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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [4, 0, -16, 0, -40, 0, 32, 0, 160, 0, -56, 0, 20, 0, -8, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 2393397489569403764736, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 4]]], [7, [[4, 4]]], [11, [[4, 4]]], [13, [[4, 4]]], [17, [[4, 4]]], [19, [[4, 4]]], [23, [[2, 8]]], [29, [[4, 4]]], [31, [[4, 4]]], [37, [[4, 4]]], [41, [[4, 4]]], [43, [[4, 4]]], [47, [[2, 4], [1, 8]]], [53, [[4, 4]]], [59, [[4, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [104, 24], 'galois_label': '16T17', 'galt': 17, 'grd': 21.686448086636275, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 3, 'label': '16.8.2393397489569403764736.3', 'local_algs': ['2.16.52.1', '3.16.12.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 4, 'ramps': [2, 3], 'rd': 21.6864480866, 'regulator': {'__RealLiteral__': 0, 'data': '79205.5923155', 'prec': 44}, 'res': {'gal': ['625,0,-1000,0,-3952,0,10776,0,1058,0,-42872,0,93124,0,-114048,0,94195,0,-55848,0,24772,0,-8560,0,2342,0,-480,0,68,0,-8,0,1'], 'sib': ['4,0,16,0,-40,0,-32,0,160,0,56,0,20,0,8,0,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['-2.0.1', '-3.0.1', '-6.0.1', '2.0.-4.0.1', '18.0.-12.0.1', '1.0.-4.0.1', '9.0.0.0.-12.0.0.0.1', '1.12.28.24.0.-12.-8.0.1', '1.0.-16.0.20.0.-8.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{15}{772} a^{14} - \\frac{122}{965} a^{12} + \\frac{311}{1930} a^{10} - \\frac{2301}{3860} a^{8} + \\frac{685}{386} a^{6} + \\frac{9081}{1930} a^{4} + \\frac{2873}{965} a^{2} - \\frac{2413}{1930} \\)', '\\( \\frac{697}{3860} a^{15} - \\frac{10797}{7720} a^{13} + \\frac{25197}{7720} a^{11} - \\frac{18053}{1930} a^{9} + \\frac{102967}{3860} a^{7} + \\frac{46879}{3860} a^{5} - \\frac{9369}{3860} a^{3} - \\frac{5693}{1930} a \\)', '\\( \\frac{439}{7720} a^{15} - \\frac{649}{1544} a^{13} + \\frac{6649}{7720} a^{11} - \\frac{2416}{965} a^{9} + \\frac{6958}{965} a^{7} + \\frac{5619}{772} a^{5} - \\frac{4923}{3860} a^{3} - \\frac{2367}{1930} a \\)', '\\( \\frac{373}{7720} a^{15} - \\frac{378}{965} a^{13} + \\frac{7939}{7720} a^{11} - \\frac{5781}{1930} a^{9} + \\frac{8231}{965} a^{7} - \\frac{573}{965} a^{5} + \\frac{7267}{3860} a^{3} - \\frac{753}{965} a \\)', '\\( \\frac{11}{772} a^{15} - \\frac{69}{772} a^{13} + \\frac{149}{1544} a^{11} - \\frac{67}{193} a^{9} + \\frac{683}{772} a^{7} + \\frac{1687}{386} a^{5} + \\frac{247}{772} a^{3} + \\frac{339}{193} a \\)', '\\( \\frac{8}{965} a^{15} - \\frac{183}{7720} a^{14} - \\frac{161}{1544} a^{13} + \\frac{1569}{7720} a^{12} + \\frac{3539}{7720} a^{11} - \\frac{4459}{7720} a^{10} - \\frac{2197}{1930} a^{9} + \\frac{6177}{3860} a^{8} + \\frac{12637}{3860} a^{7} - \\frac{8907}{1930} a^{6} - \\frac{4041}{772} a^{5} + \\frac{5727}{3860} a^{4} - \\frac{12423}{3860} a^{3} + \\frac{393}{3860} a^{2} - \\frac{677}{1930} a + \\frac{698}{965} \\)', '\\( \\frac{423}{7720} a^{15} - \\frac{223}{7720} a^{14} - \\frac{657}{1544} a^{13} + \\frac{256}{965} a^{12} + \\frac{7453}{7720} a^{11} - \\frac{1339}{1544} a^{10} - \\frac{10013}{3860} a^{9} + \\frac{9261}{3860} a^{8} + \\frac{14387}{1930} a^{7} - \\frac{13037}{1930} a^{6} + \\frac{4265}{772} a^{5} + \\frac{10227}{1930} a^{4} - \\frac{23771}{3860} a^{3} + \\frac{845}{772} a^{2} + \\frac{228}{965} a - \\frac{2837}{1930} \\)', '\\( \\frac{33}{3860} a^{15} - \\frac{59}{965} a^{14} - \\frac{221}{7720} a^{13} + \\frac{1919}{3860} a^{12} - \\frac{129}{772} a^{11} - \\frac{1233}{965} a^{10} + \\frac{949}{1930} a^{9} + \\frac{677}{193} a^{8} - \\frac{1273}{965} a^{7} - \\frac{9699}{965} a^{6} + \\frac{30387}{3860} a^{5} - \\frac{2103}{1930} a^{4} - \\frac{1219}{386} a^{3} + \\frac{4202}{965} a^{2} - \\frac{2791}{1930} a - \\frac{58}{193} \\)', '\\( \\frac{323}{3860} a^{15} - \\frac{223}{7720} a^{14} - \\frac{5333}{7720} a^{13} + \\frac{256}{965} a^{12} + \\frac{3537}{1930} a^{11} - \\frac{1339}{1544} a^{10} - \\frac{9637}{1930} a^{9} + \\frac{9261}{3860} a^{8} + \\frac{13712}{965} a^{7} - \\frac{13037}{1930} a^{6} + \\frac{871}{3860} a^{5} + \\frac{10227}{1930} a^{4} - \\frac{6999}{965} a^{3} + \\frac{845}{772} a^{2} + \\frac{1363}{1930} a - \\frac{907}{1930} \\)', '\\( \\frac{43}{3860} a^{15} + \\frac{71}{1930} a^{14} - \\frac{943}{7720} a^{13} - \\frac{249}{965} a^{12} + \\frac{461}{965} a^{11} + \\frac{823}{1930} a^{10} - \\frac{9903}{7720} a^{9} - \\frac{4951}{3860} a^{8} + \\frac{7239}{1930} a^{7} + \\frac{7321}{1930} a^{6} - \\frac{9477}{1930} a^{5} + \\frac{14777}{1930} a^{4} - \\frac{149}{965} a^{3} + \\frac{69}{965} a^{2} - \\frac{3279}{3860} a - \\frac{2003}{1930} \\)', '\\( \\frac{15}{193} a^{15} + \\frac{107}{3860} a^{14} - \\frac{1169}{1930} a^{13} - \\frac{1781}{7720} a^{12} + \\frac{10959}{7720} a^{11} + \\frac{4783}{7720} a^{10} - \\frac{30567}{7720} a^{9} - \\frac{1339}{772} a^{8} + \\frac{8761}{772} a^{7} + \\frac{19487}{3860} a^{6} + \\frac{21117}{3860} a^{5} - \\frac{2043}{3860} a^{4} - \\frac{17143}{3860} a^{3} - \\frac{931}{3860} a^{2} - \\frac{9461}{3860} a - \\frac{309}{193} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', '1/4*a^8 - 1/2*a^4 - 1/2', '1/8*a^9 - 1/2*a^6 + 1/4*a^5 - 1/4*a', '1/8*a^10 - 1/2*a^7 + 1/4*a^6 - 1/4*a^2', '1/8*a^11 + 1/4*a^7 - 1/4*a^3', '1/40*a^12 + 1/40*a^10 + 1/20*a^8 - 1/2*a^7 + 1/4*a^6 + 3/20*a^4 + 3/20*a^2 - 1/5', '1/40*a^13 + 1/40*a^11 + 1/20*a^9 + 1/4*a^7 + 3/20*a^5 + 3/20*a^3 - 1/5*a', '1/7720*a^14 - 47/3860*a^12 - 97/1930*a^10 - 27/772*a^8 - 1627/3860*a^6 - 238/965*a^4 + 203/1930*a^2 - 57/386', '1/7720*a^15 - 47/3860*a^13 - 97/1930*a^11 - 27/772*a^9 - 1627/3860*a^7 - 238/965*a^5 + 203/1930*a^3 - 57/386*a']}
Number field data - 16.8.2393397489569403764736.3