-
nf_fields • Show schema
Hide schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [16, 72, -116, 106, -51, 41, -18, 6, -2, 1], 'conductor': 0, 'degree': 9, 'dirichlet_group': [], 'disc_abs': 25311454040401, 'disc_rad': 2243, 'disc_sign': 1, 'frobs': [[2, [[4, 1], [3, 1], [2, 1]]], [3, [[9, 1]]], [5, [[6, 1], [2, 1], [1, 1]]], [7, [[9, 1]]], [11, [[2, 2], [1, 5]]], [13, [[4, 1], [2, 1], [1, 3]]], [17, [[9, 1]]], [19, [[4, 1], [2, 1], [1, 3]]], [23, [[4, 1], [3, 1], [2, 1]]], [29, [[4, 1], [3, 1], [2, 1]]], [31, [[9, 1]]], [37, [[4, 1], [2, 1], [1, 3]]], [41, [[6, 1], [2, 1], [1, 1]]], [43, [[3, 1], [2, 2], [1, 2]]], [47, [[4, 1], [3, 1], [2, 1]]], [53, [[3, 1], [2, 2], [1, 2]]], [59, [[6, 1], [2, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [324], 'galois_label': '9T30', 'galt': 30, 'grd': 47.36032094485847, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '9.1.25311454040401.1', 'local_algs': ['m2243.1.1.0', 'm2243.2.1.1', 'm2243.2.3.3'], 'monogenic': 0, 'num_ram': 1, 'r2': 4, 'ramps': [2243], 'rd': 30.8501624254, 'regulator': {'__RealLiteral__': 0, 'data': '1247.05475721', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['4.7.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1017}{33704} a^{8} - \\frac{717}{8426} a^{7} + \\frac{3705}{16852} a^{6} - \\frac{8463}{16852} a^{5} + \\frac{34997}{33704} a^{4} - \\frac{36821}{33704} a^{3} + \\frac{7177}{4213} a^{2} - \\frac{7875}{4213} a + \\frac{6663}{4213} \\)', '\\( \\frac{1795}{33704} a^{8} - \\frac{117}{4213} a^{7} + \\frac{2637}{16852} a^{6} - \\frac{8773}{16852} a^{5} + \\frac{31711}{33704} a^{4} - \\frac{83}{33704} a^{3} + \\frac{9693}{4213} a^{2} + \\frac{201}{8426} a - \\frac{593}{4213} \\)', '\\( \\frac{895}{33704} a^{8} - \\frac{457}{8426} a^{7} + \\frac{775}{16852} a^{6} - \\frac{6205}{16852} a^{5} + \\frac{1635}{33704} a^{4} - \\frac{12387}{33704} a^{3} + \\frac{620}{4213} a^{2} - \\frac{965}{4213} a - \\frac{636}{4213} \\)', '\\( \\frac{103}{16852} a^{8} + \\frac{1263}{16852} a^{7} - \\frac{179}{4213} a^{6} + \\frac{808}{4213} a^{5} - \\frac{8991}{16852} a^{4} + \\frac{4771}{4213} a^{3} - \\frac{13245}{16852} a^{2} + \\frac{1321}{8426} a + \\frac{169}{4213} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^2 - 1/2*a', '1/4*a^7 - 1/2*a^5 - 1/2*a^4 + 1/4*a^3 - 1/4*a^2', '1/33704*a^8 + 68/4213*a^7 - 3153/16852*a^6 - 2643/16852*a^5 + 12429/33704*a^4 + 11679/33704*a^3 + 848/4213*a^2 - 873/8426*a + 1821/4213']}