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{'class_group': [9], 'class_number': 9, 'cm': False, 'coeffs': [-17159528, 518192, 3575354, -420319, -146182, 22118, 1565, -312, -1, 1], 'conductor': 703, 'degree': 9, 'dirichlet_group': [256, 1, 581, 44, 16, 530, 403, 121, 157], 'disc_abs': 59654416235884558133761, 'disc_rad': 703, 'disc_sign': 1, 'frobs': [[2, [[3, 3]]], [3, [[9, 1]]], [5, [[9, 1]]], [7, [[9, 1]]], [11, [[1, 9]]], [13, [[3, 3]]], [17, [[1, 9]]], [19, [0]], [23, [[9, 1]]], [29, [[9, 1]]], [31, [[3, 3]]], [37, [0]], [41, [[9, 1]]], [43, [[9, 1]]], [47, [[9, 1]]], [53, [[9, 1]]], [59, [[3, 3]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [8, 8], 'galois_label': '9T1', 'galt': 1, 'grd': 339.33367110228545, 'inessentialp': [2], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '9.9.59654416235884558133761.2', 'local_algs': ['19.9.8.2', '37.9.8.1'], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [19, 37], 'rd': 339.333671102, 'regulator': {'__RealLiteral__': 0, 'data': '84671913.5934', 'prec': 44}, 'res': {}, 'subfield_mults': [1], 'subfields': ['1432.-234.-1.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{32267778127}{42702347759698} a^{8} + \\frac{332900943161}{85404695519396} a^{7} - \\frac{4443110419733}{21351173879849} a^{6} - \\frac{1168732379112}{21351173879849} a^{5} + \\frac{121079457069007}{7764063229036} a^{4} - \\frac{1747958714806817}{85404695519396} a^{3} - \\frac{33314506311376823}{85404695519396} a^{2} + \\frac{11862662631868591}{21351173879849} a + \\frac{3307706878201548}{1255951404697} \\)', '\\( \\frac{10026678699}{42702347759698} a^{8} - \\frac{119323361061}{85404695519396} a^{7} - \\frac{1415743509489}{21351173879849} a^{6} + \\frac{14620658089387}{21351173879849} a^{5} + \\frac{149190561315811}{85404695519396} a^{4} - \\frac{3428000467228607}{85404695519396} a^{3} + \\frac{8364089902329691}{85404695519396} a^{2} + \\frac{4231479784078367}{21351173879849} a - \\frac{657263336632127}{1255951404697} \\)', '\\( \\frac{18979834276}{21351173879849} a^{8} - \\frac{262468764289}{85404695519396} a^{7} - \\frac{10459682054861}{42702347759698} a^{6} + \\frac{85639200795893}{42702347759698} a^{5} + \\frac{677356591206937}{85404695519396} a^{4} - \\frac{10281309145753291}{85404695519396} a^{3} + \\frac{22229556233448013}{85404695519396} a^{2} + \\frac{22057408602657185}{42702347759698} a - \\frac{2029493540910268}{1255951404697} \\)', '\\( \\frac{245376163379}{21351173879849} a^{8} + \\frac{6387322961507}{85404695519396} a^{7} - \\frac{64618297088239}{21351173879849} a^{6} - \\frac{202665315485799}{42702347759698} a^{5} + \\frac{18720487375764129}{85404695519396} a^{4} - \\frac{270344515289175}{7764063229036} a^{3} - \\frac{39874000738078039}{7764063229036} a^{2} + \\frac{56364275239525038}{21351173879849} a + \\frac{33390853717327922}{1255951404697} \\)', '\\( \\frac{989668930271}{85404695519396} a^{8} + \\frac{6515243263939}{85404695519396} a^{7} - \\frac{130082316643423}{42702347759698} a^{6} - \\frac{424841966687555}{85404695519396} a^{5} + \\frac{9440527837035763}{42702347759698} a^{4} - \\frac{586065908802756}{21351173879849} a^{3} - \\frac{444136909988913673}{85404695519396} a^{2} + \\frac{115081427422431253}{42702347759698} a + \\frac{33566719602182385}{1255951404697} \\)', '\\( \\frac{36988903805}{42702347759698} a^{8} + \\frac{766590596743}{85404695519396} a^{7} - \\frac{4592667542545}{21351173879849} a^{6} - \\frac{54650633161175}{42702347759698} a^{5} + \\frac{1488947930133417}{85404695519396} a^{4} + \\frac{5145036486829331}{85404695519396} a^{3} - \\frac{46832074466905381}{85404695519396} a^{2} - \\frac{41128984200379919}{42702347759698} a + \\frac{6898659283646116}{1255951404697} \\)', '\\( \\frac{112638791637}{85404695519396} a^{8} + \\frac{876692149077}{85404695519396} a^{7} - \\frac{6955191281986}{21351173879849} a^{6} - \\frac{71843715233035}{85404695519396} a^{5} + \\frac{44188065088899}{1941015807259} a^{4} + \\frac{256537351308881}{21351173879849} a^{3} - \\frac{43707700206549921}{85404695519396} a^{2} + \\frac{2252861862123011}{42702347759698} a + \\frac{2919411374673388}{1255951404697} \\)', '\\( \\frac{10411654353}{5023805618788} a^{8} + \\frac{27102218639}{2511902809394} a^{7} - \\frac{1412128591405}{2511902809394} a^{6} - \\frac{770335532363}{5023805618788} a^{5} + \\frac{202245021038373}{5023805618788} a^{4} - \\frac{24645162961001}{456709601708} a^{3} - \\frac{203780585403233}{228354800854} a^{2} + \\frac{3460566879566351}{2511902809394} a + \\frac{4761881646618828}{1255951404697} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/2*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a', '1/2*a^6 - 1/2*a^3 - 1/2*a^2 - 1/2*a', '1/44*a^7 - 1/22*a^6 + 21/44*a^4 + 9/44*a^3 + 19/44*a^2 + 3/11*a - 4/11', '1/85404695519396*a^8 + 189176772536/21351173879849*a^7 - 1562162517835/42702347759698*a^6 - 16481788250445/85404695519396*a^5 - 5603987017891/85404695519396*a^4 + 28472923054713/85404695519396*a^3 - 4909856482767/21351173879849*a^2 + 8475395790637/21351173879849*a + 285194116217/1255951404697']}