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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 1, 'A4': 1, 'A5': -1, 'A6': -1, 'A7': -1, 'A8': -1, 'A9': 1, 'Lhash': '157729214974018933', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [-0.4082482904638631, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2532.295799300866, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [5, [1, 1]], [11, [1, 1]], [31, [1]]], 'bad_primes': [2, 3, 5, 11, 31], 'central_character': '317130.1', 'coefficient_field': '1.1.1.1', 'conductor': 317130, 'conductor_radical': 10230, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1, 1], [1, 1, 7], [1, 1], [1, 1, 13], [1, 0, 17], [1, 4, 19], [1, -9, 23], [1, 3, 29], [1], [1, -2, 37], [1, 3, 41], [1, -5, 43], [1, 0, 47], [1, -6, 53], [1, -6, 59], [1, -2, 61], [1, -2, 67], [1, -12, 71], [1, 7, 73], [1, -8, 79], [1, -6, 83], [1, -6, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 26, 'label': '2-317130-1.1-c1-0-26', 'leading_term': '2.25805592926', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/317130/y', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.258055929259204, 1.591918307268022, 0.2305936221659705, -0.299762673636265, 1.000093418464897, 3.05276016847204, 3.442292082557072, 1.495416245900004, -0.3503329474725431, 0.2761668923475799, 1.987373180408095, 1.579218592773023, -0.6225142618499669, -0.9861731099116536, 0.8999881590817593, 0.5617020040082704, -3.623229934717524, -6.137283416961002, -2.959908805362919, 0.4947812523425533, -2.311836291680545, -7.092321725908863, -5.068082502539006, 1.762076169458961, 3.514306100880885, -0.9496461376643974, -3.204849475144587, -0.6491744777135856, 0.7670959280340347, -0.6879153586880551, -0.5190750670256351, 1.335074407579518, 0.7367052505503752, -1.163003628210766, -0.5882804464216898, 0.4900937901728285, -0.6620948140727987, -1.018123922828502, 0.7207315056739556, 0.1962367081454382, -2.520507334395029, -2.085573313341088, 0.04622124994728121, -1.544270407953669, -3.478459859011899, -1.016538935884389, -0.07721909589242824, -4.345229357676566, -5.056809453339588, 0.8717593232204126, 3.341222776362225, 0.2831399330687079, 0.3750358494814358, 1.524595317216288, -3.89614459785229, -8.248652050755656, -2.666627468181169, 3.235198746110269, 0.9044472500147334, -1.423477669456403, 0.6702960507659792, 0.48592228736014, -1.033323851838121, 1.348019797324839, 2.414941924093802, -0.8826598259340936, -1.157316383905723, 1.645609079584765, 0.6867780367007194, -0.1499313923839383, 3.647821611946243, 4.320136955685188, -0.2918984798391443, -1.219322119186606, 1.298784255390711, 0.5138595598289566, -0.7799293920121546, 0.2185450516292753, -0.1869867755889297, -0.159141531592434, 2.512665042138364, 1.981232315681779, -0.9939459089369023, 0.3416436217195345, 1.429948223466377, -0.8253696948974022, 2.490457677032257, 7.732133942963989, 2.446566090329612, -3.353427321510767, 2.557256227445751, 6.138784237080624, 0.1811817323433473, -0.2157620156418805, 4.523364448928656, 1.614027178213099, -1.727364804878267, 1.919799458248319, 2.136645257341108, -1.797603129738861, -0.7056131722850231, 1.055402487415291, -0.654083178553306, 0.1309606746410999, 1.464207194977225, -0.6170370097697008, -0.7190593480571656, 0.6180083000094354, -1.107574888114042, -1.153302161033643, 0.7380465906247012, -0.5030952136902269, 0.6066034911748402, 5.138908857254678, 3.400394741378336, -0.7525440738815987, 0.5897758467021403, -0.08256848666636654, -3.038834534530688, 0.08222227321400644, 1.417230061064135], 'positive_zeros': ['0.5514857963823020', '0.8485493684875970', '1.924565459971429', '2.206928221066223', '2.926340906576468', '3.386439951959238', '3.795637589483088', '4.677907984538547', '4.866161069840810', '5.681100200627122', '6.202473094179253', '6.807991102055135', '7.145315259988035', '7.567712315882514', '8.083852781045421', '8.591873007760324', '8.894283439927114', '9.397887733284621', '9.769368946388256', '10.48547549924494', '10.58031252090553', '11.34390855658567', '11.49111244512626', '12.21529814770738', '12.78049820187655', '12.95533870773789', '13.35527664954169', '14.08219147271672', '14.55445225004934', '14.92872513635525', '15.30461151296357', '15.64571088320006', '16.18627951272696', '16.59537572501306', '17.07467992480371', '17.26765433817776', '17.98287660497482', '18.36212543360370', '18.80981812887121', '19.19511779859833', '19.45881577811979', '19.77006571941948'], 'prelabel': '2-317130-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 50.321921657473155, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 157729214974018933, 'z1': {'__RealLiteral__': 0, 'data': '0.5514857963823020', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.8485493684875970', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.924565459971429', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2532.295799300866, 'bad_primes': [2, 3, 5, 11, 31], 'central_character': '1.1', 'conductor': 317130, 'conductor_radical': 10230, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 0, -1, -4, -1, -1, 1, 9, -1, 1, 1, 1, -1, -3, 1, 0, -1, -1, 0, 1, 1, 2, 4, -1, 1, -3, 1, 5, -1, -1, -9, 0, 1, -6, -1, 0, -1, 6, -1, 1, 1, -4, 3, 6, -1, 2, 0, -1, 1, 1, 1, 2, 0, 9, -1, 12, -1, -7, -2, 1, -4, 1, 1, 8, -1, 1, 3, 6, -1, 0, -5, -3, 1, 6, 1, 1, 9, 0, 0, 4, -1, 14, 6, -1, 1], 'euler11': [1, 1, 0], 'euler13': [1, 1, 13], 'euler17': [1, 0, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, -9, 23], 'euler29': [1, 3, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 0], 'euler37': [1, -2, 37], 'euler41': [1, 3, 41], 'euler43': [1, -5, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -6, 59], 'euler61': [1, -2, 61], 'euler67': [1, -2, 67], 'euler7': [1, 1, 7], 'euler71': [1, -12, 71], 'euler73': [1, 7, 73], 'euler79': [1, -8, 79], 'euler83': [1, -6, 83], 'euler89': [1, -6, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, 1, 0], [1, 1, 7], [1, 1, 0], [1, 1, 13], [1, 0, 17], [1, 4, 19], [1, -9, 23], [1, 3, 29], [1, 0, 0], [1, -2, 37], [1, 3, 41], [1, -5, 43], [1, 0, 47], [1, -6, 53], [1, -6, 59], [1, -2, 61], [1, -2, 67], [1, -12, 71], [1, 7, 73], [1, -8, 79], [1, -6, 83], [1, -6, 89], [1, -14, 97]], 'index': 26, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/317130/y'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-317130-1.1-c1-0-26', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-317130-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 50.321921657473155, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 157729214974018933, 'z1': {'__RealLiteral__': 0, 'data': '0.5514857963823020', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '157729214974018933', 'Lhash_array': ['157729214974018933'], 'factors': ['2-317130-1.1-c1-0-26'], 'label': '2-317130-1.1-c1-0-26', 'type': 'ECQ', 'url': 'EllipticCurve/Q/317130/y'}