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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 12, 66, 208, 404, 472, 250, -120, -287, -152, 38, 80, 24, -12, -8, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 103670069459943424, 'disc_rad': 34, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[4, 4]]], [5, [[4, 4]]], [7, [[4, 4]]], [11, [[4, 4]]], [13, [[2, 8]]], [17, [0]], [19, [[2, 8]]], [23, [[4, 4]]], [29, [[4, 4]]], [31, [[4, 4]]], [37, [[4, 4]]], [41, [[2, 6], [1, 4]]], [43, [[2, 8]]], [47, [[2, 8]]], [53, [[2, 8]]], [59, [[2, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [64, 16], 'galois_label': '16T46', 'galt': 46, 'grd': 16.492422502470642, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '16.0.103670069459943424.1', 'local_algs': ['2.8.16.6', '2.8.16.6', '17.2.1.2', '17.2.1.2', '17.2.0.1', '17.2.0.1', '17.4.2.1', '17.4.2.1'], 'minimal_sibling': [1, 0, 1, 0, -2, 0, 1, 0, 1], 'monogenic': -1, 'num_ram': 2, 'r2': 8, 'ramps': [2, 17], 'rd': 11.5738629877, 'regulator': {'__RealLiteral__': 0, 'data': '312.978531942', 'prec': 44}, 'res': {'gal': ['1,0,0,0,-3,0,0,0,98,0,0,0,-765,0,0,0,2362,0,0,0,-765,0,0,0,98,0,0,0,-3,0,0,0,1'], 'sib': ['1,0,-1,0,-2,0,-1,0,1', '1,0,-10,0,26,0,-32,0,31,0,-32,0,26,0,-10,0,1', '1,0,-2,0,-14,0,-2,0,1', '1,0,-3,0,0,0,-3,0,1', '1,0,0,0,5,0,0,0,4,0,0,0,5,0,0,0,1', '1,0,0,0,9,0,0,0,-16,0,0,0,9,0,0,0,1', '1,0,1,0,-2,0,1,0,1', '1,0,10,0,26,0,32,0,31,0,32,0,26,0,10,0,1', '1,0,2,0,-14,0,2,0,1', '16,0,-18,0,13,0,-4,0,1', '16,0,18,0,13,0,4,0,1', '2,-10,19,-22,22,-16,10,-4,1', '4,0,-20,0,49,0,38,0,16,0,12,0,-4,0,-2,0,1', '4,0,20,0,49,0,-38,0,16,0,-12,0,-4,0,2,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['1.0.1', '2.0.1', '-2.0.1', '6.-4.-2.0.1', '3.-2.1.-2.1', '17.0.-8.0.1', '1.-2.1.0.1', '2.-4.5.-2.1', '1.0.0.0.1', '2.-4.-6.0.1', '2.-12.30.-44.43.-28.14.-4.1', '1.-4.8.-4.-7.8.2.-4.1', '1.0.-4.0.7.0.-4.0.1'], 'torsion_gen': '\\( \\frac{17183}{1784} a^{15} - \\frac{1987}{446} a^{14} - \\frac{133437}{1784} a^{13} - \\frac{144681}{1784} a^{12} + 267 a^{11} + \\frac{1152309}{1784} a^{10} + \\frac{131513}{1784} a^{9} - \\frac{1325499}{892} a^{8} - \\frac{8327}{4} a^{7} - \\frac{403063}{1784} a^{6} + \\frac{4426863}{1784} a^{5} + \\frac{761213}{223} a^{4} + \\frac{4220499}{1784} a^{3} + \\frac{1706743}{1784} a^{2} + \\frac{191623}{892} a + \\frac{38265}{1784} \\)', 'torsion_order': 8, 'units': ['\\( \\frac{381}{223} a^{15} - \\frac{941}{446} a^{14} - \\frac{10541}{892} a^{13} - \\frac{1104}{223} a^{12} + \\frac{209}{4} a^{11} + \\frac{33085}{446} a^{10} - \\frac{22017}{446} a^{9} - \\frac{102713}{446} a^{8} - \\frac{739}{4} a^{7} + \\frac{53733}{446} a^{6} + \\frac{79681}{223} a^{5} + \\frac{141983}{446} a^{4} + \\frac{134373}{892} a^{3} + \\frac{6836}{223} a^{2} - \\frac{2191}{892} a - \\frac{1207}{446} \\)', '\\( \\frac{12245}{1784} a^{15} - \\frac{1743}{446} a^{14} - \\frac{93819}{1784} a^{13} - \\frac{93365}{1784} a^{12} + \\frac{387}{2} a^{11} + \\frac{780461}{1784} a^{10} + \\frac{25963}{1784} a^{9} - \\frac{928891}{892} a^{8} - \\frac{5495}{4} a^{7} - \\frac{110215}{1784} a^{6} + \\frac{3064093}{1784} a^{5} + \\frac{502898}{223} a^{4} + \\frac{2722085}{1784} a^{3} + \\frac{1089743}{1784} a^{2} + \\frac{124547}{892} a + \\frac{26317}{1784} \\)', '\\( \\frac{8223}{1784} a^{15} - \\frac{9181}{1784} a^{14} - \\frac{29079}{892} a^{13} - \\frac{30807}{1784} a^{12} + \\frac{1123}{8} a^{11} + \\frac{194005}{892} a^{10} - \\frac{201905}{1784} a^{9} - \\frac{1149031}{1784} a^{8} - \\frac{4519}{8} a^{7} + \\frac{64198}{223} a^{6} + \\frac{1798731}{1784} a^{5} + \\frac{1684867}{1784} a^{4} + \\frac{424851}{892} a^{3} + \\frac{239733}{1784} a^{2} + \\frac{39163}{1784} a + \\frac{815}{446} \\)', '\\( \\frac{9037}{1784} a^{15} - \\frac{6133}{1784} a^{14} - \\frac{16997}{446} a^{13} - \\frac{62103}{1784} a^{12} + \\frac{1155}{8} a^{11} + \\frac{272503}{892} a^{10} - \\frac{23023}{1784} a^{9} - \\frac{1339419}{1784} a^{8} - \\frac{7499}{8} a^{7} + \\frac{4295}{446} a^{6} + \\frac{2178361}{1784} a^{5} + \\frac{2760935}{1784} a^{4} + \\frac{460595}{446} a^{3} + \\frac{736217}{1784} a^{2} + \\frac{171659}{1784} a + \\frac{2586}{223} \\)', '\\( \\frac{4981}{1784} a^{15} - \\frac{3291}{1784} a^{14} - \\frac{18629}{892} a^{13} - \\frac{35281}{1784} a^{12} + \\frac{625}{8} a^{11} + \\frac{151295}{892} a^{10} + \\frac{2041}{1784} a^{9} - \\frac{727821}{1784} a^{8} - \\frac{4253}{8} a^{7} - \\frac{5808}{223} a^{6} + \\frac{1182797}{1784} a^{5} + \\frac{1581641}{1784} a^{4} + \\frac{550841}{892} a^{3} + \\frac{451235}{1784} a^{2} + \\frac{98053}{1784} a + \\frac{1023}{223} \\)', '\\( \\frac{9935}{1784} a^{15} - \\frac{4273}{892} a^{14} - \\frac{73047}{1784} a^{13} - \\frac{55167}{1784} a^{12} + \\frac{655}{4} a^{11} + \\frac{545709}{1784} a^{10} - \\frac{120391}{1784} a^{9} - \\frac{180527}{223} a^{8} - 885 a^{7} + \\frac{289189}{1784} a^{6} + \\frac{2323579}{1784} a^{5} + \\frac{1307217}{892} a^{4} + \\frac{1575561}{1784} a^{3} + \\frac{559217}{1784} a^{2} + \\frac{28269}{446} a + \\frac{11165}{1784} \\)', '\\( \\frac{711}{446} a^{15} - \\frac{2225}{1784} a^{14} - \\frac{21901}{1784} a^{13} - \\frac{8375}{892} a^{12} + \\frac{399}{8} a^{11} + \\frac{165749}{1784} a^{10} - \\frac{24483}{892} a^{9} - \\frac{458793}{1784} a^{8} - \\frac{2045}{8} a^{7} + \\frac{172735}{1784} a^{6} + \\frac{96159}{223} a^{5} + \\frac{722131}{1784} a^{4} + \\frac{314667}{1784} a^{3} + \\frac{21607}{892} a^{2} - \\frac{13539}{1784} a - \\frac{4173}{1784} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/2*a^8 - 1/2*a^4 - 1/2', '1/2*a^9 - 1/2*a^5 - 1/2*a', '1/2*a^10 - 1/2*a^6 - 1/2*a^2', '1/2*a^11 - 1/2*a^7 - 1/2*a^3', '1/4*a^12 - 1/4*a^10 - 1/4*a^6 - 1/2*a^4 + 1/4*a^2 + 1/4', '1/4*a^13 - 1/4*a^11 - 1/4*a^7 - 1/2*a^5 + 1/4*a^3 + 1/4*a', '1/8*a^14 - 1/8*a^13 + 1/8*a^11 + 1/8*a^10 - 1/4*a^9 + 1/8*a^8 - 3/8*a^7 - 1/8*a^6 - 1/2*a^5 + 1/8*a^4 - 1/8*a^3 - 1/2*a^2 - 3/8*a - 1/8', '1/1784*a^15 + 81/1784*a^14 + 43/892*a^13 + 41/1784*a^12 + 1/8*a^11 + 10/223*a^10 - 395/1784*a^9 + 411/1784*a^8 + 3/8*a^7 - 283/892*a^6 - 327/1784*a^5 - 147/1784*a^4 - 65/892*a^3 + 605/1784*a^2 + 457/1784*a + 117/892']}
Number field data - 16.0.103670069459943424.1