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lfunc_lfunctions • Show schema
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{'Lhash': '2349923661084528561282445133050', 'a10': [2.6038754716096766, 0.0], 'a2': [-1.8019377358048383, 0.0], 'a3': [1.0, 0.0], 'a4': [1.246979603717467, 0.0], 'a5': [-1.445041867912629, 0.0], 'a6': [-1.8019377358048383, 0.0], 'a7': [-3.4450418679126287, 0.0], 'a8': [1.3568958678922094, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.048415382478917, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.1', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '2349923661084528561282445133050', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.8019377358048383, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.445041867912629, 0], [5.0, 0]], [[1.0, 0], [3.4450418679126287, 0], [7.0, 0]], [[1.0, 0], [-5.18598067906503, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], 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'6.89865178120035937609479784441003', '8.134379072855960489066306656933479', '8.688382530171444118859210317136908', '9.545318827431046671283032706021002', '10.04622159425429106782801160422538'], 'prelabel': '2-507-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.85376290648341535326764824068', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.52848953311962123409972105103', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.32191340047312199842370424717', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.048415382478917, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/2/a/j/1/1'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-507-1.1-c1-0-14', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-507-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85376290648341535326764824068', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2349923661084528561282445133050', 'Lhash_array': ['2349923661084528561282445133050'], 'label': '2-507-1.1-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/2/a/j/1/1'}