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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1431, 3201, -1989, 519, -145, 39, -3, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 1329725180808576, 'disc_rad': 246, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[7, 1]]], [7, [[5, 1], [1, 2]]], [11, [[4, 1], [2, 1], [1, 1]]], [13, [[4, 1], [1, 3]]], [17, [[6, 1], [1, 1]]], [19, [[4, 1], [1, 3]]], [23, [[4, 1], [3, 1]]], [29, [[7, 1]]], [31, [[3, 2], [1, 1]]], [37, [[5, 1], [2, 1]]], [41, [0]], [43, [[2, 3], [1, 1]]], [47, [[4, 1], [1, 3]]], [53, [[4, 1], [2, 1], [1, 1]]], [59, [[7, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [10920, 8680, 4320], 'galois_label': '7T7', 'galt': 7, 'grd': 718.3343720117198, 'index': 2, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '7.1.1329725180808576.1', 'local_algs': ['2.1.2.2a1.1', '2.1.2.3a1.1', '2.1.3.2a1.1', '3.1.1.0a1.1', '3.1.3.4a1.1', '3.1.3.3a1.1', '41.1.7.6a1.1'], 'monogenic': -1, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 3, 'r2': 3, 'ramps': [2, 3, 41], 'rd': 144.72295226, 'regulator': {'__RealLiteral__': 0, 'data': '1481588.34236', 'prec': 44}, 'res': {'sib': ['44930511,-25042446,26977167,-11688804,7588611,-2995626,1441923,-455736,148909,-30402,6381,-740,129,-6,1', '559133047611,-1132929664461,-372758544216,370799859348,-9668724975,10131817365,8897357088,-10503705456,631236078,-967852146,-41521488,12216792,-7430654,6181722,-430944,397904,-13881,12111,-280,180,-3,1', '-6073008997102193586733056,0,1532487110926834521101500416,0,-70853444632028819174326272,0,112416694523953969305563136,0,5172305838157468754514432,0,1188247638073775966279424,0,23936693982019849291392,0,2006707360891269882816,0,-140159522439258274080,0,-5147235025081094064,0,-350042674936626216,0,10224831933570708,0,319262794545096,0,9367613922528,0,-643989070350,0,-4450558071,0,101396022,0,-793521,0,85354,0,2583,0,6,0,1', '194520949041659904,-905830284813926400,1611865976494620672,-3132876538747551744,-2509916502153756672,-84195682397061120,-6149404834535964672,-1951324096738295808,4743515527381352448,1363048767029772288,-846316230296518656,102901997569204224,-35505956480458752,-95712484677083136,20932973143455744,-11966226795574272,953092106883072,24561998871552,-218799886102016,102532118642432,-32351992386560,10036500176640,-2161480479744,530493558528,-89198275456,18325653568,-2481970624,434458592,-46416224,6908240,-546840,69588,-3600,400,-10,1', '23175531419661140458080807,-5663230821314511769921950,31182907718061461855003481,-6428899804362043099317768,18901605934048233939433074,-3437580158529225877465452,7208362644667943608369566,-1179052815965161504018680,1995289636805753814562275,-290804231427378275055726,426725163720791736437133,-55197640096806564214560,72877036667437679664024,-8424806717021368280400,10173082532999340910248,-1050612557485538814048,1176203877438758545566,-109548631707923157948,113247635530632474402,-9827967786781866480,9108048221993047212,-755318017939105608,618759349583342388,-49825732269644688,35618859578316142,-2762923373135052,1749976907838642,-127680199355552,72081502617624,-4791848111568,2367909860648,-138680187360,58781267451,-2932615526,1054828869,-43140168,13099826,-415788,105822,-2360,495,-6,1', '769297845682176,0,-8919617602658304,0,55666411348439040,0,13018794125273600,0,190528120956703968,0,115923636115898088,0,211610422434187684,0,185657721429978660,0,99277343480244408,0,35126186146354912,0,8503960029934332,0,1503889057655790,0,206356106411169,0,22264883486685,0,1872413862864,0,121741603832,0,5765560494,0,182695458,0,3675944,0,45486,0,321,0,1', '93216223394436780504,-123175523398973808240,111453174563308139304,-69864068185401874968,34983529814215354608,-15854834118820411296,7405301883044293722,-3617720498332563480,1715905481940479448,-728996403455095572,260217845837432946,-75783130310637360,17942863874269950,-3513136216796388,590437546657650,-87650280453552,11796888340530,-1830467675700,431563917267,-98381184660,12322573578,435266772,-396133539,42446652,2572984,-821856,32799,3884,-258,-12,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{119766323767815811}{208} a^{6} - \\frac{613676387099429349}{104} a^{5} + \\frac{7101836451755156243}{208} a^{4} - \\frac{8349973259218047137}{52} a^{3} + \\frac{89796114438780237377}{208} a^{2} - \\frac{54098414303516399589}{104} a + \\frac{42027599022809821105}{208} \\)', '\\( \\frac{11430385965828941}{208} a^{6} - \\frac{1109839030757546581}{104} a^{5} + \\frac{12203821766950460353}{208} a^{4} - \\frac{18232635242446530535}{52} a^{3} + \\frac{262526536698500490223}{208} a^{2} - \\frac{188193553688589669313}{104} a + \\frac{158819789010810853019}{208} \\)', '\\( \\frac{283941642910036309436531}{24} a^{6} - \\frac{40986611240060085107291}{4} a^{5} + \\frac{3514336483573088868908315}{8} a^{4} - \\frac{2335121878490651598381544}{3} a^{3} + \\frac{35755432965214974239710591}{8} a^{2} - \\frac{55994112953798897823929857}{4} a + \\frac{63173755388303807349100229}{8} \\)'], 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2 - 1/2', '1/2*a^3 - 1/2*a', '1/4*a^4 - 1/4', '1/8*a^5 - 1/8*a^4 - 1/8*a + 1/8', '1/624*a^6 - 3/104*a^5 - 1/208*a^4 - 25/156*a^3 + 49/208*a^2 + 29/104*a + 93/208']}
Number field data - 7.1.1329725180808576.1