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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -7, 0, 329, 0, 2051, 0, 5144, 0, 7007, 0, 5733, 0, 2940, 0, 952, 0, 189, 0, 21, 0, 1], 'conductor': 0, 'degree': 21, 'dirichlet_group': [], 'disc_abs': 39987268032456435383175526376221, 'disc_rad': 16261, 'disc_sign': 1, 'frobs': [[2, [[6, 3], [3, 1]]], [3, [[21, 1]]], [5, [[12, 1], [3, 2], [2, 1], [1, 1]]], [7, [0]], [11, [[6, 3], [2, 1], [1, 1]]], [13, [[6, 3], [3, 1]]], [17, [[12, 1], [3, 2], [2, 1], [1, 1]]], [19, [[12, 1], [3, 2], [2, 1], [1, 1]]], [23, [0]], [29, [[6, 3], [3, 1]]], [31, [[6, 3], [3, 1]]], [37, [[6, 2], [3, 2], [2, 1], [1, 1]]], [41, [[21, 1]]], [43, [[4, 3], [2, 4], [1, 1]]], [47, [[6, 3], [3, 1]]], [53, [[6, 3], [2, 1], [1, 1]]], [59, [[6, 2], [3, 2], [1, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [57288, 24696, 24696], 'galois_label': '21T87', 'galt': 87, 'grd': 460.4933384155175, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '21.1.39987268032456435383175526376221.1', 'local_algs': ['7.1.0.1', '7.6.5.5', '7.14.14.13', '23.1.0.1', '23.2.1.2', '23.3.0.1', '23.3.0.1', '23.6.3.2', '23.6.3.2', '101.1.0.1', '101.1.0.1', '101.1.0.1', '101.6.3.2', '101.6.0.1', '101.6.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 10, 'ramps': [7, 23, 101], 'rd': 31.9781559319, 'regulator': {'__RealLiteral__': 0, 'data': '28539748.2764', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1.0.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{14} + 14 a^{12} + 77 a^{10} + 210 a^{8} + 294 a^{6} + 196 a^{4} + 49 a^{2} - 1 \\)', '\\( a \\)', '\\( \\frac{1}{7} a^{20} - \\frac{2}{7} a^{19} + \\frac{25}{7} a^{18} - \\frac{36}{7} a^{17} + \\frac{261}{7} a^{16} - \\frac{270}{7} a^{15} + \\frac{1492}{7} a^{14} - \\frac{1094}{7} a^{13} + \\frac{5128}{7} a^{12} - \\frac{2605}{7} a^{11} + \\frac{10929}{7} a^{10} - \\frac{3749}{7} a^{9} + \\frac{14351}{7} a^{8} - \\frac{3306}{7} a^{7} + \\frac{11140}{7} a^{6} - \\frac{1840}{7} a^{5} + \\frac{4646}{7} a^{4} - \\frac{640}{7} a^{3} + \\frac{797}{7} a^{2} - \\frac{110}{7} a + \\frac{3}{7} \\)', '\\( \\frac{5}{7} a^{20} - \\frac{3}{7} a^{19} + \\frac{90}{7} a^{18} - \\frac{54}{7} a^{17} + \\frac{668}{7} a^{16} - \\frac{405}{7} a^{15} + \\frac{2630}{7} a^{14} - \\frac{1641}{7} a^{13} + \\frac{5872}{7} a^{12} - \\frac{3897}{7} a^{11} + \\frac{7325}{7} a^{10} - \\frac{5508}{7} a^{9} + \\frac{4583}{7} a^{8} - \\frac{4497}{7} a^{7} + \\frac{897}{7} a^{6} - \\frac{1948}{7} a^{5} - \\frac{325}{7} a^{4} - \\frac{358}{7} a^{3} - \\frac{117}{7} a^{2} - \\frac{11}{7} a + \\frac{1}{7} \\)', '\\( \\frac{1}{7} a^{20} - \\frac{2}{7} a^{19} + \\frac{18}{7} a^{18} - \\frac{36}{7} a^{17} + \\frac{135}{7} a^{16} - \\frac{270}{7} a^{15} + \\frac{540}{7} a^{14} - \\frac{1087}{7} a^{13} + \\frac{1201}{7} a^{12} - \\frac{2507}{7} a^{11} + \\frac{1290}{7} a^{10} - \\frac{3217}{7} a^{9} - \\frac{41}{7} a^{8} - \\frac{1906}{7} a^{7} - \\frac{1649}{7} a^{6} - \\frac{27}{7} a^{5} - \\frac{1570}{7} a^{4} + \\frac{389}{7} a^{3} - \\frac{456}{7} a^{2} + \\frac{86}{7} a - \\frac{4}{7} \\)', '\\( \\frac{1}{7} a^{20} + \\frac{5}{7} a^{19} + \\frac{18}{7} a^{18} + \\frac{90}{7} a^{17} + \\frac{135}{7} a^{16} + \\frac{675}{7} a^{15} + \\frac{547}{7} a^{14} + \\frac{2728}{7} a^{13} + \\frac{1299}{7} a^{12} + \\frac{6411}{7} a^{11} + \\frac{1836}{7} a^{10} + \\frac{8795}{7} a^{9} + \\frac{1499}{7} a^{8} + \\frac{6641}{7} a^{7} + \\frac{647}{7} a^{6} + \\frac{2269}{7} a^{5} + \\frac{103}{7} a^{4} + \\frac{18}{7} a^{3} - \\frac{29}{7} a^{2} - \\frac{124}{7} a - \\frac{18}{7} \\)', '\\( \\frac{4}{7} a^{20} - \\frac{8}{7} a^{19} + \\frac{79}{7} a^{18} - \\frac{144}{7} a^{17} + \\frac{659}{7} a^{16} - \\frac{1080}{7} a^{15} + \\frac{3028}{7} a^{14} - \\frac{4369}{7} a^{13} + \\frac{8395}{7} a^{12} - \\frac{10315}{7} a^{11} + \\frac{14505}{7} a^{10} - \\frac{14373}{7} a^{9} + \\frac{15628}{7} a^{8} - \\frac{11390}{7} a^{7} + \\frac{10197}{7} a^{6} - \\frac{4609}{7} a^{5} + \\frac{3681}{7} a^{4} - \\frac{621}{7} a^{3} + \\frac{570}{7} a^{2} + \\frac{64}{7} a + \\frac{12}{7} \\)', '\\( \\frac{4}{7} a^{20} + \\frac{6}{7} a^{19} + \\frac{72}{7} a^{18} + \\frac{108}{7} a^{17} + \\frac{540}{7} a^{16} + \\frac{817}{7} a^{15} + \\frac{2181}{7} a^{14} + \\frac{3373}{7} a^{13} + \\frac{5112}{7} a^{12} + \\frac{8256}{7} a^{11} + \\frac{6959}{7} a^{10} + \\frac{12185}{7} a^{9} + \\frac{5142}{7} a^{8} + \\frac{10562}{7} a^{7} + \\frac{1622}{7} a^{6} + \\frac{4981}{7} a^{5} - \\frac{92}{7} a^{4} + \\frac{1031}{7} a^{3} - \\frac{123}{7} a^{2} + \\frac{22}{7} a - \\frac{2}{7} \\)', '\\( \\frac{2}{7} a^{20} - \\frac{4}{7} a^{19} + \\frac{36}{7} a^{18} - \\frac{86}{7} a^{17} + \\frac{263}{7} a^{16} - \\frac{778}{7} a^{15} + \\frac{975}{7} a^{14} - \\frac{3847}{7} a^{13} + \\frac{1779}{7} a^{12} - \\frac{11286}{7} a^{11} + \\frac{753}{7} a^{10} - \\frac{19902}{7} a^{9} - \\frac{2714}{7} a^{8} - \\frac{20297}{7} a^{7} - \\frac{4677}{7} a^{6} - \\frac{10736}{7} a^{5} - \\frac{2741}{7} a^{4} - \\frac{2204}{7} a^{3} - \\frac{513}{7} a^{2} + \\frac{46}{7} a + \\frac{41}{7} \\)', '\\( \\frac{10}{7} a^{20} + \\frac{1}{7} a^{19} + \\frac{208}{7} a^{18} + \\frac{32}{7} a^{17} + \\frac{1854}{7} a^{16} + \\frac{366}{7} a^{15} + \\frac{9236}{7} a^{14} + \\frac{2122}{7} a^{13} + \\frac{28117}{7} a^{12} + \\frac{7032}{7} a^{11} + \\frac{53731}{7} a^{10} + \\frac{13848}{7} a^{9} + \\frac{63780}{7} a^{8} + \\frac{16073}{7} a^{7} + \\frac{44977}{7} a^{6} + \\frac{10496}{7} a^{5} + \\frac{17158}{7} a^{4} + \\frac{3533}{7} a^{3} + \\frac{2769}{7} a^{2} + \\frac{475}{7} a + \\frac{37}{7} \\)'], 'used_grh': True, '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', 'a^15', 'a^16', 'a^17', 'a^18', 'a^19', '1/7*a^20 - 2/7*a^19 - 3/7*a^18 - 1/7*a^17 + 2/7*a^16 + 3/7*a^15 + 1/7*a^14 - 2/7*a^13 - 3/7*a^12 - 1/7*a^11 + 2/7*a^10 + 3/7*a^9 + 1/7*a^8 - 2/7*a^7 + 3/7*a^6 + 1/7*a^5 - 2/7*a^4 - 3/7*a^3 - 1/7*a^2 + 2/7*a + 3/7']}