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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -6, 20, -46, 77, -104, 127, -142, 138, -118, 92, -62, 35, -18, 8, -2, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 3091162921500672, 'disc_rad': 1158, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 1], [4, 2]]], [7, [[8, 2]]], [11, [[8, 1], [2, 4]]], [13, [[4, 3], [2, 2]]], [17, [[8, 1], [2, 4]]], [19, [[8, 1], [2, 4]]], [23, [[8, 2]]], [29, [[8, 1], [2, 4]]], [31, [[8, 2]]], [37, [[4, 3], [1, 4]]], [41, [[8, 1], [4, 2]]], [43, [[8, 2]]], [47, [[8, 1], [2, 4]]], [53, [[8, 1], [4, 2]]], [59, [[8, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [1024, 512, 768], 'galois_label': '16T1202', 'galt': 1202, 'grd': 179.373633178251, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '16.0.3091162921500672.1', 'local_algs': ['m2.2.8.16', '3.8.4.1', '3.8.4.1', '193.1.0.1', '193.1.0.1', '193.1.0.1', '193.1.0.1', '193.2.0.1', '193.2.0.1', '193.2.0.1', '193.2.0.1', '193.4.3.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 8, 'ramps': [2, 3, 193], 'rd': 9.29250104192, 'regulator': {'__RealLiteral__': 0, 'data': '43.8698041698', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1, 1, 1], 'subfields': ['1.-1.1', '1.0.1', '-3.0.1', '1.0.-1.0.1', '1.-2.7.-14.18.-16.10.-4.1'], 'torsion_gen': '\\( -\\frac{6292}{19} a^{15} + 420 a^{14} - \\frac{44503}{19} a^{13} + \\frac{80699}{19} a^{12} - \\frac{161213}{19} a^{11} + 14327 a^{10} - \\frac{379820}{19} a^{9} + \\frac{464770}{19} a^{8} - \\frac{528516}{19} a^{7} + \\frac{507094}{19} a^{6} - \\frac{428407}{19} a^{5} + \\frac{341220}{19} a^{4} - \\frac{235054}{19} a^{3} + \\frac{117624}{19} a^{2} - \\frac{39894}{19} a + \\frac{8599}{19} \\)', 'torsion_order': 12, 'units': ['\\( \\frac{11035}{19} a^{15} - 736 a^{14} + \\frac{78039}{19} a^{13} - \\frac{141447}{19} a^{12} + \\frac{282615}{19} a^{11} - 25111 a^{10} + \\frac{665696}{19} a^{9} - \\frac{814433}{19} a^{8} + \\frac{926139}{19} a^{7} - \\frac{888417}{19} a^{6} + \\frac{750494}{19} a^{5} - \\frac{597678}{19} a^{4} + \\frac{411679}{19} a^{3} - \\frac{205878}{19} a^{2} + \\frac{69757}{19} a - \\frac{15027}{19} \\)', '\\( 418 a^{15} - 530 a^{14} + 2956 a^{13} - 5360 a^{12} + 10706 a^{11} - 18078 a^{10} + 25221 a^{9} - 30858 a^{8} + 35091 a^{7} - 33662 a^{6} + 28437 a^{5} - 22648 a^{4} + 15600 a^{3} - 7802 a^{2} + 2645 a - 570 \\)', '\\( \\frac{4694}{19} a^{15} - 312 a^{14} + \\frac{33182}{19} a^{13} - \\frac{60023}{19} a^{12} + \\frac{120035}{19} a^{11} - 10657 a^{10} + \\frac{282489}{19} a^{9} - \\frac{345468}{19} a^{8} + \\frac{392791}{19} a^{7} - \\frac{376619}{19} a^{6} + \\frac{318052}{19} a^{5} - \\frac{253238}{19} a^{4} + \\frac{174352}{19} a^{3} - \\frac{87088}{19} a^{2} + \\frac{29448}{19} a - \\frac{6337}{19} \\)', '\\( \\frac{9936}{19} a^{15} - 662 a^{14} + \\frac{70254}{19} a^{13} - \\frac{127279}{19} a^{12} + \\frac{254322}{19} a^{11} - 22598 a^{10} + \\frac{598940}{19} a^{9} - \\frac{732839}{19} a^{8} + \\frac{833317}{19} a^{7} - \\frac{799329}{19} a^{6} + \\frac{675306}{19} a^{5} - \\frac{537846}{19} a^{4} + \\frac{370454}{19} a^{3} - \\frac{185277}{19} a^{2} + \\frac{62835}{19} a - \\frac{13556}{19} \\)', '\\( \\frac{11321}{19} a^{15} - 754 a^{14} + \\frac{80042}{19} a^{13} - \\frac{144983}{19} a^{12} + \\frac{289714}{19} a^{11} - 25741 a^{10} + \\frac{682204}{19} a^{9} - \\frac{834678}{19} a^{8} + \\frac{949038}{19} a^{7} - \\frac{910268}{19} a^{6} + \\frac{768916}{19} a^{5} - \\frac{612352}{19} a^{4} + \\frac{421719}{19} a^{3} - \\frac{210848}{19} a^{2} + \\frac{71446}{19} a - \\frac{15398}{19} \\)', '\\( \\frac{212}{19} a^{15} - 15 a^{14} + \\frac{1506}{19} a^{13} - \\frac{2818}{19} a^{12} + \\frac{5546}{19} a^{11} - 496 a^{10} + \\frac{13196}{19} a^{9} - \\frac{16104}{19} a^{8} + \\frac{18347}{19} a^{7} - \\frac{17635}{19} a^{6} + \\frac{14872}{19} a^{5} - \\frac{11817}{19} a^{4} + \\frac{8175}{19} a^{3} - \\frac{4061}{19} a^{2} + \\frac{1343}{19} a - \\frac{277}{19} \\)', '\\( \\frac{1635}{19} a^{15} - 108 a^{14} + \\frac{11541}{19} a^{13} - \\frac{20826}{19} a^{12} + \\frac{41641}{19} a^{11} - 3698 a^{10} + \\frac{97866}{19} a^{9} - \\frac{119710}{19} a^{8} + \\frac{136025}{19} a^{7} - \\frac{130322}{19} a^{6} + \\frac{110002}{19} a^{5} - \\frac{87577}{19} a^{4} + \\frac{60219}{19} a^{3} - \\frac{30031}{19} a^{2} + \\frac{10125}{19} a - \\frac{2176}{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 + 8/19*a^13 - 2/19*a^12 - 7/19*a^11 - 3/19*a^9 + 9/19*a^8 + 4/19*a^7 - 1/19*a^6 - 8/19*a^5 - 6/19*a^4 + 8/19*a^3 + 8/19*a^2 - 2/19*a + 9/19']}
Number field data - 16.0.3091162921500672.1