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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-256, 384, 496, -16, -60, -8, 5, -3, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 295740809071407, 'disc_rad': 357, 'disc_sign': -1, 'frobs': [[2, [[2, 4]]], [3, [0]], [5, [[8, 1]]], [7, [0]], [11, [[7, 1], [1, 1]]], [13, [[8, 1]]], [17, [0]], [19, [[6, 1], [1, 2]]], [23, [[4, 2]]], [29, [[3, 2], [1, 2]]], [31, [[8, 1]]], [37, [[3, 2], [1, 2]]], [41, [[8, 1]]], [43, [[2, 4]]], [47, [[6, 1], [1, 2]]], [53, [[4, 2]]], [59, [[8, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [288, 280, 288], 'galois_label': '8T43', 'galt': 43, 'grd': 147.1905561284069, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '8.2.295740809071407.1', 'local_algs': ['3.1.0.1', '3.7.6.1', '7.1.0.1', '7.1.0.1', '7.6.5.6', '17.1.0.1', '17.7.6.1'], 'monogenic': -1, 'num_ram': 3, 'r2': 3, 'ramps': [3, 7, 17], 'rd': 64.3967436701, 'regulator': {'__RealLiteral__': 0, 'data': '84835.3817395', 'prec': 44}, 'res': {'sib': ['-247115776,671232256,-1160847488,1228815920,2664728024,-11417348936,23471281510,-37153664979,41093542586,-30453633695,16727782825,-7330841161,2537379409,-813709427,242923145,-53646926,14867791,-4838410,705976,-439697,90860,-36387,9839,-2181,881,-41,49,0,1', '-741376,-9680896,-31065088,-22993024,48274896,79843936,-144657580,132043616,-125060091,78679012,-34180687,17130784,-5784007,709980,-16626,-167924,94510,-5300,-2566,652,-267,-40,25,-4,1', '1053591680,1711487416,1704435688,-2902385148,984670345,50198422,-76338241,18264641,-46818304,39688277,-14693214,3849876,-1426410,554010,-119424,15526,-5707,1718,-149,13,-8,1', '200704,-157696,547072,-331712,438752,-137804,43920,-28119,1905,-518,536,-26,10,-1,1', '2225923204862336,-17687152821640736,-13323625666977304,60489667849459660,-9588934992725102,-77454849526395061,130392938534650953,-123521232284087946,73534290960707976,-28051561368664289,3871976946778029,2263600067454696,-706247509274384,-946703958208150,1286854780631770,-828122978268412,362385425579264,-117682353684650,31278500348686,-9930553966636,4483777235794,-1908942374375,529972095803,-17155631846,-63224544052,37070751673,-14067002401,4790479272,-1772305280,674704118,-225696246,62869620,-15072252,3417034,-779526,145212,-4318,-10241,4673,-1210,204,-21,1', '2835753106816,-26116150144,-1650728904160,157150546224,1245356999544,-479202565492,-153003778088,104136316865,24213189247,3592031374,-3723774772,-724589160,826071680,94659682,-80802860,-40813613,9926723,5884056,-1513798,-237449,76423,-1786,3928,-1324,-354,198,-10,-7,1', '29632,-5488,87716,-101878,151225,-100476,63290,-37280,15436,-7934,4190,-1260,142,8,8,-4,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{367}{4352} a^{7} - \\frac{73}{4352} a^{6} + \\frac{1423}{4352} a^{5} + \\frac{115}{1088} a^{4} - \\frac{5821}{1088} a^{3} - \\frac{2435}{136} a^{2} - \\frac{2719}{272} a + \\frac{441}{68} \\)', '\\( \\frac{293}{4352} a^{7} - \\frac{835}{4352} a^{6} + \\frac{389}{4352} a^{5} + \\frac{1457}{1088} a^{4} - \\frac{10655}{1088} a^{3} + \\frac{1967}{136} a^{2} + \\frac{6899}{272} a - \\frac{881}{68} \\)', '\\( \\frac{2769}{4352} a^{7} + \\frac{817}{4352} a^{6} + \\frac{16185}{4352} a^{5} + \\frac{6471}{1088} a^{4} - \\frac{24635}{1088} a^{3} - \\frac{13793}{136} a^{2} - \\frac{14117}{272} a + \\frac{2931}{68} \\)', '\\( \\frac{28025}{64} a^{7} - \\frac{8007}{64} a^{6} + \\frac{105989}{64} a^{5} + \\frac{3255}{8} a^{4} - \\frac{111101}{4} a^{3} - \\frac{727727}{8} a^{2} - 44856 a + 39787 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', '1/2*a^3 - 1/2*a^2 - 1/2*a', '1/4*a^4 - 1/4*a^3 - 1/4*a^2 - 1/2*a', '1/16*a^5 - 1/16*a^4 - 1/16*a^3 - 3/8*a^2 - 1/4*a', '1/32*a^6 - 1/32*a^5 - 1/32*a^4 - 3/16*a^3 - 1/8*a^2', '1/4352*a^7 + 25/4352*a^6 - 111/4352*a^5 - 31/1088*a^4 - 135/1088*a^3 + 5/34*a^2 - 5/272*a - 29/68']}