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{'class_group': [2, 2, 2, 134660], 'class_number': 1077280, 'cm': True, 'coeffs': [718836830208, 0, 59903069184, 0, 1835265600, 0, 26655048, 0, 197064, 0, 714, 0, 1], 'conductor': 2856, 'degree': 12, 'dirichlet_group': [1, 2435, 1633, 1801, 395, 2209, 1067, 1475, 169, 2041, 251, 803], 'disc_abs': 6401594233356076787154812928, 'disc_rad': 714, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[12, 1]]], [7, [0]], [11, [[12, 1]]], [13, [[1, 12]]], [17, [0]], [19, [[3, 4]]], [23, [[12, 1]]], [29, [[4, 3]]], [31, [[12, 1]]], [37, [[12, 1]]], [41, [[4, 3]]], [43, [[2, 6]]], [47, [[6, 2]]], [53, [[6, 2]]], [59, [[6, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [18, 6, 10, 9], 'galois_label': '12T1', 'galt': 1, 'grd': 207.58247157811073, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.0.6401594233356076787154812928.1', 'local_algs': ['2.6.9.5', '2.6.9.5', '3.12.6.1', '7.12.10.5', '17.12.9.1'], 'monogenic': 0, 'num_ram': 4, 'r2': 6, 'ramps': [2, 3, 7, 17], 'rd': 207.582471578, 'regulator': {'__RealLiteral__': 0, 'data': '1059.5454270327698', 'prec': 60}, 'relative_class_number': 1077280, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-4.-1.1', '1.-2.-1.1', '119952.0.714.0.1', '-13.-25.57.11.-17.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{5}{1090672128} a^{10} + \\frac{1457}{545336064} a^{8} + \\frac{71}{127296} a^{6} + \\frac{2177}{42432} a^{4} + \\frac{209}{104} a^{2} + \\frac{327}{13} \\)', '\\( \\frac{1}{409002048} a^{10} + \\frac{61}{45444672} a^{8} + \\frac{49}{190944} a^{6} + \\frac{167}{7956} a^{4} + \\frac{233}{312} a^{2} + \\frac{138}{13} \\)', '\\( \\frac{1}{1636008192} a^{10} + \\frac{5}{16039296} a^{8} + \\frac{25}{668304} a^{6} - \\frac{199}{63648} a^{4} - \\frac{77}{104} a^{2} - \\frac{336}{13} \\)', '\\( \\frac{1}{3272016384} a^{10} + \\frac{215}{545336064} a^{8} + \\frac{401}{2673216} a^{6} + \\frac{991}{42432} a^{4} + \\frac{463}{312} a^{2} + \\frac{352}{13} \\)', '\\( \\frac{1}{363557376} a^{10} + \\frac{635}{545336064} a^{8} + \\frac{307}{2673216} a^{6} - \\frac{35}{7488} a^{4} - \\frac{133}{156} a^{2} - \\frac{238}{13} \\)'], 'used_grh': True, 'zk': ['1', 'a', '1/6*a^2', '1/6*a^3', '1/612*a^4', '1/612*a^5', '1/25704*a^6', '1/51408*a^7 - 1/1224*a^5 - 1/2*a', '1/10487232*a^8 - 1/102816*a^6 - 1/1224*a^4 + 1/24*a^2', '1/20974464*a^9 - 1/205632*a^7 - 1/2448*a^5 - 1/16*a^3 - 1/2*a', '1/3272016384*a^10 + 1/77905152*a^8 - 5/891072*a^6 + 61/127296*a^4 - 5/312*a^2 + 1/13', '1/6544032768*a^11 + 1/155810304*a^9 - 5/1782144*a^7 + 61/254592*a^5 - 5/624*a^3 + 1/26*a']}