{1356}{59} a^{12} + \\frac{993}{59} a^{11} + \\frac{355}{59} a^{10} - \\frac{1994}{59} a^{9} + \\frac{3494}{59} a^{8} - \\frac{3902}{59} a^{7} + \\frac{3504}{59} a^{6} - \\frac{1828}{59} a^{5} + \\frac{261}{59} a^{4} + \\frac{1099}{59} a^{3} - \\frac{1400}{59} a^{2} + \\frac{1069}{59} a - \\frac{340}{59} \\)', '\\( \\frac{126}{59} a^{15} - \\frac{682}{59} a^{14} + \\frac{1147}{59} a^{13} - \\frac{628}{59} a^{12} - \\frac{488}{59} a^{11} + \\frac{1648}{59} a^{10} - \\frac{2402}{59} a^{9} + \\frac{2613}{59} a^{8} - \\frac{1689}{59} a^{7} + \\frac{492}{59} a^{6} + \\frac{645}{59} a^{5} - \\frac{1224}{59} a^{4} + \\frac{1184}{59} a^{3} - \\frac{417}{59} a^{2} - \\frac{228}{59} a + \\frac{203}{59} \\)'], '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', '1/59*a^14 + 18/59*a^12 - 19/59*a^11 - 14/59*a^10 - 14/59*a^9 - 4/59*a^8 - 7/59*a^7 - 4/59*a^6 - 14/59*a^5 - 14/59*a^4 - 19/59*a^3 + 18/59*a^2 + 1/59', '1/59*a^15 + 18/59*a^13 - 19/59*a^12 - 14/59*a^11 - 14/59*a^10 - 4/59*a^9 - 7/59*a^8 - 4/59*a^7 - 14/59*a^6 - 14/59*a^5 - 19/59*a^4 + 18/59*a^3 + 1/59*a']}