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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-2, 4, 0, 12, 0, 0, -18, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 17, 'dirichlet_group': [], 'disc_abs': 63885424359899999574753280, 'disc_rad': 1949628428952026354210, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[17, 1]]], [5, [0]], [7, [0]], [11, [[11, 1], [4, 1], [2, 1]]], [13, [[13, 1], [4, 1]]], [17, [[8, 2], [1, 1]]], [19, [[12, 1], [5, 1]]], [23, [[7, 1], [4, 1], [3, 1], [2, 1], [1, 1]]], [29, [[7, 2], [1, 3]]], [31, [[17, 1]]], [37, [[9, 1], [4, 1], [2, 2]]], [41, [[16, 1], [1, 1]]], [43, [[15, 1], [2, 1]]], [47, [[8, 1], [5, 1], [2, 1], [1, 2]]], [53, [[9, 1], [5, 1], [2, 1], [1, 1]]], [59, [[10, 1], [5, 1], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_label': '17T10', 'galt': 10, 'index': 1, 'inessentialp': [], 'is_galois': False, 'iso_number': 1, 'label': '17.1.63885424359899999574753280.1', 'local_algs': ['2.17.16.1', '5.2.1.2', '5.3.0.1', '5.12.0.1', '7.1.0.1', '7.2.1.2', '7.14.0.1', 'm27851834699314662203.1.2.0', 'm27851834699314662203.2.1.1', 'm27851834699314662203.1.6.0', 'm27851834699314662203.1.7.0'], 'monogenic': 0, 'num_ram': 4, 'r2': 8, 'ramps': [2, 5, 7, 27851834699314662203], 'rd': 32.9583006276, 'regulator': {'__RealLiteral__': 0, 'data': '2034427.1525', 'prec': 40}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a - 1 \\)', '\\( \\frac{57592}{367423} a^{16} + \\frac{26150}{367423} a^{15} + \\frac{13124}{367423} a^{14} + \\frac{54190}{367423} a^{13} + \\frac{26213}{367423} a^{12} + \\frac{74360}{367423} a^{11} + \\frac{53056}{367423} a^{10} + \\frac{26234}{367423} a^{9} + \\frac{325140}{367423} a^{8} + \\frac{157278}{367423} a^{7} + \\frac{78737}{367423} a^{6} - \\frac{718320}{367423} a^{5} - \\frac{313296}{367423} a^{4} - \\frac{35023}{367423} a^{3} + \\frac{4536}{52489} a^{2} - \\frac{84}{52489} a + \\frac{26255}{367423} \\)', '\\( \\frac{152392}{367423} a^{16} + \\frac{106044}{367423} a^{15} + \\frac{38861}{367423} a^{14} + \\frac{33301}{367423} a^{13} + \\frac{87837}{367423} a^{12} - \\frac{22039}{367423} a^{11} - \\frac{6396}{367423} a^{10} + \\frac{81768}{367423} a^{9} + \\frac{567229}{367423} a^{8} + \\frac{527022}{367423} a^{7} + \\frac{235189}{367423} a^{6} - \\frac{2781432}{367423} a^{5} - \\frac{1418184}{367423} a^{4} - \\frac{586109}{367423} a^{3} + \\frac{211277}{52489} a^{2} + \\frac{76765}{52489} a + \\frac{810545}{367423} \\)', '\\( \\frac{8748}{52489} a^{16} - \\frac{162}{52489} a^{15} + \\frac{3}{52489} a^{14} + \\frac{2916}{52489} a^{13} - \\frac{54}{52489} a^{12} + \\frac{1}{52489} a^{11} + \\frac{972}{52489} a^{10} - \\frac{18}{52489} a^{9} + \\frac{17496}{52489} a^{8} - \\frac{324}{52489} a^{7} + \\frac{6}{52489} a^{6} - \\frac{151632}{52489} a^{5} - \\frac{49681}{52489} a^{4} - \\frac{52}{52489} a^{3} + \\frac{106921}{52489} a^{2} + \\frac{51481}{52489} a + \\frac{52507}{52489} \\)', '\\( \\frac{14904}{52489} a^{16} - \\frac{276}{52489} a^{15} - \\frac{5827}{52489} a^{14} + \\frac{4968}{52489} a^{13} - \\frac{92}{52489} a^{12} + \\frac{15554}{52489} a^{11} + \\frac{1656}{52489} a^{10} - \\frac{17527}{52489} a^{9} + \\frac{82297}{52489} a^{8} - \\frac{552}{52489} a^{7} - \\frac{11654}{52489} a^{6} - \\frac{205847}{52489} a^{5} - \\frac{47705}{52489} a^{4} + \\frac{135994}{52489} a^{3} + \\frac{145225}{52489} a^{2} - \\frac{36710}{52489} a - \\frac{87451}{52489} \\)', '\\( \\frac{299088}{367423} a^{16} + \\frac{239410}{367423} a^{15} + \\frac{22783}{367423} a^{14} + \\frac{47207}{367423} a^{13} + \\frac{114796}{367423} a^{12} + \\frac{147565}{367423} a^{11} + \\frac{85721}{367423} a^{10} + \\frac{73258}{367423} a^{9} + \\frac{1385511}{367423} a^{8} + \\frac{1056199}{367423} a^{7} + \\frac{150544}{367423} a^{6} - \\frac{4869258}{367423} a^{5} - \\frac{3869832}{367423} a^{4} + \\frac{357437}{367423} a^{3} + \\frac{475812}{52489} a^{2} + \\frac{166152}{52489} a - \\frac{335703}{367423} \\)', '\\( \\frac{148685}{367423} a^{16} + \\frac{72092}{367423} a^{15} + \\frac{53098}{367423} a^{14} + \\frac{67058}{367423} a^{13} + \\frac{94016}{367423} a^{12} + \\frac{52692}{367423} a^{11} + \\frac{39849}{367423} a^{10} + \\frac{101324}{367423} a^{9} + \\frac{769771}{367423} a^{8} + \\frac{196673}{367423} a^{7} + \\frac{316152}{367423} a^{6} - \\frac{2069813}{367423} a^{5} - \\frac{1057135}{367423} a^{4} - \\frac{640424}{367423} a^{3} + \\frac{108836}{52489} a^{2} + \\frac{23257}{52489} a + \\frac{476055}{367423} \\)', '\\( \\frac{21780}{52489} a^{16} + \\frac{17093}{52489} a^{15} + \\frac{27872}{52489} a^{14} + \\frac{7260}{52489} a^{13} + \\frac{23194}{52489} a^{12} + \\frac{26787}{52489} a^{11} + \\frac{2420}{52489} a^{10} + \\frac{42724}{52489} a^{9} + \\frac{96049}{52489} a^{8} + \\frac{86675}{52489} a^{7} + \\frac{160722}{52489} a^{6} - \\frac{377520}{52489} a^{5} - \\frac{156308}{52489} a^{4} - \\frac{395633}{52489} a^{3} + \\frac{188009}{52489} a^{2} - \\frac{74439}{52489} a + \\frac{114743}{52489} \\)'], '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', '1/367423*a^16 - 156495/367423*a^15 + 104960/367423*a^14 - 69985/367423*a^13 + 157791/367423*a^12 - 104984/367423*a^11 + 151635/367423*a^10 - 104870/367423*a^9 - 52487/367423*a^8 - 155523/367423*a^7 + 104942/367423*a^6 + 174946/367423*a^5 - 16848/367423*a^4 + 312/367423*a^3 + 5833/52489*a^2 + 864/52489*a - 108/367423']}
Number field data - 17.1.63885424359899999574753280.1