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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 0, 8, 0, 4, 0, -120, 0, 198, 0, 120, 0, 4, 0, -8, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 4668406261161555656704, 'disc_rad': 38, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[12, 1], [4, 1]]], [5, [[6, 2], [2, 2]]], [7, [[2, 8]]], [11, [[2, 8]]], [13, [[3, 4], [1, 4]]], [17, [[6, 2], [2, 2]]], [19, [0]], [23, [[12, 1], [4, 1]]], [29, [[3, 4], [1, 4]]], [31, [[4, 4]]], [37, [[4, 4]]], [41, [[6, 2], [2, 2]]], [43, [[12, 1], [4, 1]]], [47, [[12, 1], [4, 1]]], [53, [[6, 2], [2, 2]]], [59, [[12, 1], [4, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [114, 32], 'galois_label': '16T60', 'galt': 60, 'grd': 36.93589613868019, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '16.0.4668406261161555656704.1', 'local_algs': ['m2.16.1.38', '19.4.0.1', '19.12.8.1'], 'monogenic': 0, 'num_ram': 2, 'r2': 8, 'ramps': [2, 19], 'rd': 22.611170258840176, 'regulator': {'__RealLiteral__': 0, 'data': '60925.785768593894', 'prec': 60}, 'res': {'sib': ['1,0,0,0,-16,0,0,0,-78,0,0,0,-294,0,0,0,-155,0,0,0,2,0,0,0,1']}, 'subfield_mults': [1, 1, 1], 'subfields': ['1.0.1', '2.-8.10.-2.1', '36.24.8.-8.-8.-4.0.0.1'], 'torsion_gen': '\\( \\frac{19}{80} a^{14} - \\frac{61}{32} a^{12} + \\frac{81}{80} a^{10} + \\frac{4541}{160} a^{8} + \\frac{3701}{80} a^{6} - \\frac{4499}{160} a^{4} + \\frac{75}{16} a^{2} + \\frac{159}{160} \\)', 'torsion_order': 4, 'units': ['\\( a \\)', '\\( \\frac{1}{128} a^{15} + \\frac{33}{640} a^{14} - \\frac{1}{128} a^{13} - \\frac{49}{128} a^{12} - \\frac{49}{128} a^{11} - \\frac{13}{640} a^{10} + \\frac{125}{128} a^{9} + \\frac{3981}{640} a^{8} + \\frac{1043}{128} a^{7} + \\frac{8827}{640} a^{6} + \\frac{1621}{128} a^{5} + \\frac{721}{640} a^{4} - \\frac{123}{128} a^{3} - \\frac{139}{128} a^{2} - \\frac{9}{128} a - \\frac{561}{640} \\)', '\\( \\frac{117}{640} a^{15} + \\frac{89}{640} a^{14} - \\frac{183}{128} a^{13} - \\frac{143}{128} a^{12} + \\frac{303}{640} a^{11} + \\frac{391}{640} a^{10} + \\frac{14099}{640} a^{9} + \\frac{10583}{640} a^{8} + \\frac{25703}{640} a^{7} + \\frac{17291}{640} a^{6} - \\frac{9481}{640} a^{5} - \\frac{9977}{640} a^{4} - \\frac{343}{128} a^{3} + \\frac{633}{128} a^{2} + \\frac{81}{640} a + \\frac{517}{640} \\)', '\\( \\frac{239}{640} a^{15} + \\frac{127}{640} a^{14} - \\frac{391}{128} a^{13} - \\frac{207}{128} a^{12} + \\frac{1321}{640} a^{11} + \\frac{653}{640} a^{10} + \\frac{28343}{640} a^{9} + \\frac{15219}{640} a^{8} + \\frac{42221}{640} a^{7} + \\frac{22853}{640} a^{6} - \\frac{34657}{640} a^{5} - \\frac{19921}{640} a^{4} + \\frac{2135}{128} a^{3} + \\frac{299}{128} a^{2} - \\frac{603}{640} a + \\frac{1521}{640} \\)', '\\( \\frac{139}{320} a^{15} + \\frac{3}{4} a^{14} - \\frac{29}{8} a^{13} - \\frac{97}{16} a^{12} + \\frac{951}{320} a^{11} + \\frac{7}{2} a^{10} + \\frac{8199}{160} a^{9} + \\frac{359}{4} a^{8} + \\frac{21821}{320} a^{7} + 141 a^{6} - \\frac{6213}{80} a^{5} - \\frac{1637}{16} a^{4} + \\frac{1645}{64} a^{3} + \\frac{41}{4} a^{2} - \\frac{509}{160} a + \\frac{43}{8} \\)', '\\( \\frac{3}{40} a^{15} - \\frac{7}{64} a^{14} - \\frac{37}{64} a^{13} + \\frac{53}{64} a^{12} + \\frac{23}{160} a^{11} - \\frac{5}{64} a^{10} + \\frac{2863}{320} a^{9} - \\frac{845}{64} a^{8} + \\frac{1399}{80} a^{7} - \\frac{1741}{64} a^{6} - \\frac{807}{320} a^{5} + \\frac{111}{64} a^{4} + \\frac{95}{32} a^{3} + \\frac{49}{64} a^{2} + \\frac{417}{320} a + \\frac{17}{64} \\)', '\\( \\frac{51}{160} a^{15} + \\frac{1}{80} a^{14} - \\frac{161}{64} a^{13} - \\frac{3}{32} a^{12} + \\frac{41}{40} a^{11} - \\frac{1}{80} a^{10} + \\frac{12219}{320} a^{9} + \\frac{259}{160} a^{8} + \\frac{10779}{160} a^{7} + \\frac{259}{80} a^{6} - \\frac{9131}{320} a^{5} - \\frac{301}{160} a^{4} + \\frac{29}{16} a^{3} - \\frac{55}{16} a^{2} + \\frac{101}{320} a - \\frac{79}{160} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2', '1/4*a^5 - 1/4*a^4 - 1/2*a^3 - 1/2*a^2 - 1/4*a + 1/4', '1/4*a^6 - 1/4*a^4 + 1/4*a^2 - 1/4', '1/4*a^7 - 1/4*a^4 - 1/4*a^3 - 1/2*a^2 - 1/2*a + 1/4', '1/16*a^8 + 1/8*a^4 - 1/2*a^2 + 1/16', '1/16*a^9 - 1/8*a^5 - 1/4*a^4 - 1/2*a^2 + 5/16*a + 1/4', '1/16*a^10 - 1/8*a^6 - 1/4*a^4 - 3/16*a^2 + 1/4', '1/32*a^11 - 1/32*a^10 - 1/32*a^9 - 1/32*a^8 + 1/16*a^7 - 1/16*a^6 - 1/16*a^5 - 1/16*a^4 + 9/32*a^3 + 7/32*a^2 + 7/32*a - 9/32', '1/64*a^12 - 1/32*a^10 + 1/64*a^8 + 1/16*a^6 + 15/64*a^4 - 5/32*a^2 + 31/64', '1/64*a^13 - 1/32*a^10 - 1/64*a^9 - 1/32*a^8 - 1/8*a^7 - 1/16*a^6 - 5/64*a^5 - 1/16*a^4 - 1/8*a^3 + 7/32*a^2 + 29/64*a - 9/32', '1/320*a^14 + 9/320*a^10 + 1/160*a^8 - 1/320*a^6 - 17/80*a^4 + 27/64*a^2 + 69/160', '1/640*a^15 - 1/640*a^14 - 1/128*a^13 - 1/128*a^12 - 1/640*a^11 + 1/640*a^10 + 17/640*a^9 - 7/640*a^8 + 19/640*a^7 + 61/640*a^6 - 23/640*a^5 - 87/640*a^4 - 47/128*a^3 - 1/128*a^2 - 77/640*a - 53/640']}
Number field data - 16.0.4668406261161555656704.1