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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1349, 2865, 1926, -6643, 441, 4794, -1350, -1164, 393, 106, -36, -3, 1], 'conductor': 315, 'degree': 12, 'dirichlet_group': [64, 1, 211, 97, 169, 202, 13, 274, 307, 118, 106, 223], 'disc_abs': 9891413435408203125, 'disc_rad': 105, 'disc_sign': 1, 'frobs': [[2, [[12, 1]]], [3, [0]], [5, [0]], [7, [0]], [11, [[3, 4]]], [13, [[12, 1]]], [17, [[4, 3]]], [19, [[1, 12]]], [23, [[12, 1]]], [29, [[6, 2]]], [31, [[6, 2]]], [37, [[4, 3]]], [41, [[6, 2]]], [43, [[12, 1]]], [47, [[12, 1]]], [53, [[4, 3]]], [59, [[3, 4]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [16, 9, 6], 'galois_label': '12T1', 'galt': 1, 'grd': 38.27702679912765, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.12.9891413435408203125.1', 'local_algs': ['3.4.3.16a2.1', '5.3.4.9a1.1', '7.6.2.6a1.1'], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 3, 'r2': 0, 'ramps': [3, 5, 7], 'rd': 38.2770267991, 'regulator': {'__RealLiteral__': 0, 'data': '413348.51768', 'prec': 40}, 'res': {}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-1.-1.1', '-1.-3.0.1', '11.9.-9.-1.1', '-1.3.9.-4.-9.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{11907}{2045521} a^{11} - \\frac{30819}{2045521} a^{10} - \\frac{456557}{2045521} a^{9} + \\frac{1094634}{2045521} a^{8} + \\frac{5694762}{2045521} a^{7} - \\frac{12163826}{2045521} a^{6} - \\frac{27520701}{2045521} a^{5} + \\frac{51702033}{2045521} a^{4} + \\frac{50198830}{2045521} a^{3} - \\frac{79273935}{2045521} a^{2} - \\frac{29759274}{2045521} a + \\frac{1997934}{107659} \\)', '\\( \\frac{3604572825}{1045156909429} a^{11} - \\frac{132880481}{55008258391} a^{10} - \\frac{148199930155}{1045156909429} a^{9} + \\frac{76839931740}{1045156909429} a^{8} + \\frac{2036505254960}{1045156909429} a^{7} - \\frac{717988514170}{1045156909429} a^{6} - \\frac{124535807451}{11743336061} a^{5} + \\frac{3955478826560}{1045156909429} a^{4} + \\frac{23776442709100}{1045156909429} a^{3} - \\frac{11032674479345}{1045156909429} a^{2} - \\frac{14217501004015}{1045156909429} a + \\frac{439233737907}{55008258391} \\)', '\\( \\frac{3604572825}{1045156909429} a^{11} - \\frac{132880481}{55008258391} a^{10} - \\frac{148199930155}{1045156909429} a^{9} + \\frac{76839931740}{1045156909429} a^{8} + \\frac{2036505254960}{1045156909429} a^{7} - \\frac{717988514170}{1045156909429} a^{6} - \\frac{124535807451}{11743336061} a^{5} + \\frac{3955478826560}{1045156909429} a^{4} + \\frac{23776442709100}{1045156909429} a^{3} - \\frac{11032674479345}{1045156909429} a^{2} - \\frac{14217501004015}{1045156909429} a + \\frac{384225479516}{55008258391} \\)', '\\( \\frac{251832218}{55008258391} a^{11} - \\frac{10300838629}{1045156909429} a^{10} - \\frac{186879209874}{1045156909429} a^{9} + \\frac{353799003752}{1045156909429} a^{8} + \\frac{2403780332209}{1045156909429} a^{7} - \\frac{3670615391235}{1045156909429} a^{6} - \\frac{136735027706}{11743336061} a^{5} + \\frac{13629186519807}{1045156909429} a^{4} + \\frac{23187183661440}{1045156909429} a^{3} - \\frac{15679241004492}{1045156909429} a^{2} - \\frac{647538098810}{55008258391} a + \\frac{328092812039}{55008258391} \\)', '\\( \\frac{29210587230}{1045156909429} a^{11} - \\frac{67652199719}{1045156909429} a^{10} - \\frac{1091939638094}{1045156909429} a^{9} + \\frac{2327886531933}{1045156909429} a^{8} + \\frac{12875475712758}{1045156909429} a^{7} - \\frac{24448087064585}{1045156909429} a^{6} - \\frac{610584948585}{11743336061} a^{5} + \\frac{95136321659787}{1045156909429} a^{4} + \\frac{74322030269016}{1045156909429} a^{3} - \\frac{116505524485975}{1045156909429} a^{2} - \\frac{31467810678154}{1045156909429} a + \\frac{2123218762305}{55008258391} \\)', '\\( \\frac{3718638927}{1045156909429} a^{11} - \\frac{282256083}{1045156909429} a^{10} - \\frac{147345877217}{1045156909429} a^{9} - \\frac{23922657801}{1045156909429} a^{8} + \\frac{1883520078282}{1045156909429} a^{7} + \\frac{802749626184}{1045156909429} a^{6} - \\frac{99133422651}{11743336061} a^{5} - \\frac{4991402659572}{1045156909429} a^{4} + \\frac{15263429647440}{1045156909429} a^{3} + \\frac{10630393017660}{1045156909429} a^{2} - \\frac{8679476581308}{1045156909429} a - \\frac{349612057236}{55008258391} \\)', '\\( \\frac{35319832053}{1045156909429} a^{11} - \\frac{84434960703}{1045156909429} a^{10} - \\frac{1325727613341}{1045156909429} a^{9} + \\frac{2923498603812}{1045156909429} a^{8} + \\frac{15778510617696}{1045156909429} a^{7} - \\frac{31014526080954}{1045156909429} a^{6} - \\frac{766008053661}{11743336061} a^{5} + \\frac{6424097679966}{55008258391} a^{4} + \\frac{98008681866550}{1045156909429} a^{3} - \\frac{154461203381364}{1045156909429} a^{2} - \\frac{44764750197339}{1045156909429} a + \\frac{2994407251965}{55008258391} \\)', '\\( \\frac{15622399366}{1045156909429} a^{11} - \\frac{22101358371}{1045156909429} a^{10} - \\frac{597958696371}{1045156909429} a^{9} + \\frac{37552590467}{55008258391} a^{8} + \\frac{7285554742584}{1045156909429} a^{7} - \\frac{6814448403570}{1045156909429} a^{6} - \\frac{360163325950}{11743336061} a^{5} + \\frac{25967494266789}{1045156909429} a^{4} + \\frac{48828300883818}{1045156909429} a^{3} - \\frac{32732367001119}{1045156909429} a^{2} - \\frac{21963873701197}{1045156909429} a + \\frac{736939629057}{55008258391} \\)', '\\( \\frac{66329694413}{1045156909429} a^{11} - \\frac{200902424471}{1045156909429} a^{10} - \\frac{2341296207875}{1045156909429} a^{9} + \\frac{6953722511280}{1045156909429} a^{8} + \\frac{24465995118315}{1045156909429} a^{7} - \\frac{72866787907915}{1045156909429} a^{6} - \\frac{827658998152}{11743336061} a^{5} + \\frac{266868616404356}{1045156909429} a^{4} - \\frac{11476162102950}{1045156909429} a^{3} - \\frac{248308272685383}{1045156909429} a^{2} + \\frac{83429468760477}{1045156909429} a + \\frac{1252071764481}{55008258391} \\)', '\\( \\frac{108237957450}{1045156909429} a^{11} - \\frac{11832723557}{55008258391} a^{10} - \\frac{4109127951103}{1045156909429} a^{9} + \\frac{7696763139963}{1045156909429} a^{8} + \\frac{2621349493031}{55008258391} a^{7} - \\frac{80595277109816}{1045156909429} a^{6} - \\frac{2493620734873}{11743336061} a^{5} + \\frac{320333380291695}{1045156909429} a^{4} + \\frac{345049411852922}{1045156909429} a^{3} - \\frac{22263873407848}{55008258391} a^{2} - \\frac{169404883324736}{1045156909429} a + \\frac{8936505707850}{55008258391} \\)', '\\( \\frac{217717789388}{1045156909429} a^{11} - \\frac{417272433938}{1045156909429} a^{10} - \\frac{8293146598225}{1045156909429} a^{9} + \\frac{14094373437874}{1045156909429} a^{8} + \\frac{100952130791220}{1045156909429} a^{7} - \\frac{144069820737013}{1045156909429} a^{6} - \\frac{5070905779424}{11743336061} a^{5} + \\frac{554691523327267}{1045156909429} a^{4} + \\frac{700923820280822}{1045156909429} a^{3} - \\frac{686944750664067}{1045156909429} a^{2} - \\frac{326064108878025}{1045156909429} a + \\frac{14323875602157}{55008258391} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/19*a^9 + 4/19*a^8 + 1/19*a^7 + 8/19*a^6 + 8/19*a^5 + 1/19*a^4 - 5/19*a^3 - 8/19*a^2 + 9/19*a', '1/19*a^10 + 4/19*a^8 + 4/19*a^7 - 5/19*a^6 + 7/19*a^5 - 9/19*a^4 - 7/19*a^3 + 3/19*a^2 + 2/19*a', '1/1045156909429*a^11 - 2242936008/1045156909429*a^10 - 24144692793/1045156909429*a^9 + 33669755457/1045156909429*a^8 + 316103098293/1045156909429*a^7 + 99583078814/1045156909429*a^6 - 5713060868/11743336061*a^5 - 443185672267/1045156909429*a^4 + 71685496487/1045156909429*a^3 + 420826743567/1045156909429*a^2 - 234702917662/1045156909429*a + 20409816750/55008258391']}
Number field data - 12.12.9891413435408203125.1