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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [9, 0, 0, 0, 54, 0, 0, 0, 87, 0, 0, 0, 6, 0, 0, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 328683126924509184, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 2]]], [7, [[2, 8]]], [11, [[4, 4]]], [13, [[4, 4]]], [17, [[8, 2]]], [19, [[2, 8]]], [23, [[2, 8]]], [29, [[8, 2]]], [31, [[2, 8]]], [37, [[2, 4], [1, 8]]], [41, [[8, 2]]], [43, [[2, 8]]], [47, [[2, 8]]], [53, [[8, 2]]], [59, [[4, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [84, 28], 'galois_label': '16T35', 'galt': 35, 'grd': 16.131874566820663, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 2, 'label': '16.0.328683126924509184.2', 'local_algs': ['2.2.8.36b2.32', '3.2.8.14a1.2'], 'maximal_cm_subfield': [1, 0, -1, 0, 1], 'minimal_sibling': [3, 0, -12, 0, 15, 0, -6, 0, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 8, 'ramps': [2, 3], 'rd': 12.4393757955, 'regulator': {'__RealLiteral__': 0, 'data': '763.555572776', 'prec': 44}, 'res': {'gal': ['4,-48,288,-1152,3440,-7920,14016,-18960,19984,-17280,13608,-12120,14504,-17640,16704,-12288,8530,-5616,3120,-1608,1136,-648,360,-24,-20,48,24,-12,2,0,0,0,1'], 'sib': ['3,0,-12,0,15,0,-6,0,1', '3,0,0,0,-3,0,0,0,1', '-2,8,-16,48,-136,256,-320,240,-56,-120,220,-220,158,-84,32,-8,1', '1,-8,20,0,-70,68,88,-156,-5,108,-44,4,8,-12,8,-4,1', '3,0,-12,12,36,-96,60,84,-173,112,4,-68,76,-56,28,-8,1']}, 'subfield_mults': [1, 1, 1, 2, 2, 1, 2, 2, 1], 'subfields': ['1.-1.1', '-3.0.1', '1.0.1', '3.0.-3.0.1', '1.-2.0.-2.1', '1.0.-1.0.1', '3.0.-12.0.15.0.-6.0.1', '3.0.0.0.-3.0.0.0.1', '1.-4.8.-10.7.-2.2.-2.1'], 'torsion_gen': '\\( \\frac{97}{414} a^{14} + \\frac{91}{69} a^{10} + \\frac{1370}{69} a^{6} + \\frac{239}{46} a^{2} \\)', 'torsion_order': 12, 'units': ['\\( \\frac{37}{828} a^{14} + \\frac{3}{92} a^{12} + \\frac{17}{69} a^{10} + \\frac{49}{276} a^{8} + \\frac{262}{69} a^{6} + \\frac{263}{92} a^{4} + \\frac{39}{92} a^{2} + \\frac{11}{23} \\)', '\\( \\frac{121}{828} a^{14} - \\frac{1}{23} a^{12} + \\frac{223}{276} a^{10} - \\frac{73}{276} a^{8} + \\frac{3403}{276} a^{6} - \\frac{343}{92} a^{4} + \\frac{51}{23} a^{2} - \\frac{143}{92} \\)', '\\( \\frac{55}{207} a^{14} - \\frac{10}{69} a^{12} + \\frac{209}{138} a^{10} - \\frac{19}{23} a^{8} + \\frac{3125}{138} a^{6} - \\frac{282}{23} a^{4} + \\frac{359}{46} a^{2} - \\frac{77}{23} \\)', '\\( \\frac{41}{138} a^{15} - \\frac{13}{828} a^{14} - \\frac{5}{69} a^{13} + \\frac{1}{23} a^{12} + \\frac{118}{69} a^{11} - \\frac{9}{92} a^{10} - \\frac{19}{46} a^{9} + \\frac{73}{276} a^{8} + \\frac{585}{23} a^{7} - \\frac{385}{276} a^{6} - \\frac{141}{23} a^{5} + \\frac{343}{92} a^{4} + \\frac{228}{23} a^{3} - \\frac{30}{23} a^{2} - \\frac{50}{23} a + \\frac{189}{92} \\)', '\\( \\frac{41}{276} a^{15} - \\frac{40}{207} a^{14} - \\frac{49}{276} a^{13} + \\frac{5}{69} a^{12} + \\frac{59}{69} a^{11} - \\frac{76}{69} a^{10} - \\frac{277}{276} a^{9} + \\frac{19}{46} a^{8} + \\frac{585}{46} a^{7} - \\frac{2279}{138} a^{6} - \\frac{1391}{92} a^{5} + \\frac{141}{23} a^{4} + \\frac{433}{92} a^{3} - \\frac{259}{46} a^{2} - \\frac{199}{46} a + \\frac{77}{46} \\)', '\\( \\frac{3}{23} a^{15} - \\frac{2}{69} a^{14} + \\frac{41}{276} a^{12} + \\frac{49}{69} a^{11} - \\frac{41}{276} a^{10} + \\frac{59}{69} a^{8} + \\frac{503}{46} a^{7} - \\frac{221}{92} a^{6} + \\frac{585}{46} a^{4} + \\frac{21}{23} a^{3} + \\frac{35}{92} a^{2} - \\frac{1}{2} a + \\frac{433}{92} \\)', '\\( \\frac{61}{207} a^{15} + \\frac{2}{69} a^{14} - \\frac{7}{92} a^{13} - \\frac{1}{276} a^{12} + \\frac{153}{92} a^{11} + \\frac{41}{276} a^{10} - \\frac{61}{138} a^{9} - \\frac{2}{69} a^{8} + \\frac{6913}{276} a^{7} + \\frac{221}{92} a^{6} - \\frac{303}{46} a^{5} - \\frac{21}{46} a^{4} + \\frac{637}{92} a^{3} - \\frac{35}{92} a^{2} - \\frac{233}{92} a - \\frac{33}{92} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/2*a^6 - 1/2*a^5 - 1/2*a^3 - 1/2*a - 1/2', '1/2*a^7 - 1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2', '1/6*a^8 - 1/2*a^4 - 1/2', '1/6*a^9 - 1/2*a^5 - 1/2*a', '1/6*a^10 - 1/2*a^5 - 1/2*a^3 - 1/2*a^2 - 1/2*a - 1/2', '1/6*a^11 - 1/2*a^5 - 1/2*a^4 - 1/2*a^2 - 1/2', '1/276*a^12 - 1/12*a^10 + 2/69*a^8 - 1/4*a^6 - 1/2*a^5 - 1/23*a^4 - 1/2*a^3 + 1/4*a^2 - 1/2*a - 13/92', '1/276*a^13 - 1/12*a^11 + 2/69*a^9 - 1/4*a^7 + 21/46*a^5 - 1/2*a^4 - 1/4*a^3 - 1/2*a^2 + 33/92*a - 1/2', '1/828*a^14 - 5/276*a^10 - 1/12*a^8 + 19/276*a^6 + 1/4*a^4 - 3/23*a^2 + 1/4', '1/828*a^15 - 5/276*a^11 - 1/12*a^9 + 19/276*a^7 + 1/4*a^5 - 3/23*a^3 + 1/4*a']}
Number field data - 16.0.328683126924509184.2