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lfunc_lfunctions • Show schema
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{'Lhash': '545953404415572843696792945240', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [-0.8090169943749475, -0.5877852522924731], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-0.3042600354473643, 0.41877801191167063], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.630445396272019, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '3267.838', 'coefficient_field': 'CDF', 'conductor': 3267, 'conductor_radical': 33, 'conjugate': '1553568910763570360456978195876', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-0.8090169943749475, 0.5877852522924731]], [[1.0, 0], [0.3042600354473643, -0.41877801191167063], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.837300102699998, 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1.27688895220846, 'root_angle': -0.4056526705857819, 'root_number': '0.29207992649256031162726024308126 - 0.95639391285186490620951187015434*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.20282633529289096', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.43068129681576193715264096459', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23750292159158818923295133690', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15197777062040201778723862841', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.630445396272019, 'bad_primes': [3, 11], 'central_character': '11.2', 'conductor': 3267, 'conductor_radical': 33, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3267/1/l/a/838/2'], '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': '2-3267-11.2-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3267-11.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.27688895220846, 'root_angle': -0.20282633529289096, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.43068129681576193715264096459', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '545953404415572843696792945240', 'Lhash_array': ['545953404415572843696792945240'], 'label': '2-3267-11.2-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3267/1/l/a/838/2'}