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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [11, -24, 60, -108, 172, -244, 305, -336, 331, -281, 211, -137, 76, -36, 14, -4, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 148333301025390625, 'disc_rad': 785, 'disc_sign': 1, 'frobs': [[2, [[12, 1], [4, 1]]], [3, [[4, 4]]], [5, [0]], [7, [[12, 1], [4, 1]]], [11, [[3, 4], [1, 4]]], [13, [[4, 4]]], [17, [[4, 4]]], [19, [[6, 2], [2, 2]]], [23, [[4, 4]]], [29, [[2, 8]]], [31, [[3, 4], [1, 4]]], [37, [[4, 4]]], [41, [[4, 4]]], [43, [[12, 1], [4, 1]]], [47, [[4, 4]]], [53, [[12, 1], [4, 1]]], [59, [[4, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [72, 48], 'galois_label': '16T181', 'galt': 181, 'grd': 41.89646002154997, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '16.0.148333301025390625.1', 'local_algs': ['5.4.4.12a1.4', '157.4.1.0a1.1', '157.4.1.0a1.1', '157.4.2.4a1.2'], 'minimal_sibling': [-1, -12, -30, 26, 49, -4, -32, -15, 17, 8, -7, -1, 1], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 8, 'ramps': [5, 157], 'rd': 11.8359307729, 'regulator': {'__RealLiteral__': 0, 'data': '374.86019186', 'prec': 40}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-1.-1.1', '1.-1.1.-1.1', '6.-1.6.-1.1', '1.3.5.3.-1.-3.5.-3.1'], 'torsion_gen': '\\( -\\frac{8419}{53553} a^{15} + \\frac{21221}{53553} a^{14} - \\frac{61628}{53553} a^{13} + \\frac{116101}{53553} a^{12} - \\frac{143311}{53553} a^{11} + \\frac{127894}{53553} a^{10} + \\frac{13503}{17851} a^{9} - \\frac{119706}{17851} a^{8} + \\frac{670178}{53553} a^{7} - \\frac{1000268}{53553} a^{6} + \\frac{1034759}{53553} a^{5} - \\frac{281001}{17851} a^{4} + \\frac{657436}{53553} a^{3} - \\frac{379060}{53553} a^{2} + \\frac{191234}{53553} a - \\frac{44903}{17851} \\)', 'torsion_order': 10, 'units': ['\\( \\frac{6652}{53553} a^{15} - \\frac{14369}{53553} a^{14} + \\frac{30272}{53553} a^{13} - \\frac{31864}{53553} a^{12} - \\frac{46784}{53553} a^{11} + \\frac{242969}{53553} a^{10} - \\frac{203894}{17851} a^{9} + \\frac{381928}{17851} a^{8} - \\frac{1588589}{53553} a^{7} + \\frac{1896680}{53553} a^{6} - \\frac{1845533}{53553} a^{5} + \\frac{485633}{17851} a^{4} - \\frac{1052431}{53553} a^{3} + \\frac{658267}{53553} a^{2} - \\frac{278762}{53553} a + \\frac{40137}{17851} \\)', '\\( \\frac{12856}{53553} a^{15} - \\frac{68249}{53553} a^{14} + \\frac{238196}{53553} a^{13} - \\frac{645577}{53553} a^{12} + \\frac{1389391}{53553} a^{11} - \\frac{2515804}{53553} a^{10} + \\frac{1283691}{17851} a^{9} - \\frac{1682904}{17851} a^{8} + \\frac{5705740}{53553} a^{7} - \\frac{5561080}{53553} a^{6} + \\frac{4699099}{53553} a^{5} - \\frac{1168363}{17851} a^{4} + \\frac{2326964}{53553} a^{3} - \\frac{1402100}{53553} a^{2} + \\frac{647821}{53553} a - \\frac{75542}{17851} \\)', '\\( \\frac{6956}{53553} a^{15} - \\frac{14972}{53553} a^{14} + \\frac{14960}{17851} a^{13} - \\frac{76300}{53553} a^{12} + \\frac{30433}{17851} a^{11} - \\frac{27614}{17851} a^{10} - \\frac{30287}{53553} a^{9} + \\frac{70969}{17851} a^{8} - \\frac{398104}{53553} a^{7} + \\frac{214970}{17851} a^{6} - \\frac{235463}{17851} a^{5} + \\frac{674672}{53553} a^{4} - \\frac{605573}{53553} a^{3} + \\frac{130087}{17851} a^{2} - \\frac{236639}{53553} a + \\frac{136691}{53553} \\)', '\\( \\frac{13397}{53553} a^{15} - \\frac{14084}{17851} a^{14} + \\frac{122324}{53553} a^{13} - \\frac{87861}{17851} a^{12} + \\frac{434116}{53553} a^{11} - \\frac{600883}{53553} a^{10} + \\frac{654746}{53553} a^{9} - \\frac{172560}{17851} a^{8} + \\frac{301370}{53553} a^{7} + \\frac{18140}{53553} a^{6} - \\frac{196574}{53553} a^{5} + \\frac{179410}{53553} a^{4} - \\frac{181532}{53553} a^{3} + \\frac{145282}{53553} a^{2} - \\frac{20515}{17851} a + \\frac{62125}{53553} \\)', '\\( \\frac{2978}{17851} a^{15} - \\frac{44615}{53553} a^{14} + \\frac{154021}{53553} a^{13} - \\frac{397840}{53553} a^{12} + \\frac{837896}{53553} a^{11} - \\frac{1442093}{53553} a^{10} + \\frac{2118182}{53553} a^{9} - \\frac{868919}{17851} a^{8} + \\frac{910232}{17851} a^{7} - \\frac{2422865}{53553} a^{6} + \\frac{1801214}{53553} a^{5} - \\frac{1128839}{53553} a^{4} + \\frac{223094}{17851} a^{3} - \\frac{288823}{53553} a^{2} + \\frac{111073}{53553} a + \\frac{42499}{53553} \\)', '\\( \\frac{3011}{17851} a^{15} - \\frac{12373}{17851} a^{14} + \\frac{38520}{17851} a^{13} - \\frac{95080}{17851} a^{12} + \\frac{182269}{17851} a^{11} - \\frac{301638}{17851} a^{10} + \\frac{418514}{17851} a^{9} - \\frac{498132}{17851} a^{8} + \\frac{521842}{17851} a^{7} - \\frac{472293}{17851} a^{6} + \\frac{379099}{17851} a^{5} - \\frac{294681}{17851} a^{4} + \\frac{180585}{17851} a^{3} - \\frac{108025}{17851} a^{2} + \\frac{41225}{17851} a - \\frac{7398}{17851} \\)', '\\( \\frac{19886}{53553} a^{15} - \\frac{97813}{53553} a^{14} + \\frac{326092}{53553} a^{13} - \\frac{860939}{53553} a^{12} + \\frac{1813424}{53553} a^{11} - \\frac{3211019}{53553} a^{10} + \\frac{1629052}{17851} a^{9} - \\frac{2114996}{17851} a^{8} + \\frac{7175477}{53553} a^{7} - \\frac{7057886}{53553} a^{6} + \\frac{5961149}{53553} a^{5} - \\frac{1490916}{17851} a^{4} + \\frac{2954074}{53553} a^{3} - \\frac{1579489}{53553} a^{2} + \\frac{762836}{53553} a - \\frac{86908}{17851} \\)'], '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', '1/3*a^14 + 1/3*a^13 - 1/3*a^12 - 1/3*a^11 + 1/3*a^10 - 1/3*a^9 + 1/3*a^6 - 1/3*a^5 + 1/3*a^4 - 1/3*a^2 + 1/3*a + 1/3', '1/53553*a^15 - 8399/53553*a^14 - 1831/53553*a^13 + 19349/53553*a^12 - 26381/53553*a^11 + 8852/53553*a^10 - 5489/17851*a^9 + 680/17851*a^8 + 11491/53553*a^7 - 18328/53553*a^6 + 23947/53553*a^5 - 5066/17851*a^4 - 11566/53553*a^3 + 4873/53553*a^2 - 12134/53553*a + 8317/17851']}
Number field data - 16.0.148333301025390625.1