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lfunc_lfunctions • Show schema
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{'Lhash': '1176227305546502090663347113162', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8983170227394044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1800.1601', 'coefficient_field': 'CDF', 'conductor': 1800, 'conductor_radical': 30, 'conjugate': '1718615864703258790201755849222', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0], [1.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [0, 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-0.19591327601530362, 'root_number': '0.81649658092772603273242802490216 - 0.57735026918962576450914878050208*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.09795663800765182', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.927879736999085279198485373471', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.60133102228583573717590057644', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50745555893537077493993703579', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8983170227394044, 'bad_primes': [2, 3, 5], 'central_character': '3.2', 'conductor': 1800, 'conductor_radical': 30, 'degree': 2, 'index': 0, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1800/1/l/a/1601/2', 'ArtinRepresentation/2.1800.24t22.c.b'], 'is_instance_Artin': True, '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': '2-1800-3.2-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': '2-1800-3.2-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9477958760932674, 'root_angle': -0.09795663800765181, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.927879736999085279198485373471', 'prec': 107}}
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lfunc_instances • Show schema
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id: 24598932
{'Lhash': '1176227305546502090663347113162', 'Lhash_array': ['1176227305546502090663347113162'], 'label': '2-1800-3.2-c0-0-0', 'type': 'Artin', 'url': 'ArtinRepresentation/2.1800.24t22.c.b'}
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id: 19819074
{'Lhash': '1176227305546502090663347113162', 'Lhash_array': ['1176227305546502090663347113162'], 'label': '2-1800-3.2-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1800/1/l/a/1601/2'}