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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -8, 30, -70, 110, -114, 67, -5, -24, 16, -6, 12, -15, 7, 2, -3, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 232322192503515625, 'disc_rad': 132965, 'disc_sign': 1, 'frobs': [[2, [[8, 2]]], [3, [[4, 4]]], [5, [0]], [7, [0]], [11, [[4, 4]]], [13, [[4, 4]]], [17, [[8, 2]]], [19, [[4, 2], [2, 4]]], [23, [[8, 1], [4, 1], [2, 2]]], [29, [0]], [31, [[8, 1], [4, 1], [2, 2]]], [37, [[8, 2]]], [41, [[8, 1], [4, 1], [2, 2]]], [43, [[8, 2]]], [47, [[8, 2]]], [53, [[4, 4]]], [59, [[8, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [8192, 8192, 8192, 8192], 'galois_label': '16T1772', 'galt': 1772, 'grd': 364.64366167534024, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '16.4.232322192503515625.1', 'local_algs': ['5.16.8.1', '7.2.0.1', '7.2.0.1', '7.2.0.1', '7.2.0.1', '7.4.0.1', '7.4.2.2', '29.4.0.1', '29.4.0.1', '29.8.4.1', '131.4.2.1', '131.4.0.1', '131.8.0.1'], 'monogenic': 0, 'num_ram': 4, 'r2': 6, 'ramps': [5, 7, 29, 131], 'rd': 12.1725248157, 'regulator': {'__RealLiteral__': 0, 'data': '155.818339721', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-1.-1.1', '1.1.-3.-1.1', '1.-3.-1.5.1.1.-2.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{15} - 3 a^{14} + 2 a^{13} + 7 a^{12} - 15 a^{11} + 12 a^{10} - 6 a^{9} + 16 a^{8} - 24 a^{7} - 5 a^{6} + 67 a^{5} - 114 a^{4} + 110 a^{3} - 70 a^{2} + 30 a - 7 \\)', '\\( a \\)', '\\( \\frac{10558}{133} a^{15} - \\frac{24922}{133} a^{14} + 38 a^{13} + \\frac{11052}{19} a^{12} - \\frac{108845}{133} a^{11} + \\frac{56237}{133} a^{10} - \\frac{3793}{19} a^{9} + \\frac{151603}{133} a^{8} - \\frac{156203}{133} a^{7} - \\frac{154258}{133} a^{6} + \\frac{609675}{133} a^{5} - \\frac{811655}{133} a^{4} + \\frac{90912}{19} a^{3} - \\frac{46458}{19} a^{2} + \\frac{104164}{133} a - \\frac{16052}{133} \\)', '\\( \\frac{10558}{133} a^{15} - \\frac{24922}{133} a^{14} + 38 a^{13} + \\frac{11052}{19} a^{12} - \\frac{108845}{133} a^{11} + \\frac{56237}{133} a^{10} - \\frac{3793}{19} a^{9} + \\frac{151603}{133} a^{8} - \\frac{156203}{133} a^{7} - \\frac{154258}{133} a^{6} + \\frac{609675}{133} a^{5} - \\frac{811655}{133} a^{4} + \\frac{90912}{19} a^{3} - \\frac{46458}{19} a^{2} + \\frac{104164}{133} a - \\frac{15919}{133} \\)', '\\( \\frac{6183}{133} a^{15} - \\frac{14676}{133} a^{14} + \\frac{169}{7} a^{13} + \\frac{45181}{133} a^{12} - \\frac{64361}{133} a^{11} + \\frac{34166}{133} a^{10} - \\frac{16323}{133} a^{9} + \\frac{89158}{133} a^{8} - \\frac{92531}{133} a^{7} - \\frac{88411}{133} a^{6} + \\frac{357880}{133} a^{5} - \\frac{480841}{133} a^{4} + \\frac{54553}{19} a^{3} - \\frac{28287}{19} a^{2} + \\frac{64915}{133} a - \\frac{10435}{133} \\)', '\\( \\frac{271}{133} a^{15} - \\frac{112}{19} a^{14} + \\frac{15}{7} a^{13} + \\frac{2201}{133} a^{12} - \\frac{3653}{133} a^{11} + \\frac{1646}{133} a^{10} - \\frac{671}{133} a^{9} + \\frac{4324}{133} a^{8} - \\frac{5798}{133} a^{7} - \\frac{4420}{133} a^{6} + \\frac{18304}{133} a^{5} - \\frac{25180}{133} a^{4} + \\frac{2843}{19} a^{3} - \\frac{1508}{19} a^{2} + \\frac{3510}{133} a - \\frac{563}{133} \\)', '\\( 66 a^{15} - \\frac{1088}{7} a^{14} + \\frac{228}{7} a^{13} + \\frac{3368}{7} a^{12} - \\frac{4758}{7} a^{11} + 360 a^{10} - \\frac{1199}{7} a^{9} + \\frac{6632}{7} a^{8} - 974 a^{7} - \\frac{6625}{7} a^{6} + \\frac{26610}{7} a^{5} - \\frac{35618}{7} a^{4} + 4024 a^{3} - 2078 a^{2} + 675 a - \\frac{748}{7} \\)', '\\( \\frac{11667}{133} a^{15} - \\frac{27969}{133} a^{14} + \\frac{332}{7} a^{13} + \\frac{85773}{133} a^{12} - \\frac{123159}{133} a^{11} + \\frac{64534}{133} a^{10} - \\frac{30139}{133} a^{9} + \\frac{168555}{133} a^{8} - \\frac{178194}{133} a^{7} - \\frac{24012}{19} a^{6} + \\frac{681425}{133} a^{5} - \\frac{915459}{133} a^{4} + \\frac{103408}{19} a^{3} - \\frac{53304}{19} a^{2} + \\frac{121257}{133} a - \\frac{19086}{133} \\)', '\\( \\frac{5184}{133} a^{15} - \\frac{12385}{133} a^{14} + \\frac{146}{7} a^{13} + \\frac{38112}{133} a^{12} - \\frac{54603}{133} a^{11} + \\frac{28565}{133} a^{10} - \\frac{12867}{133} a^{9} + \\frac{74633}{133} a^{8} - \\frac{78928}{133} a^{7} - \\frac{74602}{133} a^{6} + \\frac{303118}{133} a^{5} - \\frac{405647}{133} a^{4} + \\frac{45589}{19} a^{3} - \\frac{23286}{19} a^{2} + \\frac{52158}{133} a - \\frac{8083}{133} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', '1/7*a^14 + 1/7*a^13 + 2/7*a^12 - 3/7*a^11 + 3/7*a^9 - 1/7*a^8 + 1/7*a^6 - 1/7*a^5 + 3/7*a^4 + 2/7', '1/133*a^15 - 1/133*a^14 + 1/19*a^12 - 1/133*a^11 + 10/133*a^10 + 2/19*a^9 + 44/133*a^8 + 64/133*a^7 - 10/133*a^6 + 47/133*a^5 - 20/133*a^4 - 9/19*a^3 - 9/19*a^2 + 37/133*a + 66/133']}