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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [81, 0, -72, 0, 252, 0, -248, 0, 118, 0, -56, 0, 28, 0, -8, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 1530046740449765049237504, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[8, 2]]], [7, [[8, 1], [4, 1], [2, 2]]], [11, [[4, 4]]], [13, [[8, 2]]], [17, [[4, 2], [2, 4]]], [19, [[4, 3], [2, 1], [1, 2]]], [23, [[4, 4]]], [29, [[8, 2]]], [31, [[8, 1], [4, 1], [2, 2]]], [37, [[8, 2]]], [41, [[4, 4]]], [43, [[4, 3], [2, 1], [1, 2]]], [47, [[4, 4]]], [53, [[8, 2]]], [59, [[2, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [5252, 512], 'galois_label': '16T1276', 'galt': 1276, 'grd': 60.60594865478429, 'inessentialp': [3], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 74, 'label': '16.0.1530046740449765049237504.74', 'local_algs': ['2.1.16.74c1.182', '3.2.1.0a1.1', '3.2.1.0a1.1', '3.2.1.0a1.1', '3.2.1.0a1.1', 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\\frac{763}{432} a^{9} - \\frac{5}{6} a^{8} - \\frac{1655}{432} a^{7} + \\frac{4}{3} a^{6} + \\frac{3361}{432} a^{5} - \\frac{25}{8} a^{4} - \\frac{97}{16} a^{3} + \\frac{51}{8} a^{2} + \\frac{13}{48} a - 2 \\)', '\\( -\\frac{1}{216} a^{15} + \\frac{1}{144} a^{14} + \\frac{5}{216} a^{13} - \\frac{5}{144} a^{12} - \\frac{5}{108} a^{11} + \\frac{13}{144} a^{10} + \\frac{1}{27} a^{9} - \\frac{29}{144} a^{8} - \\frac{19}{216} a^{7} + \\frac{79}{144} a^{6} + \\frac{11}{216} a^{5} - \\frac{107}{144} a^{4} + \\frac{7}{12} a^{3} + \\frac{11}{16} a^{2} - \\frac{2}{3} a + \\frac{5}{16} \\)', '\\( \\frac{29}{432} a^{15} + \\frac{1}{18} a^{14} - \\frac{187}{432} a^{13} - \\frac{13}{36} a^{12} + \\frac{533}{432} a^{11} + \\frac{35}{36} a^{10} - \\frac{895}{432} a^{9} - \\frac{13}{9} a^{8} + \\frac{2351}{432} a^{7} + \\frac{35}{9} a^{6} - \\frac{4105}{432} a^{5} - \\frac{253}{36} a^{4} + \\frac{215}{48} a^{3} + \\frac{3}{4} a^{2} - \\frac{229}{48} a - \\frac{1}{2} \\)', '\\( -\\frac{29}{432} a^{15} + \\frac{1}{18} a^{14} + \\frac{187}{432} a^{13} - \\frac{13}{36} a^{12} - \\frac{533}{432} a^{11} + \\frac{35}{36} a^{10} + \\frac{895}{432} a^{9} - \\frac{13}{9} a^{8} - \\frac{2351}{432} a^{7} + \\frac{35}{9} a^{6} + \\frac{4105}{432} a^{5} - \\frac{253}{36} a^{4} - \\frac{215}{48} a^{3} + \\frac{3}{4} a^{2} + \\frac{229}{48} a - \\frac{1}{2} \\)', '\\( -\\frac{7}{72} a^{15} + \\frac{5}{48} a^{14} + \\frac{49}{72} a^{13} - \\frac{103}{144} a^{12} - \\frac{77}{36} a^{11} + \\frac{109}{48} a^{10} + \\frac{137}{36} a^{9} - \\frac{607}{144} a^{8} - \\frac{625}{72} a^{7} + \\frac{467}{48} a^{6} + \\frac{1171}{72} a^{5} - \\frac{2473}{144} a^{4} - \\frac{145}{12} a^{3} + \\frac{731}{48} a^{2} - \\frac{11}{4} a - \\frac{73}{16} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2', '1/2*a^5 - 1/2*a', '1/2*a^6 - 1/2*a^2', '1/4*a^7 - 1/4*a^6 - 1/4*a^5 - 1/4*a^4 - 1/4*a^3 + 1/4*a^2 + 1/4*a + 1/4', '1/12*a^8 + 1/6*a^6 + 1/6*a^4 - 1/6*a^2 - 1/4', '1/12*a^9 - 1/12*a^7 - 1/4*a^6 - 1/12*a^5 - 1/4*a^4 + 1/12*a^3 + 1/4*a^2 + 1/4', '1/24*a^10 - 1/24*a^8 + 1/12*a^6 - 1/12*a^4 - 1/8*a^2 + 1/8', '1/24*a^11 - 1/24*a^9 + 1/12*a^7 - 1/12*a^5 - 1/8*a^3 + 1/8*a', '1/72*a^12 + 1/72*a^8 - 1/6*a^6 - 5/72*a^4 - 1/2*a^2 + 3/8', '1/144*a^13 - 1/144*a^12 + 1/144*a^9 - 1/144*a^8 - 1/12*a^7 + 1/12*a^6 + 31/144*a^5 - 31/144*a^4 - 1/4*a^3 + 1/4*a^2 + 7/16*a - 7/16', '1/144*a^14 - 1/144*a^12 + 1/144*a^10 - 1/144*a^8 - 5/144*a^6 + 29/144*a^4 + 1/48*a^2 - 3/16', '1/432*a^15 + 1/432*a^13 + 1/432*a^11 - 11/432*a^9 - 53/432*a^7 - 5/432*a^5 + 11/48*a^3 + 7/48*a']}