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lfunc_lfunctions • Show schema
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{'Lhash': '2308136740557282043508602445778', 'a10': [7718.394884859279, 0.0], 'a2': [37.595259636646766, 0.0], 'a3': [0.0, 0.0], 'a4': [901.4035471468816, 0.0], 'a5': [205.30234288728283, 0.0], 'a6': [0.0, 0.0], 'a7': [7435.129589695645, 0.0], 'a8': [14639.727458418232, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 199.31886859541896, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [43, [[1.0, 0], [-3418801.0, 0]]]], 'bad_primes': [3, 43], 'central_character': '387.1', 'coefficient_field': 'CDF', 'conductor': 387, 'conductor_radical': 129, 'degree': 2, 'euler_factors': [[[1.0, 0], [-37.595259636646766, 0], [512.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-205.30234288728283, 0], [1953125.0, 0]], [[1.0, 0], [-7435.129589695645, 0], [40353607.0, 0]], [[1.0, 0], [30246.855316517747, 0], [2357947691.0, 0]], [[1.0, 0], [147839.09312024576, 0], [10604499373.0, 0]], [[1.0, 0], 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'3.69679622428583599209902323215', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 199.31886859541896, 'bad_primes': [3, 43], 'central_character': '1.1', 'conductor': 387, 'conductor_radical': 129, 'degree': 2, 'index': 155, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/387/10/a/e/1/17'], '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': '2-387-1.1-c9-0-155', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 1, 'prelabel': '2-387-1.1-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 14.118033453545113, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.82079883852989318535015293966', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2308136740557282043508602445778', 'Lhash_array': ['2308136740557282043508602445778'], 'label': '2-387-1.1-c9-0-155', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/387/10/a/e/1/17'}