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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [81, 0, 0, 0, -108, 0, 0, 0, -306, 0, 0, 0, -60, 0, 0, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 627414791505681780502953984, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[4, 4]]], [7, [[2, 6], [1, 4]]], [11, [[8, 2]]], [13, [[4, 4]]], [17, [[2, 8]]], [19, [[8, 2]]], [23, [[8, 2]]], [29, [[4, 4]]], [31, [[8, 2]]], [37, [[4, 4]]], [41, [[4, 2], [2, 2], [1, 4]]], [43, [[8, 2]]], [47, [[2, 6], [1, 4]]], [53, [[4, 4]]], [59, [[8, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [610, 96], 'galois_label': '16T362', 'galt': 362, 'grd': 62.00647089400047, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 196, 'label': '16.4.627414791505681780502953984.196', 'local_algs': ['2.1.16.70e1.3299', '3.2.4.6a1.1', '3.2.4.6a1.1'], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 6, 'ramps': [2, 3], 'rd': 47.29847866504108, 'regulator': {'__RealLiteral__': 0, 'data': '40271886.96234334', 'prec': 57}, 'res': {'ae': ['81,0,0,0,108,0,0,0,-306,0,0,0,60,0,0,0,1'], 'sib': ['15752961,0,0,0,-162555336,0,0,0,24660612,0,0,0,-7890696,0,0,0,-1365498,0,0,0,166536,0,0,0,-1404,0,0,0,72,0,0,0,1', '15752961,0,0,0,162555336,0,0,0,24660612,0,0,0,7890696,0,0,0,-1365498,0,0,0,-166536,0,0,0,-1404,0,0,0,-72,0,0,0,1', '34012224,0,0,0,-10077696,0,0,0,-4245696,0,0,0,513216,0,0,0,583200,0,0,0,37152,0,0,0,1080,0,0,0,-72,0,0,0,1', '6561,0,0,0,0,0,0,0,341172,0,0,0,0,0,0,0,80838,0,0,0,0,0,0,0,756,0,0,0,0,0,0,0,1', '65610000,0,314088192,0,1133880768,0,-404227584,0,154734624,0,169921152,0,278901792,0,157137408,0,58829976,0,13089600,0,1902096,0,134784,0,72,0,-1440,0,-72,0,0,0,1']}, 'subfield_mults': [1, 1, 1], 'subfields': ['-2.0.1', '18.0.-12.0.1', '1.0.12.0.26.0.-12.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( -\\frac{2}{189} a^{12} + \\frac{9}{14} a^{8} + \\frac{19}{7} a^{4} - \\frac{9}{14} \\)', '\\( \\frac{37}{2268} a^{14} - \\frac{737}{756} a^{10} - \\frac{439}{84} a^{6} - \\frac{251}{84} a^{2} \\)', '\\( -\\frac{25}{756} a^{14} + \\frac{1}{84} a^{12} + \\frac{1489}{756} a^{10} - \\frac{59}{84} a^{8} + \\frac{2771}{252} a^{6} - \\frac{365}{84} a^{4} + \\frac{659}{84} a^{2} - \\frac{139}{28} \\)', '\\( \\frac{37}{2268} a^{14} + \\frac{19}{756} a^{12} - \\frac{737}{756} a^{10} - \\frac{383}{252} a^{8} - \\frac{439}{84} a^{6} - \\frac{587}{84} a^{4} - \\frac{251}{84} a^{2} - \\frac{1}{28} \\)', '\\( -\\frac{37}{1134} a^{14} - \\frac{1}{63} a^{12} + \\frac{737}{378} a^{10} + \\frac{59}{63} a^{8} + \\frac{439}{42} a^{6} + \\frac{124}{21} a^{4} + \\frac{293}{42} a^{2} + \\frac{30}{7} \\)', '\\( -\\frac{7}{324} a^{15} - \\frac{20}{567} a^{14} + \\frac{5}{252} a^{13} + \\frac{5}{126} a^{12} + \\frac{47}{36} a^{11} + \\frac{398}{189} a^{10} - \\frac{103}{84} a^{9} - \\frac{103}{42} a^{8} + \\frac{215}{36} a^{7} + \\frac{1441}{126} a^{6} - \\frac{319}{84} a^{5} - \\frac{52}{7} a^{4} + \\frac{55}{12} a^{3} + \\frac{103}{14} a^{2} - \\frac{59}{28} a - \\frac{26}{7} \\)', '\\( \\frac{20}{567} a^{15} + \\frac{17}{2268} a^{14} - \\frac{5}{189} a^{13} - \\frac{1}{126} a^{12} - \\frac{398}{189} a^{11} - \\frac{113}{252} a^{10} + \\frac{199}{126} a^{9} + \\frac{59}{126} a^{8} - \\frac{1441}{126} a^{7} - \\frac{607}{252} a^{6} + \\frac{355}{42} a^{5} + \\frac{55}{21} a^{4} - \\frac{103}{14} a^{3} - \\frac{107}{84} a^{2} + \\frac{43}{7} a + \\frac{15}{7} \\)', '\\( -\\frac{13}{756} a^{15} + \\frac{23}{756} a^{14} + \\frac{13}{756} a^{13} + \\frac{11}{252} a^{12} + \\frac{767}{756} a^{11} - \\frac{1427}{756} a^{10} - \\frac{293}{252} a^{9} - \\frac{691}{252} a^{8} + \\frac{1591}{252} a^{7} - \\frac{1333}{252} a^{6} + \\frac{263}{84} a^{5} - \\frac{461}{84} a^{4} + \\frac{481}{84} a^{3} - \\frac{277}{84} a^{2} + \\frac{73}{28} a - \\frac{29}{28} \\)', '\\( \\frac{47}{108} a^{15} + \\frac{386}{567} a^{14} + \\frac{397}{756} a^{13} + \\frac{43}{756} a^{12} - \\frac{2863}{108} a^{11} - \\frac{2609}{63} a^{10} - \\frac{8041}{252} a^{9} - \\frac{869}{252} a^{8} - \\frac{3923}{36} a^{7} - \\frac{21911}{126} a^{6} - \\frac{3817}{28} a^{5} - \\frac{1285}{84} a^{4} + \\frac{673}{12} a^{3} + \\frac{3011}{42} a^{2} + \\frac{1259}{28} a + \\frac{95}{28} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4', '1/3*a^5', '1/6*a^6 - 1/6*a^4 - 1/2*a^2 - 1/2', '1/6*a^7 - 1/6*a^5 - 1/2*a^3 - 1/2*a', '1/18*a^8 - 1/2', '1/18*a^9 - 1/2*a', '1/54*a^10 - 1/18*a^6 - 1/6*a^4 + 1/3*a^2 - 1/2', '1/108*a^11 - 1/108*a^10 - 1/36*a^9 - 1/36*a^8 + 1/18*a^7 - 1/18*a^6 - 1/6*a^5 - 1/6*a^4 + 5/12*a^3 - 5/12*a^2 - 1/4*a - 1/4', '1/756*a^12 - 1/252*a^8 + 1/28*a^4 - 3/28', '1/756*a^13 - 1/252*a^9 + 1/28*a^5 - 3/28*a', '1/2268*a^14 - 1/756*a^10 + 17/252*a^6 - 1/6*a^4 + 13/28*a^2 - 1/2', '1/2268*a^15 - 1/756*a^11 + 17/252*a^7 - 1/6*a^5 + 13/28*a^3 - 1/2*a']}
Number field data - 16.4.627414791505681780502953984.196