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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -3, 2, -9, -2, 0, -1, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 32913169, 'disc_rad': 5737, 'disc_sign': 1, 'frobs': [[2, [[7, 1]]], [3, [[3, 2], [1, 1]]], [5, [[7, 1]]], [7, [[7, 1]]], [11, [[3, 2], [1, 1]]], [13, [[2, 2], [1, 3]]], [17, [[7, 1]]], [19, [[7, 1]]], [23, [[4, 1], [2, 1], [1, 1]]], [29, [[3, 2], [1, 1]]], [31, [[4, 1], [2, 1], [1, 1]]], [37, [[7, 1]]], [41, [[2, 2], [1, 3]]], [43, [[4, 1], [2, 1], [1, 1]]], [47, [[3, 2], [1, 1]]], [53, [[4, 1], [2, 1], [1, 1]]], [59, [[3, 2], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [84], 'galois_label': '7T5', 'galt': 5, 'grd': 75.7429864739964, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '7.3.32913169.1', 'local_algs': ['m5737.1.1.0', 'm5737.1.1.0', 'm5737.1.1.0', 'm5737.2.2.2'], 'monogenic': 0, 'num_ram': 1, 'r2': 2, 'ramps': [5737], 'rd': 11.8552292654, 'regulator': {'__RealLiteral__': 0, 'data': '13.6434515247', 'prec': 44}, 'res': {'ae': ['-1,-1,5,-4,0,3,-2,1'], 'sib': ['3584,-2123,1370,-102,187,-45,27,-4,1', '-1,-5,-4,21,83,72,80,-147,217,139,-101,51,-95,54,-114,64,-34,34,-17,4,-3,1', '-557,-4335,-4248,-1184,3831,2907,-167,-1405,-338,263,65,-7,-3,-4,1', '-9969,-6214,10008,7131,-10041,1540,-2293,-151,-239,-270,-6,-42,9,-1,1', '-589979,1619274,-236490,-3117968,806087,2855683,5646720,-15171868,6085359,16013070,-26155784,14851001,2915355,-13479079,26859717,-27750130,-10426144,42400568,-20303511,-18653326,21574704,-1960702,-6396372,3718349,-895644,-243442,672068,-514483,83385,132682,-79814,-1190,13920,-504,-3528,578,770,-351,-18,60,-12,-3,1', '1,13,-9,268,426,2271,20574,-5754,228890,-54587,838237,-319729,780950,-197741,-1667030,1480215,-3725239,4658709,-4269558,4361871,-3425427,2354859,-1332858,730209,-621597,562950,-328975,79133,21126,-70351,86478,-67287,40011,-20715,9586,-3967,1442,-461,190,-79,29,-6,1', '1,9,42,123,294,712,1811,4397,8501,13313,18482,20370,10811,-6608,-19047,-19552,-12737,-6445,-2252,-922,213,159,194,48,27,13,4,-1,1', '111556,-386772,-890577,3025731,13817553,19903379,13793031,2298362,-3185097,-2424566,771392,1207456,835109,89829,-31731,-42106,5279,6115,4749,1192,510,74,32,-1,1', '1404693333,2804465187,-10087592823,-59947670052,-158922929304,-289957343238,-405427947604,-459844278408,-440525856437,-364040438285,-261948106925,-164711024361,-89032172153,-39899618206,-13879514177,-3016179105,-204896104,-252071303,-664146863,-792038995,-628320921,-426552153,-247392173,-129349596,-60237191,-20828945,-5472285,262747,1365038,822412,746508,268493,217070,48193,37699,3685,4843,113,428,-31,20,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( \\frac{18}{53} a^{6} - \\frac{19}{53} a^{5} + \\frac{4}{53} a^{4} - \\frac{48}{53} a^{3} - \\frac{177}{53} a^{2} + \\frac{37}{53} a - \\frac{59}{53} \\)', '\\( \\frac{24}{53} a^{6} + \\frac{10}{53} a^{5} - \\frac{30}{53} a^{4} - \\frac{64}{53} a^{3} - \\frac{289}{53} a^{2} - \\frac{251}{53} a - \\frac{8}{53} \\)', '\\( \\frac{30}{53} a^{6} - \\frac{14}{53} a^{5} - \\frac{11}{53} a^{4} - \\frac{80}{53} a^{3} - \\frac{295}{53} a^{2} - \\frac{115}{53} a - \\frac{63}{53} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/53*a^6 - 4/53*a^5 + 12/53*a^4 + 15/53*a^3 - 1/53*a^2 + 5/53*a - 18/53']}
Number field data - 7.3.32913169.1