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nf_fields • Show schema
{'class_group': [70], 'class_number': 70, 'cm': False, 'coeffs': [679104, 0, 0, 0, 2096, 0, 0, 0, 1], 'conductor': 0, 'degree': 8, 'dirichlet_group': [], 'disc_abs': 177721081810499787554816, 'disc_rad': 262, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [[2, 3], [1, 2]]], [5, [[4, 2]]], [7, [[8, 1]]], [11, [[2, 3], [1, 2]]], [13, [[4, 2]]], [17, [[8, 1]]], [19, [[2, 4]]], [23, [[2, 4]]], [29, [[4, 1], [1, 4]]], [31, [[2, 4]]], [37, [[4, 1], [1, 4]]], [41, [[4, 2]]], [43, [[2, 3], [1, 2]]], [47, [[2, 2], [1, 4]]], [53, [[2, 4]]], [59, [[2, 3], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [236, 56], 'galois_label': '8T26', 'galt': 26, 'grd': 917.6149756300749, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 3, 'label': '8.0.177721081810499787554816.3', 'local_algs': ['2.1.8.28a1.55', '131.1.8.7a1.1'], 'maximal_cm_subfield': [10611, 0, 262, 0, 1], 'minimal_sibling': [42444, 0, 0, 0, -524, 0, 0, 0, 1], 'monogenic': 0, 'narrow_class_group': [70], 'narrow_class_number': 70, 'num_ram': 2, 'r2': 4, 'ramps': [2, 131], 'rd': 805.781641671, 'regulator': {'__RealLiteral__': 0, 'data': '12058586.9407', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-262.0.1', '10611.0.262.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{3242859}{20} a^{4} + \\frac{1374531643}{5} \\)', '\\( \\frac{6095040527596598036442574266468971029707846028491096460803375107363538820747}{1080} a^{7} + \\frac{57813962225278747032172223560818993213127627567862846753875027769829778160123}{360} a^{6} - \\frac{202768656239026162047209833059778846962892987988671995597276736059298818230987}{120} a^{5} + \\frac{87214076239123446413359296286160145935836438915465323055919763672811927135991}{10} a^{4} + \\frac{305166060768985421863804058645971313213854487785964417157490058434453560794857}{135} a^{3} + \\frac{5789250794922011824255966206552087023142308032459910262208964864688362912519941}{90} a^{2} - \\frac{10152206829752452293645520485341852463720565030399914658586473734433916794418492}{15} a + \\frac{17466512958524353628897010253590646867556339874523255723508363354381002961747529}{5} \\)', '\\( \\frac{4985786905730823950369272037491585945998667975439488462752278518952309025846606563}{2160} a^{7} + \\frac{742953082607191519743781170030925382739109953120407487325145869643613593763128959}{60} a^{6} + \\frac{3857360935073897250410699073620237066097878139404495192999442365464744845972099581}{120} a^{5} - \\frac{88898823086022634462455692264886415229073551060316486849417111964216209789397069}{2} a^{4} + \\frac{1056648140912397893573785206878023697269249348486233600758513404270278493941924422483}{270} a^{3} + \\frac{314911169837472941486646335572282779291683929356010588225565928366449477581210899353}{15} a^{2} + \\frac{817498488792010417684091251880888259815440724587032098296577740436602447187955803111}{15} a - 75362046488729247843237204805604614506250899898322599344473648941359516679946536335 \\)'], 'used_grh': True, 'zk': ['1', 'a', '1/2*a^2', '1/4*a^3', '1/40*a^4 + 1/5', '1/240*a^5 + 1/30*a', '1/1440*a^6 + 1/180*a^2', '1/8640*a^7 - 89/1080*a^3 - 1/2*a']}
Number field data - 8.0.177721081810499787554816.3