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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-243, -243, 351, 72, -12, 11, 60, -17, 4, -1, 1], 'conductor': 0, 'degree': 10, 'dirichlet_group': [], 'disc_abs': 14461892424733, 'disc_rad': 1027, 'disc_sign': 1, 'frobs': [[2, [[10, 1]]], [3, [[2, 4], [1, 2]]], [5, [[10, 1]]], [7, [[2, 5]]], [11, [[10, 1]]], [13, [0]], [17, [[2, 4], [1, 2]]], [19, [[10, 1]]], [23, [[5, 2]]], [29, [[2, 4], [1, 2]]], [31, [[10, 1]]], [37, [[2, 5]]], [41, [[2, 5]]], [43, [[2, 4], [1, 2]]], [47, [[2, 5]]], [53, [[2, 4], [1, 2]]], [59, [[2, 5]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [10, 10], 'galois_label': '10T3', 'galt': 3, 'grd': 32.046840717924134, 'inessentialp': [3], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '10.2.14461892424733.1', 'local_algs': ['13.10.5.1', '79.1.0.1', '79.1.0.1', '79.2.1.2', '79.2.1.2', '79.2.1.2', '79.2.1.2'], 'monogenic': -1, 'num_ram': 2, 'r2': 4, 'ramps': [13, 79], 'rd': 20.7024866219, 'regulator': {'__RealLiteral__': 0, 'data': '835.981549877', 'prec': 44}, 'res': {'gal': ['764449,-1548001,2232239,-1639236,1206536,-1701067,1465830,-767027,407949,-212266,84906,-33580,15203,-6180,2222,-710,220,-62,21,-6,1'], 'sib': ['38089,-28461,9073,-1028,237,-318,143,-24,-3,-2,1', '764449,-1548001,2232239,-1639236,1206536,-1701067,1465830,-767027,407949,-212266,84906,-33580,15203,-6180,2222,-710,220,-62,21,-6,1']}, 'subfield_mults': [1, 1], 'subfields': ['-3.-1.1', '-1.3.-2.1.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{8483848}{4993284123} a^{9} - \\frac{28154455}{4993284123} a^{8} + \\frac{34719958}{4993284123} a^{7} - \\frac{215965577}{4993284123} a^{6} + \\frac{258739295}{1664428041} a^{5} - \\frac{740941627}{4993284123} a^{4} - \\frac{375277978}{1664428041} a^{3} - \\frac{15699589}{554809347} a^{2} + \\frac{35592310}{184936449} a - \\frac{71409377}{61645483} \\)', '\\( \\frac{233161}{184936449} a^{9} - \\frac{28569}{61645483} a^{8} + \\frac{276598}{61645483} a^{7} - \\frac{1423755}{61645483} a^{6} + \\frac{3323667}{61645483} a^{5} + \\frac{4066587}{61645483} a^{4} + \\frac{2471418}{61645483} a^{3} + \\frac{7454673}{61645483} a^{2} - \\frac{28085206}{184936449} a + \\frac{19670607}{61645483} \\)', '\\( \\frac{242847}{61645483} a^{9} - \\frac{9686}{61645483} a^{8} + \\frac{885681}{61645483} a^{7} - \\frac{3298605}{61645483} a^{6} + \\frac{10299555}{61645483} a^{5} + \\frac{12642318}{61645483} a^{4} + \\frac{9285597}{61645483} a^{3} + \\frac{24899238}{61645483} a^{2} + \\frac{107603316}{61645483} a + \\frac{36193939}{61645483} \\)', '\\( \\frac{2469352}{184936449} a^{9} + \\frac{781346}{1664428041} a^{8} + \\frac{17808481}{1664428041} a^{7} - \\frac{433419700}{1664428041} a^{6} + \\frac{640734305}{1664428041} a^{5} + \\frac{633835496}{554809347} a^{4} + \\frac{301510687}{1664428041} a^{3} - \\frac{356049161}{184936449} a^{2} + \\frac{36690071}{61645483} a + \\frac{99999652}{61645483} \\)', '\\( \\frac{118032197}{554809347} a^{9} + \\frac{11311439}{184936449} a^{8} + \\frac{459098261}{554809347} a^{7} - \\frac{1508871883}{554809347} a^{6} + \\frac{4891442185}{554809347} a^{5} + \\frac{2759323672}{184936449} a^{4} + \\frac{8205614695}{554809347} a^{3} + \\frac{12831017779}{554809347} a^{2} + \\frac{15062097598}{184936449} a + \\frac{2532061898}{61645483} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/3*a^6 - 1/3*a^5 + 1/3*a^4 + 1/3*a^3 - 1/3*a', '1/9*a^7 - 1/9*a^6 + 4/9*a^5 + 1/9*a^4 - 1/3*a^3 + 2/9*a^2 - 1/3*a', '1/27*a^8 - 1/27*a^7 + 4/27*a^6 + 10/27*a^5 + 2/9*a^4 + 11/27*a^3 - 4/9*a^2 - 1/3*a', '1/4993284123*a^9 - 30339040/4993284123*a^8 - 238976480/4993284123*a^7 + 513466369/4993284123*a^6 - 770434874/1664428041*a^5 + 1025156918/4993284123*a^4 + 68538139/554809347*a^3 + 69072736/184936449*a^2 - 87082253/184936449*a - 22978149/61645483']}
Number field data - 10.2.14461892424733.1