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nf_fields • Show schema
{'class_group': [6], 'class_number': 6, 'cm': False, 'coeffs': [5832, 0, 0, 0, 0, 0, 3996, 0, 0, 0, 0, 0, -58, 0, 0, 0, 0, 0, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 414563852462258547447973281792, 'disc_rad': 42, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[2, 9]]], [7, [0]], [11, [[2, 8], [1, 2]]], [13, [[6, 3]]], [17, [[2, 8], [1, 2]]], [19, [[3, 6]]], [23, [[2, 9]]], [29, [[2, 9]]], [31, [[6, 3]]], [37, [[6, 3]]], [41, [[2, 8], [1, 2]]], [43, [[3, 6]]], [47, [[2, 9]]], [53, [[2, 9]]], [59, [[2, 8], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [66, 42, 24], 'galois_label': '18T12', 'galt': 12, 'grd': 46.98167351748441, 'inessentialp': [3], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '18.0.414563852462258547447973281792.2', 'local_algs': ['2.1.6.11a1.1', '2.2.6.22a1.1', '3.1.3.3a1.1', '3.1.3.3a1.1', '3.1.6.7a1.1', '3.1.6.7a1.1', '7.6.3.12a1.3'], 'maximal_cm_subfield': [2, 0, 1], 'monogenic': -1, 'narrow_class_group': [6], 'narrow_class_number': 6, 'num_ram': 3, 'r2': 9, 'ramps': [2, 3, 7], 'rd': 44.1999467562, 'regulator': {'__RealLiteral__': 0, 'data': '50024296.556075595', 'prec': 60}, 'res': {'sib': ['-384,0,768,0,-5760,0,3268,0,-2472,0,888,0,-332,0,60,0,-12,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['2.0.1', '-7.0.0.1', '-2.0.0.1', '1.5.-1.1', '-14.0.0.1', '57.84.12.-14.6.0.1', '98.0.0.0.0.0.1', '2.0.0.0.0.0.1', '204.168.12.-28.6.0.1', '27.0.0.27.0.0.-5.0.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{19}{87480} a^{16} - \\frac{121}{8748} a^{10} + \\frac{394}{405} a^{4} - 1 \\)', '\\( \\frac{11}{524880} a^{16} - \\frac{5}{17496} a^{14} - \\frac{7}{14580} a^{12} - \\frac{67}{26244} a^{10} + \\frac{43}{2187} a^{8} + \\frac{19}{1458} a^{6} + \\frac{757}{4860} a^{4} - \\frac{187}{162} a^{2} - \\frac{224}{135} \\)', '\\( \\frac{1}{9720} a^{12} + \\frac{8}{243} a^{6} - \\frac{13}{90} \\)', '\\( \\frac{103}{524880} a^{17} + \\frac{19}{87480} a^{16} - \\frac{13}{29160} a^{14} - \\frac{7}{14580} a^{13} - \\frac{74}{6561} a^{11} - \\frac{121}{8748} a^{10} + \\frac{35}{1458} a^{8} + \\frac{19}{1458} a^{7} + \\frac{3971}{4860} a^{5} + \\frac{394}{405} a^{4} - \\frac{371}{270} a^{2} - \\frac{224}{135} a - 1 \\)', '\\( \\frac{13}{34992} a^{16} - \\frac{175}{8748} a^{10} + \\frac{479}{324} a^{4} - 2 \\)', '\\( \\frac{433}{524880} a^{17} + \\frac{7}{7290} a^{16} + \\frac{11}{10935} a^{15} + \\frac{1}{1080} a^{14} - \\frac{2}{3645} a^{13} + \\frac{1}{4860} a^{12} - \\frac{667}{13122} a^{11} - \\frac{157}{2916} a^{10} - \\frac{293}{4374} a^{9} - \\frac{1}{27} a^{8} - \\frac{13}{1458} a^{7} + \\frac{16}{243} a^{6} + \\frac{16241}{4860} a^{5} + \\frac{1061}{270} a^{4} + \\frac{1723}{405} a^{3} + \\frac{91}{30} a^{2} - \\frac{31}{135} a - \\frac{148}{45} \\)', '\\( \\frac{49}{87480} a^{17} + \\frac{173}{524880} a^{16} + \\frac{17}{43740} a^{15} + \\frac{5}{8748} a^{14} - \\frac{1}{5832} a^{13} - \\frac{59}{29160} a^{12} - \\frac{295}{8748} a^{11} - \\frac{391}{26244} a^{10} - \\frac{127}{8748} a^{9} - \\frac{86}{2187} a^{8} - \\frac{40}{729} a^{7} + \\frac{14}{729} a^{6} + \\frac{949}{405} a^{5} + \\frac{5671}{4860} a^{4} + \\frac{503}{810} a^{3} + \\frac{25}{81} a^{2} - \\frac{77}{54} a - \\frac{943}{270} \\)', '\\( \\frac{119}{43740} a^{15} + \\frac{47}{1215} a^{12} + \\frac{1541}{8748} a^{9} - \\frac{59}{486} a^{6} - \\frac{619}{810} a^{3} + \\frac{76}{45} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6', '1/2*a^7', '1/12*a^8 + 1/6*a^2', '1/12*a^9 + 1/6*a^3', '1/36*a^10 + 7/18*a^4', '1/108*a^11 - 1/36*a^9 - 1/6*a^7 + 25/54*a^5 - 7/18*a^3 - 1/3*a', '1/9720*a^12 + 8/243*a^6 - 13/90', '1/29160*a^13 + 259/1458*a^7 - 103/270*a', '1/29160*a^14 + 8/729*a^8 + 77/270*a^2', '1/87480*a^15 - 211/8748*a^9 + 16/405*a^3', '1/524880*a^16 + 1/87480*a^14 - 1/29160*a^12 + 259/26244*a^10 - 211/8748*a^8 - 259/1458*a^6 - 1453/4860*a^4 + 16/405*a^2 + 103/270', '1/524880*a^17 + 4/6561*a^11 + 1/36*a^9 + 1/6*a^7 + 1157/4860*a^5 + 7/18*a^3 + 1/3*a']}
Number field data - 18.0.414563852462258547447973281792.2