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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -4, 15, -36, 73, -118, 159, -182, 176, -149, 112, -77, 50, -29, 14, -5, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 4919707275390625, 'disc_rad': 335, 'disc_sign': 1, 'frobs': [[2, [[12, 1], [4, 1]]], [3, [[12, 1], [4, 1]]], [5, [0]], [7, [[12, 1], [4, 1]]], [11, [[4, 4]]], [13, [[4, 4]]], [17, [[4, 4]]], [19, [[2, 8]]], [23, [[4, 4]]], [29, [[6, 2], [2, 2]]], [31, [[4, 4]]], [37, [[4, 4]]], [41, [[2, 4], [1, 8]]], [43, [[12, 1], [4, 1]]], [47, [[4, 4]]], [53, [[12, 1], [4, 1]]], [59, [[6, 2], [2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [72, 48], 'galois_label': '16T181', 'galt': 181, 'grd': 27.369376545007917, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '16.0.4919707275390625.1', 'local_algs': ['5.16.12.1', '67.4.0.1', '67.4.0.1', '67.8.4.1'], 'minimal_sibling': [1, 0, 1, -1, -5, 2, 9, 2, -5, -1, 1, 0, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 8, 'ramps': [5, 67], 'rd': 9.56634862885, 'regulator': {'__RealLiteral__': 0, 'data': '48.4508350282', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-1.-1.1', '1.-1.1.-1.1', '1.-3.-1.-2.1', '1.0.-3.0.-1.0.-2.0.1'], 'torsion_gen': '\\( \\frac{217}{19} a^{15} - \\frac{1015}{19} a^{14} + \\frac{2626}{19} a^{13} - \\frac{5042}{19} a^{12} + \\frac{8162}{19} a^{11} - \\frac{12010}{19} a^{10} + \\frac{17057}{19} a^{9} - \\frac{21846}{19} a^{8} + \\frac{24053}{19} a^{7} - \\frac{22588}{19} a^{6} + \\frac{17035}{19} a^{5} - \\frac{10419}{19} a^{4} + \\frac{5040}{19} a^{3} - \\frac{1541}{19} a^{2} + \\frac{435}{19} a + \\frac{36}{19} \\)', 'torsion_order': 10, 'units': ['\\( \\frac{195}{19} a^{15} - \\frac{974}{19} a^{14} + \\frac{2653}{19} a^{13} - \\frac{5303}{19} a^{12} + \\frac{8830}{19} a^{11} - \\frac{13211}{19} a^{10} + \\frac{18871}{19} a^{9} - \\frac{24650}{19} a^{8} + \\frac{28060}{19} a^{7} - \\frac{27427}{19} a^{6} + \\frac{21959}{19} a^{5} - \\frac{14290}{19} a^{4} + \\frac{7463}{19} a^{3} - \\frac{2742}{19} a^{2} + \\frac{792}{19} a - \\frac{82}{19} \\)', '\\( \\frac{183}{19} a^{15} - \\frac{1000}{19} a^{14} + \\frac{2894}{19} a^{13} - \\frac{6024}{19} a^{12} + \\frac{10305}{19} a^{11} - \\frac{15697}{19} a^{10} + \\frac{22612}{19} a^{9} - \\frac{30128}{19} a^{8} + \\frac{35329}{19} a^{7} - \\frac{35725}{19} a^{6} + \\frac{30160}{19} a^{5} - \\frac{20901}{19} a^{4} + \\frac{11816}{19} a^{3} - \\frac{5038}{19} a^{2} + \\frac{1593}{19} a - \\frac{326}{19} \\)', '\\( a \\)', '\\( \\frac{22}{19} a^{15} - \\frac{41}{19} a^{14} - \\frac{27}{19} a^{13} + \\frac{261}{19} a^{12} - \\frac{668}{19} a^{11} + \\frac{1201}{19} a^{10} - \\frac{1814}{19} a^{9} + \\frac{2804}{19} a^{8} - \\frac{4007}{19} a^{7} + \\frac{4839}{19} a^{6} - \\frac{4924}{19} a^{5} + \\frac{3871}{19} a^{4} - \\frac{2423}{19} a^{3} + \\frac{1201}{19} a^{2} - \\frac{357}{19} a + \\frac{118}{19} \\)', '\\( \\frac{99}{19} a^{15} - \\frac{422}{19} a^{14} + \\frac{1009}{19} a^{13} - \\frac{1837}{19} a^{12} + \\frac{2884}{19} a^{11} - \\frac{4181}{19} a^{10} + \\frac{5916}{19} a^{9} - \\frac{7332}{19} a^{8} + \\frac{7666}{19} a^{7} - \\frac{6886}{19} a^{6} + \\frac{4803}{19} a^{5} - \\frac{2749}{19} a^{4} + \\frac{1209}{19} a^{3} - \\frac{191}{19} a^{2} + \\frac{56}{19} a + \\frac{75}{19} \\)', '\\( \\frac{105}{19} a^{15} - \\frac{542}{19} a^{14} + \\frac{1506}{19} a^{13} - \\frac{3025}{19} a^{12} + \\frac{5025}{19} a^{11} - \\frac{7498}{19} a^{10} + \\frac{10686}{19} a^{9} - \\frac{13998}{19} a^{8} + \\frac{15954}{19} a^{7} - \\frac{15467}{19} a^{6} + \\frac{12245}{19} a^{5} - \\frac{7813}{19} a^{4} + \\frac{3906}{19} a^{3} - \\frac{1380}{19} a^{2} + \\frac{349}{19} a - \\frac{31}{19} \\)', '\\( \\frac{46}{19} a^{15} - \\frac{65}{19} a^{14} - \\frac{167}{19} a^{13} + \\frac{829}{19} a^{12} - \\frac{1927}{19} a^{11} + \\frac{3380}{19} a^{10} - \\frac{5116}{19} a^{9} + \\frac{7775}{19} a^{8} - \\frac{10869}{19} a^{7} + \\frac{12847}{19} a^{6} - \\frac{12947}{19} a^{5} + \\frac{10367}{19} a^{4} - \\frac{6645}{19} a^{3} + \\frac{3437}{19} a^{2} - \\frac{1123}{19} a + \\frac{359}{19} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', 'a^14', '1/19*a^15 - 1/19*a^14 - 9/19*a^13 - 8/19*a^12 - 1/19*a^11 - 5/19*a^10 - 3/19*a^9 - 9/19*a^8 + 7/19*a^7 - 2/19*a^6 - 1/19*a^5 - 8/19*a^4 + 3/19*a^3 - 5/19*a^2 - 5/19*a - 5/19']}
Number field data - 16.0.4919707275390625.1