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{'class_group': [2, 4], 'class_number': 8, 'cm': True, 'coeffs': [28561, 0, -4394, 0, 1859, 0, 260, 0, 114, 0, 18, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 33045608803078144, 'disc_rad': 182, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[6, 2]]], [5, [[6, 2]]], [7, [0]], [11, [[3, 4]]], [13, [0]], [17, [[6, 2]]], [19, [[6, 2]]], [23, [[3, 4]]], [29, [[2, 4], [1, 4]]], [31, [[6, 2]]], [37, [[3, 4]]], [41, [[2, 6]]], [43, [[2, 4], [1, 4]]], [47, [[6, 2]]], [53, [[3, 4]]], [59, [[6, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [36, 20, 12], 'galois_label': '12T7', 'galt': 7, 'grd': 51.61370512661073, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '12.0.33045608803078144.1', 'local_algs': ['2.6.6.1', '2.6.6.1', '7.6.5.5', '7.6.5.5', '13.2.0.1', '13.2.0.1', '13.4.2.1', '13.4.2.1'], 'minimal_sibling': [1183, 0, 364, 0, 35, 0, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 6, 'ramps': [2, 7, 13], 'rd': 23.8008689519, 'regulator': {'__RealLiteral__': 0, 'data': '1615.30314445', 'prec': 44}, 'res': {'gal': ['1,-50,1794,26200,149593,483852,1081836,1829292,2386593,2499518,2736312,2278450,2507033,1428978,744652,206120,72609,8282,1566,-110,1,-10,32,-8,1'], 'sib': ['1183,0,364,0,35,0,1', '3266,312,-138,494,253,-26,-24,0,1', '9317,35574,38962,1890,2674,-2338,2780,96,557,-22,44,-4,1']}, 'subfield_mults': [1, 1, 1, 1, 1], 'subfields': ['2.-1.1', '1.-2.-1.1', '1.-1.1.-1.1.-1.1', '1183.0.364.0.35.0.1', '-169.0.104.0.-19.0.1'], 'torsion_gen': '\\( -\\frac{1142}{65670527} a^{10} - \\frac{73105}{131341054} a^{8} - \\frac{506174}{65670527} a^{6} - \\frac{613833}{10103158} a^{4} - \\frac{113585}{777166} a^{2} + \\frac{3902}{29891} \\)', 'torsion_order': 14, 'units': ['\\( \\frac{1219}{65670527} a^{10} + \\frac{6862}{65670527} a^{8} - \\frac{16371}{65670527} a^{6} - \\frac{107314}{5051579} a^{4} - \\frac{54401}{388583} a^{2} + \\frac{3059}{29891} \\)', '\\( \\frac{12451}{131341054} a^{10} + \\frac{98799}{65670527} a^{8} + \\frac{311829}{65670527} a^{6} - \\frac{183571}{10103158} a^{4} + \\frac{174379}{777166} a^{2} + \\frac{30117}{59782} \\)', '\\( \\frac{11798}{65670527} a^{11} - \\frac{10656}{65670527} a^{10} + \\frac{474869}{131341054} a^{9} - \\frac{200882}{65670527} a^{8} + \\frac{3332729}{131341054} a^{7} - \\frac{2320381}{131341054} a^{6} + \\frac{579507}{10103158} a^{5} + \\frac{17163}{5051579} a^{4} + \\frac{51957}{388583} a^{3} + \\frac{9671}{777166} a^{2} - \\frac{72195}{59782} a + \\frac{183955}{59782} \\)', '\\( \\frac{3281}{65670527} a^{11} - \\frac{12187}{131341054} a^{10} + \\frac{59591}{65670527} a^{9} - \\frac{149697}{65670527} a^{8} + \\frac{1255497}{131341054} a^{7} - \\frac{3136895}{131341054} a^{6} + \\frac{292035}{5051579} a^{5} - \\frac{792553}{10103158} a^{4} + \\frac{200147}{777166} a^{3} - \\frac{160378}{388583} a^{2} + \\frac{13647}{59782} a + \\frac{7550}{29891} \\)', '\\( \\frac{31479}{131341054} a^{11} - \\frac{4203}{10103158} a^{10} + \\frac{526257}{131341054} a^{9} - \\frac{23232}{5051579} a^{8} + \\frac{1931691}{131341054} a^{7} + \\frac{49789}{5051579} a^{6} - \\frac{415865}{5051579} a^{5} + \\frac{2348435}{10103158} a^{4} + \\frac{51123}{777166} a^{3} - \\frac{690709}{777166} a^{2} + \\frac{16656}{29891} a + \\frac{103143}{59782} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', '1/26*a^6 - 4/13*a^4 - 3/26*a^2 - 1/2', '1/26*a^7 - 4/13*a^5 - 3/26*a^3 - 1/2*a', '1/338*a^8 + 5/338*a^6 + 49/338*a^4 + 5/13*a^2 - 1/2', '1/338*a^9 + 5/338*a^7 + 49/338*a^5 + 5/13*a^3 - 1/2*a', '1/131341054*a^10 + 52603/131341054*a^8 - 2136423/131341054*a^6 - 1232588/5051579*a^4 + 359383/777166*a^2 + 7615/29891', '1/131341054*a^11 + 52603/131341054*a^9 - 2136423/131341054*a^7 - 1232588/5051579*a^5 + 359383/777166*a^3 + 7615/29891*a']}