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lfunc_lfunctions • Show schema
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{'Lhash': '2306235288161940072275693145815', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-2.732050807568877, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [3.4641016151377544, 0.0], 'a8': [0.0, 0.0], 'a9': [4.464101615137754, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.152220905106582, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 13], 'central_character': '520.1', 'coefficient_field': 'CDF', 'conductor': 520, 'conductor_radical': 130, 'conjugate': '2306235288161940072275693145815', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.732050807568877, 0], [3.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [7.0, 0]], [[1.0, 0], [4.732050807568878, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.4641016151377544, 0], [17.0, 0]], [[1.0, 0], [3.267949192431123, 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'8.288065314053177400713893649315098', '9.985991761166376446029206978185139', '10.67939226300009498683036175790616'], 'prelabel': '2-520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.037699905556896, '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': '1.81929885707206905671207715858', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.88298379110998166088159572425', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.11478040052637747315415565434', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.152220905106582, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 520, 'conductor_radical': 130, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/520/2/a/d/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': '2-520-1.1-c1-0-8', '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': '2-520-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.037699905556896, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.81929885707206905671207715858', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2306235288161940072275693145815', 'Lhash_array': ['2306235288161940072275693145815'], 'label': '2-520-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/520/2/a/d/1/1'}