-
nf_fields • Show schema
Hide schema
{'class_group': [], 'class_number': 1, 'cm': True, 'coeffs': [1, 3, 4, 9, 12, -12, 8, 54, -19, -54, 8, 12, 12, -9, 4, -3, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 1132927402587890625, 'disc_rad': 435, 'disc_sign': 1, 'frobs': [[2, [[4, 4]]], [3, [0]], [5, [0]], [7, [[4, 4]]], [11, [[2, 8]]], [13, [[4, 4]]], [17, [[4, 4]]], [19, [[2, 8]]], [23, [[4, 4]]], [29, [0]], [31, [[2, 4], [1, 8]]], [37, [[4, 4]]], [41, [[2, 8]]], [43, [[4, 4]]], [47, [[4, 4]]], [53, [[4, 4]]], [59, [[2, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [16, 24, 16], 'galois_label': '16T21', 'galt': 21, 'grd': 31.187971562966524, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '16.0.1132927402587890625.1', 'local_algs': ['3.8.4.1', '3.8.4.1', '5.8.6.1', '5.8.6.1', '29.2.0.1', '29.2.0.1', '29.2.0.1', '29.2.0.1', '29.4.2.1', '29.4.2.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 8, 'ramps': [3, 5, 29], 'rd': 13.4396398271, 'regulator': {'__RealLiteral__': 0, 'data': '3158.73230855', 'prec': 44}, 'res': {'gal': ['1,-1,-5,18,-18,81,255,-1311,918,6642,6096,-8070,-13896,-33822,-37458,41189,165787,41189,-37458,-33822,-13896,-8070,6096,6642,918,-1311,255,81,-18,18,-5,-1,1'], 'sib': ['10531,-408,3044,-13258,12586,-1746,-1178,466,1007,-912,308,-92,81,-34,21,-6,1', '130321,0,-46208,0,-3110,0,-1858,0,1659,0,-122,0,-5,0,-7,0,1', '958441,-104753,-224187,49433,-282,-44313,15194,6759,-3307,182,581,-230,-17,29,-8,-2,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['4.-1.1', '-1.-1.1', '1.-1.1', '1.-1.1.-1.1', '76.4.-19.-1.1', '1.4.-4.-1.1', '11.-1.6.-1.1', '19.-2.8.-1.1', '1.1.2.-1.1', '1.1.-3.-1.1', '1.1.4.-1.9.1.4.-1.1', '361.-171.23.-35.36.-5.-3.-2.1', '31.-7.2.0.11.0.8.-1.1', '1.-1.0.1.-1.1.0.-1.1', '121.-11.-65.16.24.-4.-5.-1.1', '1.3.5.3.4.-3.5.-3.1', '1.0.-17.0.44.0.-13.0.1'], 'torsion_gen': '\\( \\frac{18133}{342200} a^{15} + \\frac{6001}{171100} a^{14} - \\frac{162059}{342200} a^{13} + \\frac{20307}{34220} a^{12} - \\frac{501719}{342200} a^{11} + \\frac{1283023}{342200} a^{10} + \\frac{63899}{34220} a^{9} - \\frac{1073567}{342200} a^{8} - \\frac{1003129}{85550} a^{7} + \\frac{259233}{68440} a^{6} + \\frac{4734049}{342200} a^{5} - \\frac{4104}{725} a^{4} - \\frac{70737}{68440} a^{3} + \\frac{159699}{42775} a^{2} - \\frac{30179}{342200} a + \\frac{19319}{85550} \\)', 'torsion_order': 30, 'units': ['\\( \\frac{23169}{85550} a^{15} - \\frac{136443}{171100} a^{14} + \\frac{177411}{171100} a^{13} - \\frac{83121}{34220} a^{12} + \\frac{140424}{42775} a^{11} + \\frac{269329}{85550} a^{10} + \\frac{103953}{34220} a^{9} - \\frac{2666397}{171100} a^{8} - \\frac{1001361}{171100} a^{7} + \\frac{222009}{17110} a^{6} + \\frac{268721}{42775} a^{5} - \\frac{561873}{171100} a^{4} + \\frac{91353}{34220} a^{3} + \\frac{112797}{171100} a^{2} + \\frac{76833}{85550} a + \\frac{30259}{42775} \\)', '\\( \\frac{40487}{342200} a^{15} - \\frac{21961}{171100} a^{14} - \\frac{144941}{342200} a^{13} + \\frac{20763}{34220} a^{12} - \\frac{649241}{342200} a^{11} + \\frac{2332577}{342200} a^{10} - \\frac{15119}{34220} a^{9} - \\frac{1675713}{342200} a^{8} - \\frac{699373}{42775} a^{7} + \\frac{1016487}{68440} a^{6} + \\frac{3807911}{342200} a^{5} - \\frac{397389}{42775} a^{4} + \\frac{83177}{68440} a^{3} + \\frac{236347}{85550} a^{2} + \\frac{266579}{342200} a - \\frac{3992}{42775} \\)', '\\( \\frac{3754}{42775} a^{15} - \\frac{171297}{342200} a^{14} + \\frac{205927}{171100} a^{13} - \\frac{144731}{68440} a^{12} + \\frac{307621}{85550} a^{11} - \\frac{960763}{342200} a^{10} - \\frac{68679}{68440} a^{9} - \\frac{708719}{171100} a^{8} + \\frac{4256821}{342200} a^{7} + \\frac{70947}{34220} a^{6} - \\frac{5906839}{342200} a^{5} + \\frac{1557103}{342200} a^{4} + \\frac{117967}{17110} a^{3} - \\frac{1344537}{342200} a^{2} + \\frac{23787}{171100} a + \\frac{308269}{342200} \\)', '\\( \\frac{79941}{342200} a^{15} - \\frac{122493}{171100} a^{14} + \\frac{337237}{342200} a^{13} - \\frac{75309}{34220} a^{12} + \\frac{1035517}{342200} a^{11} + \\frac{849011}{342200} a^{10} + \\frac{67929}{34220} a^{9} - \\frac{4456319}{342200} a^{8} - \\frac{310953}{85550} a^{7} + \\frac{824757}{68440} a^{6} + \\frac{899693}{342200} a^{5} - \\frac{200229}{85550} a^{4} + \\frac{191119}{68440} a^{3} + \\frac{33443}{42775} a^{2} + \\frac{311097}{342200} a + \\frac{28409}{42775} \\)', '\\( \\frac{39286}{42775} a^{15} - \\frac{260237}{85550} a^{14} + \\frac{767473}{171100} a^{13} - \\frac{316569}{34220} a^{12} + \\frac{2279703}{171100} a^{11} + \\frac{349361}{42775} a^{10} + \\frac{52233}{17110} a^{9} - \\frac{8884571}{171100} a^{8} - \\frac{435673}{171100} a^{7} + \\frac{394027}{6844} a^{6} - \\frac{771419}{85550} a^{5} - \\frac{636966}{42775} a^{4} + \\frac{539427}{34220} a^{3} + \\frac{861821}{171100} a^{2} + \\frac{159513}{171100} a + \\frac{138169}{85550} \\)', '\\( \\frac{111367}{171100} a^{15} - \\frac{899529}{342200} a^{14} + \\frac{877639}{171100} a^{13} - \\frac{704893}{68440} a^{12} + \\frac{1435247}{85550} a^{11} - \\frac{2161441}{342200} a^{10} + \\frac{423529}{68440} a^{9} - \\frac{6744283}{171100} a^{8} + \\frac{9599447}{342200} a^{7} + \\frac{671707}{34220} a^{6} - \\frac{9111173}{342200} a^{5} + \\frac{3282271}{342200} a^{4} + \\frac{137751}{17110} a^{3} - \\frac{719459}{342200} a^{2} + \\frac{162909}{171100} a + \\frac{435673}{342200} \\)', '\\( \\frac{74543}{342200} a^{15} - \\frac{35611}{42775} a^{14} + \\frac{516881}{342200} a^{13} - \\frac{25857}{8555} a^{12} + \\frac{1625111}{342200} a^{11} - \\frac{205707}{342200} a^{10} + \\frac{20027}{17110} a^{9} - \\frac{4259227}{342200} a^{8} + \\frac{1004897}{171100} a^{7} + \\frac{628803}{68440} a^{6} - \\frac{2584281}{342200} a^{5} + \\frac{406671}{171100} a^{4} + \\frac{253443}{68440} a^{3} - \\frac{525999}{171100} a^{2} + \\frac{679711}{342200} a - \\frac{44351}{85550} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/2*a^10 - 1/2*a^5 - 1/2', '1/2*a^11 - 1/2*a^6 - 1/2*a', '1/20*a^12 - 1/4*a^11 - 1/4*a^10 - 1/10*a^9 + 1/4*a^7 - 1/20*a^6 - 1/4*a^5 + 1/10*a^3 - 1/4*a^2 + 1/4*a + 1/20', '1/20*a^13 + 3/20*a^10 - 1/2*a^9 + 1/4*a^8 + 1/5*a^7 + 1/4*a^5 + 1/10*a^4 + 1/4*a^3 - 1/5*a - 1/4', '1/2360*a^14 - 13/1180*a^13 + 13/2360*a^12 + 69/1180*a^11 + 37/2360*a^10 + 479/2360*a^9 + 237/1180*a^8 - 919/2360*a^7 + 44/295*a^6 - 583/2360*a^5 + 553/2360*a^4 - 231/590*a^3 + 931/2360*a^2 + 141/590*a + 353/2360', '1/342200*a^15 + 7/171100*a^14 - 6573/342200*a^13 - 15/1711*a^12 - 54033/342200*a^11 - 62469/342200*a^10 + 10601/34220*a^9 + 77631/342200*a^8 + 71299/171100*a^7 - 11201/68440*a^6 + 156593/342200*a^5 + 5983/42775*a^4 - 483/13688*a^3 + 51647/171100*a^2 + 116487/342200*a + 4479/42775']}