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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, -3, 7, -20, 38, -49, 53, -49, 38, -20, 7, -3, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 2699554153024, 'disc_rad': 118, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[3, 4]]], [5, [[6, 2]]], [7, [[6, 2]]], [11, [[4, 2], [2, 2]]], [13, [[2, 6]]], [17, [[2, 4], [1, 4]]], [19, [[3, 4]]], [23, [[4, 2], [2, 2]]], [29, [[6, 2]]], [31, [[4, 2], [2, 2]]], [37, [[4, 2], [2, 2]]], [41, [[3, 4]]], [43, [[4, 2], [2, 2]]], [47, [[2, 6]]], [53, [[6, 2]]], [59, [0]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [72, 24], 'galois_label': '12T21', 'galt': 21, 'grd': 21.72556098240043, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.0.2699554153024.1', 'local_algs': ['2.4.0.1', '2.4.6.2', '2.4.0.1', '59.2.1.2', '59.2.1.2', '59.4.2.1', '59.4.2.1'], 'minimal_sibling': [1, -1, 2, 0, 2, -1, 1], 'monogenic': 0, 'num_ram': 2, 'r2': 6, 'ramps': [2, 59], 'rd': 10.8627804912, 'regulator': {'__RealLiteral__': 0, 'data': '16.1282227893', 'prec': 44}, 'res': {'sib': ['-11,19,-16,8,-2,-1,1', '1,-1,2,0,2,-1,1', '1,-2,1,0,1,0,1,-2,1', '3,16,-62,62,-38,16,5,-2,1']}, 'subfield_mults': [1, 3, 1, 1, 1], 'subfields': ['15.-1.1', '-1.2.0.1', '1.-1.2.0.2.-1.1', '-11.19.-16.8.-2.-1.1', '4.-14.21.-15.10.-3.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{15}{17} a^{11} - \\frac{112}{51} a^{10} + \\frac{274}{51} a^{9} - \\frac{800}{51} a^{8} + \\frac{1388}{51} a^{7} - \\frac{1757}{51} a^{6} + \\frac{644}{17} a^{5} - \\frac{1672}{51} a^{4} + \\frac{1291}{51} a^{3} - \\frac{610}{51} a^{2} + \\frac{245}{51} a - \\frac{74}{51} \\)', '\\( \\frac{80}{51} a^{11} - \\frac{67}{17} a^{10} + \\frac{472}{51} a^{9} - \\frac{464}{17} a^{8} + \\frac{803}{17} a^{7} - \\frac{965}{17} a^{6} + \\frac{3055}{51} a^{5} - \\frac{880}{17} a^{4} + \\frac{1940}{51} a^{3} - \\frac{245}{17} a^{2} + \\frac{224}{51} a - \\frac{124}{51} \\)', '\\( a \\)', '\\( \\frac{15}{17} a^{11} - \\frac{112}{51} a^{10} + \\frac{274}{51} a^{9} - \\frac{800}{51} a^{8} + \\frac{1388}{51} a^{7} - \\frac{1757}{51} a^{6} + \\frac{644}{17} a^{5} - \\frac{1672}{51} a^{4} + \\frac{1291}{51} a^{3} - \\frac{610}{51} a^{2} + \\frac{194}{51} a - \\frac{74}{51} \\)', '\\( \\frac{23}{51} a^{11} - \\frac{41}{51} a^{10} + \\frac{100}{51} a^{9} - \\frac{322}{51} a^{8} + \\frac{448}{51} a^{7} - \\frac{151}{17} a^{6} + \\frac{533}{51} a^{5} - \\frac{419}{51} a^{4} + \\frac{290}{51} a^{3} - \\frac{70}{51} a^{2} + \\frac{61}{51} a + \\frac{2}{17} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/3*a^6 - 1/3*a^4 - 1/3*a^3 - 1/3*a^2 + 1/3', '1/3*a^7 - 1/3*a^5 - 1/3*a^4 - 1/3*a^3 + 1/3*a', '1/3*a^8 - 1/3*a^5 + 1/3*a^4 - 1/3*a^3 + 1/3', '1/3*a^9 + 1/3*a^5 + 1/3*a^4 - 1/3*a^3 - 1/3*a^2 + 1/3*a + 1/3', '1/3*a^10 + 1/3*a^5 - 1/3*a^2 + 1/3*a - 1/3', '1/51*a^11 - 4/51*a^10 - 2/17*a^9 + 1/17*a^8 + 1/51*a^7 + 1/51*a^6 + 1/51*a^5 - 16/51*a^4 - 14/51*a^3 + 11/51*a^2 - 4/51*a + 1/51']}