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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [16, -24, -180, 269, 414, -1107, 684, 876, -2253, 2191, -1008, -204, 749, -672, 384, -156, 45, -9, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 36163754150128780430177325000000000000, 'disc_rad': 413835630, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[4, 3], [2, 3]]], [11, [[6, 3]]], [13, [0]], [17, [[4, 2], [2, 3], [1, 4]]], [19, [[12, 1], [6, 1]]], [23, [[12, 1], [6, 1]]], [29, [[3, 6]]], [31, [[12, 1], [6, 1]]], [37, [[4, 2], [2, 5]]], [41, [[6, 2], [3, 2]]], [43, [[12, 1], [6, 1]]], [47, [[4, 4], [2, 1]]], [53, [[6, 2], [3, 2]]], [59, [[12, 1], [3, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_label': '18T623', 'galt': 623, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '18.10.36163754150128780430177325000000000000.1', 'local_algs': ['2.1.3.2a1.1', '2.1.3.2a1.1', '2.4.3.8a1.2', '3.6.3.24a1.1', '5.2.3.4a1.2', '5.2.6.10a1.2', '13.2.1.0a1.1', '13.2.1.0a1.1', '13.2.1.0a1.1', '13.2.2.2a1.2', '13.4.2.4a1.2', 'm1061117.1.2.0', 'm1061117.1.2.0', 'm1061117.2.1.1', 'm1061117.1.4.0', 'm1061117.1.4.0', 'm1061117.1.4.0'], 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 5, 'r2': 4, 'ramps': [2, 3, 5, 13, 1061117], 'rd': 122.059265, 'regulator': 5673649067000, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-14.-12.0.1', '-10.-10.0.1', '125.0.-450.-195.300.180.-35.-30.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{243}{100} a^{16} - \\frac{486}{25} a^{15} + \\frac{9153}{100} a^{14} - \\frac{30051}{100} a^{13} + \\frac{69363}{100} a^{12} - \\frac{113967}{100} a^{11} + \\frac{57141}{50} a^{10} - \\frac{2817}{25} a^{9} - \\frac{45006}{25} a^{8} + \\frac{344877}{100} a^{7} - \\frac{161309}{50} a^{6} + \\frac{30042}{25} a^{5} + \\frac{17817}{25} a^{4} - \\frac{117521}{100} a^{3} + \\frac{30393}{100} a^{2} + \\frac{8823}{50} a - \\frac{1483}{25} \\)', '\\( \\frac{333}{50} a^{16} - \\frac{1332}{25} a^{15} + \\frac{6289}{25} a^{14} - \\frac{20713}{25} a^{13} + \\frac{96153}{50} a^{12} - \\frac{79796}{25} a^{11} + \\frac{82011}{25} a^{10} - \\frac{27043}{50} a^{9} - \\frac{236199}{50} a^{8} + \\frac{236331}{25} a^{7} - \\frac{459993}{50} a^{6} + \\frac{98239}{25} a^{5} + \\frac{34759}{25} a^{4} - \\frac{147971}{50} a^{3} + \\frac{43933}{50} a^{2} + \\frac{19211}{50} a - \\frac{3481}{25} \\)', '\\( \\frac{2}{5} a^{16} - \\frac{16}{5} a^{15} + \\frac{149}{10} a^{14} - \\frac{483}{10} a^{13} + 109 a^{12} - \\frac{1717}{10} a^{11} + \\frac{771}{5} a^{10} + \\frac{331}{10} a^{9} - \\frac{3407}{10} a^{8} + \\frac{1125}{2} a^{7} - \\frac{4483}{10} a^{6} + \\frac{299}{5} a^{5} + \\frac{1182}{5} a^{4} - \\frac{1244}{5} a^{3} + 46 a^{2} + \\frac{447}{10} a - 19 \\)', '\\( \\frac{3}{10} a^{16} - \\frac{12}{5} a^{15} + \\frac{57}{5} a^{14} - \\frac{189}{5} a^{13} + \\frac{177}{2} a^{12} - \\frac{744}{5} a^{11} + \\frac{781}{5} a^{10} - \\frac{319}{10} a^{9} - \\frac{2147}{10} a^{8} + 443 a^{7} - \\frac{4387}{10} a^{6} + \\frac{964}{5} a^{5} + \\frac{312}{5} a^{4} - \\frac{1413}{10} a^{3} + \\frac{85}{2} a^{2} + \\frac{37}{2} a - \\frac{31}{5} \\)', '\\( \\frac{11}{50} a^{16} - \\frac{44}{25} a^{15} + \\frac{213}{25} a^{14} - \\frac{721}{25} a^{13} + \\frac{3491}{50} a^{12} - \\frac{3102}{25} a^{11} + \\frac{3632}{25} a^{10} - \\frac{3331}{50} a^{9} - \\frac{6533}{50} a^{8} + \\frac{8957}{25} a^{7} - \\frac{21241}{50} a^{6} + \\frac{6718}{25} a^{5} - \\frac{322}{25} a^{4} - \\frac{6557}{50} a^{3} + \\frac{3851}{50} a^{2} - \\frac{353}{50} a - \\frac{507}{25} \\)', '\\( \\frac{253}{50} a^{17} - \\frac{2017}{50} a^{16} + \\frac{4686}{25} a^{15} - \\frac{30269}{50} a^{14} + \\frac{33977}{25} a^{13} - \\frac{21203}{10} a^{12} + \\frac{92679}{50} a^{11} + \\frac{5289}{10} a^{10} - \\frac{216641}{50} a^{9} + \\frac{172018}{25} a^{8} - \\frac{25886}{5} a^{7} + \\frac{5678}{25} a^{6} + \\frac{15458}{5} a^{5} - \\frac{132179}{50} a^{4} - \\frac{573}{25} a^{3} + \\frac{23564}{25} a^{2} - \\frac{664}{25} a - \\frac{1749}{25} \\)', '\\( \\frac{17}{20} a^{16} - \\frac{34}{5} a^{15} + \\frac{643}{20} a^{14} - \\frac{2121}{20} a^{13} + \\frac{4933}{20} a^{12} - \\frac{8213}{20} a^{11} + \\frac{4241}{10} a^{10} - \\frac{367}{5} a^{9} - \\frac{3031}{5} a^{8} + \\frac{24447}{20} a^{7} - \\frac{11931}{10} a^{6} + \\frac{2537}{5} a^{5} + \\frac{942}{5} a^{4} - \\frac{7871}{20} a^{3} + \\frac{2343}{20} a^{2} + \\frac{507}{10} a - \\frac{91}{5} \\)', '\\( \\frac{1}{100} a^{16} - \\frac{2}{25} a^{15} - \\frac{39}{100} a^{14} + \\frac{413}{100} a^{13} - \\frac{1899}{100} a^{12} + \\frac{5661}{100} a^{11} - \\frac{5273}{50} a^{10} + \\frac{5817}{50} a^{9} - \\frac{719}{50} a^{8} - \\frac{20371}{100} a^{7} + \\frac{8461}{25} a^{6} - \\frac{6026}{25} a^{5} + \\frac{104}{25} a^{4} + \\frac{13573}{100} a^{3} - \\frac{4889}{100} a^{2} - \\frac{562}{25} a + \\frac{89}{25} \\)', '\\( \\frac{347}{100} a^{17} - \\frac{2583}{100} a^{16} + \\frac{11563}{100} a^{15} - \\frac{8974}{25} a^{14} + \\frac{19074}{25} a^{13} - \\frac{5552}{5} a^{12} + \\frac{79771}{100} a^{11} + \\frac{3209}{5} a^{10} - \\frac{64461}{25} a^{9} + \\frac{352689}{100} a^{8} - \\frac{41227}{20} a^{7} - \\frac{13964}{25} a^{6} + \\frac{8881}{5} a^{5} - \\frac{109161}{100} a^{4} - \\frac{20077}{50} a^{3} + \\frac{42067}{100} a^{2} + \\frac{1232}{25} a - \\frac{823}{25} \\)', '\\( \\frac{1}{100} a^{16} - \\frac{2}{25} a^{15} - \\frac{49}{100} a^{14} + \\frac{483}{100} a^{13} - \\frac{2199}{100} a^{12} + \\frac{6551}{100} a^{11} - \\frac{6163}{50} a^{10} + \\frac{3511}{25} a^{9} - \\frac{727}{25} a^{8} - \\frac{22021}{100} a^{7} + \\frac{19527}{50} a^{6} - \\frac{7656}{25} a^{5} + \\frac{1064}{25} a^{4} + \\frac{13393}{100} a^{3} - \\frac{6289}{100} a^{2} - \\frac{679}{50} a + \\frac{169}{25} \\)', '\\( \\frac{9039}{100} a^{17} - \\frac{3066}{5} a^{16} + \\frac{258223}{100} a^{15} - \\frac{746451}{100} a^{14} + \\frac{282929}{20} a^{13} - \\frac{1713929}{100} a^{12} + \\frac{109357}{25} a^{11} + \\frac{1342397}{50} a^{10} - \\frac{1358446}{25} a^{9} + \\frac{205565}{4} a^{8} - \\frac{159233}{50} a^{7} - \\frac{1920109}{50} a^{6} + \\frac{812114}{25} a^{5} - \\frac{279001}{100} a^{4} - \\frac{448939}{20} a^{3} + \\frac{7877}{5} a^{2} + \\frac{284939}{50} a + \\frac{27183}{25} \\)', '\\( \\frac{90239}{20} a^{17} - \\frac{4289259}{100} a^{16} + \\frac{22477347}{100} a^{15} - \\frac{40890237}{50} a^{14} + \\frac{107363019}{50} a^{13} - \\frac{103028701}{25} a^{12} + \\frac{547042581}{100} a^{11} - \\frac{92432539}{25} a^{10} - \\frac{133447653}{50} a^{9} + \\frac{1123621187}{100} a^{8} - \\frac{1586535641}{100} a^{7} + \\frac{600317437}{50} a^{6} - \\frac{75322511}{25} a^{5} - \\frac{346096169}{100} a^{4} + \\frac{181176449}{50} a^{3} - \\frac{62741949}{100} a^{2} - \\frac{24631219}{50} a + \\frac{3549769}{25} \\)', '\\( \\frac{46479037}{50} a^{17} - \\frac{702600803}{100} a^{16} + \\frac{1585143291}{50} a^{15} - \\frac{9931709249}{100} a^{14} + \\frac{21381165071}{100} a^{13} - \\frac{31654204097}{100} a^{12} + \\frac{4802612413}{20} a^{11} + \\frac{7812385501}{50} a^{10} - \\frac{35579710073}{50} a^{9} + \\frac{25278023781}{25} a^{8} - \\frac{63743885163}{100} a^{7} - \\frac{518643216}{5} a^{6} + \\frac{12148904487}{25} a^{5} - \\frac{16440158857}{50} a^{4} - \\frac{8870686149}{100} a^{3} + \\frac{12198934827}{100} a^{2} + \\frac{207410403}{25} a - \\frac{258315739}{25} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', '1/5*a^12 - 1/5*a^11 + 1/5*a^10 - 1/5*a^7 + 1/5*a^6 - 1/5*a^5 + 1/5*a^2 - 1/5*a + 1/5', '1/5*a^13 + 1/5*a^10 - 1/5*a^8 - 1/5*a^5 + 1/5*a^3 + 1/5', '1/10*a^14 - 1/10*a^13 + 1/10*a^11 + 2/5*a^10 - 1/10*a^9 + 1/10*a^8 - 1/2*a^7 - 1/10*a^6 - 2/5*a^5 - 2/5*a^4 + 2/5*a^3 + 1/10*a + 2/5', '1/10*a^15 - 1/10*a^13 - 1/10*a^12 - 3/10*a^11 + 1/10*a^10 - 2/5*a^8 - 2/5*a^7 + 3/10*a^6 + 2/5*a^5 + 2/5*a^3 - 1/10*a^2 - 3/10*a + 1/5', '1/100*a^16 + 1/50*a^15 + 1/100*a^14 + 3/100*a^13 - 9/100*a^12 - 29/100*a^11 - 9/25*a^10 - 3/50*a^9 + 11/50*a^8 - 11/100*a^7 + 17/50*a^6 + 9/25*a^5 - 11/25*a^4 + 13/100*a^3 + 1/100*a^2 - 19/50*a - 6/25', '1/100*a^17 - 3/100*a^15 + 1/100*a^14 + 1/20*a^13 + 9/100*a^12 + 1/50*a^11 + 3/50*a^10 + 17/50*a^9 + 1/4*a^8 + 9/25*a^7 - 3/25*a^6 + 11/25*a^5 + 1/100*a^4 - 1/20*a^3 - 1/5*a^2 + 8/25*a - 3/25']}
Number field data - 18.10.36163754150128780430177325000000000000.1