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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 1, 1, -1, -1, -1, 0, 1], 'conductor': 0, 'degree': 7, 'dirichlet_group': [], 'disc_abs': 207911, 'disc_rad': 207911, 'disc_sign': -1, 'frobs': [[2, [[7, 1]]], [3, [[7, 1]]], [5, [[3, 1], [2, 2]]], [7, [[4, 1], [3, 1]]], [11, [0]], [13, [[4, 1], [3, 1]]], [17, [[5, 1], [1, 2]]], [19, [[7, 1]]], [23, [[7, 1]]], [29, [[6, 1], [1, 1]]], [31, [[6, 1], [1, 1]]], [37, [[6, 1], [1, 1]]], [41, [0]], [43, [[3, 1], [2, 1], [1, 2]]], [47, [[7, 1]]], [53, [[6, 1], [1, 1]]], [59, [[3, 2], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': False, 'galois_disc_exponents': [2520, 2520, 2520], 'galois_label': '7T7', 'galt': 7, 'grd': 455.9725868953089, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '7.1.207911.1', 'local_algs': ['11.2.1.2', '11.5.0.1', '41.1.0.1', '41.2.1.1', '41.4.0.1', 'm461.1.1.0', 'm461.1.1.0', 'm461.2.1.1', 'm461.1.3.0'], 'monogenic': 1, 'num_ram': 3, 'r2': 3, 'ramps': [11, 41, 461], 'rd': 5.75038312609, 'regulator': {'__RealLiteral__': 0, 'data': '0.413665504587', 'prec': 47}, 'res': {'sib': ['1,1,0,3,4,3,5,7,4,7,3,5,1,1,3,-6,4,-4,0,1,-1,1', '23710927903841901506521,47879473222829023702,-18585161533293238270,-27718893572645956,2995097288718225,42660193653092,3047009125767,-1424293432,-1131337765,-29283110,3851362,18502,-3976,-4,1', '-867358951855134874092779688077680759124459,74948517808668897928044245944328467507394,80264256693892702542292255212500969287356,-10646706059653390751105261260729389364796,-2073024751106303977790509196859423178750,358561460415848924901711953959472510240,-1569231567120970651067979140157492774,339812011975399888208647908737390864,740233461236149311943655062386593234,-285980442683863673606697366376567980,-799559766071076410390572523205923,8046818222641147657713875765092347,-439154991344205450075863859745641,-118546302790789180876202968226982,10431439394290184085497983892380,1067216754681577672194256472105,-116715402613255149807585459054,-4586060683751899430951897998,553478274322988633309266922,-38998840214374540973366648,3979410469515009658252363,1100917775953698852548044,-116607292276933357128721,-12516087433918238767003,1460173659400121360009,76480193239921082073,-12153582334073687189,-62032254854715881,64259443913607810,-3847505444883311,-117364336380024,45700769549974,-1424044739357,-314372996531,17362935437,1465113252,-107826372,-4536128,420864,8393,-966,-7,1', '1,-1,0,-3,2,4,4,-9,-17,23,20,-14,-47,45,10,-3,-46,50,-15,0,-9,19,-12,5,8,-17,16,-15,15,-14,9,-4,0,2,-1,1', '1,-7,29,-86,205,-415,745,-1216,1832,-2565,3351,-4138,4962,-5997,7455,-9340,11248,-12459,12413,-11213,9737,-9083,9737,-11213,12413,-12459,11248,-9340,7455,-5997,4962,-4138,3351,-2565,1832,-1216,745,-415,205,-86,29,-7,1', '1450267100096,-5524933838156,8695399407029,-6898041073465,2633489412660,-59426224804,-480761765501,303385078173,-98115398794,16163980252,-9608367704,5104545860,3052130578,-2618663208,73696494,44281795,181193174,-43697893,-11814357,-2705804,2715217,200116,-77871,-60931,4995,2568,455,-150,-18,0,1', '6001374985544738799340259537300503419108547457,1554944060279873062230988665993718094161811925,655805390186430239826075660851715027705510330,-5786655409412793887844182321470031163106581,29107490257761397953710162827128708973632853,1262511738466102721145252181243269869572439,1881318756973876178807883926210150655944952,-172171617806366490949045150138968088089356,82076642749295925600758656204218328684398,-7739074646665847944444965409269603763257,2127048531887908278347014500677694703786,-144422110039032140833380509801885237982,34021399215694490560133969075940193459,-1605201375972624348144938698935933625,347924567657211184609931391825002207,-12843766728142257527577921356920623,2472030672963454369176992331323343,-96371845213550570502945335185711,14617523846422739726660067841435,-783483102008730460224769208953,88922896856353760622669053649,-5976604155838123124919905442,557821081485783716541951451,-37447422451903678046474646,3132645045677230183839841,-186413931253096370351576,14542681071557779127941,-737699512010906978116,54861183782208234519,-2342169345203983792,169250329009563590,-6019856630657967,430620539796912,-12538896193212,901205522221,-20917654057,1532285729,-26606830,2032399,-22985,1903,-10,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a^{6} - a^{4} - a^{2} \\)', '\\( a^{5} - a^{3} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6']}