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lfunc_lfunctions • Show schema
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{'Lhash': '2997099647641057583979508031354', 'a10': [-1.5909716680261965, -2.7556437624239773], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.5909716680261965, -2.7556437624239773], 'a6': [0.0, 0.0], 'a7': [-2.5623816969241155, -0.6589385701780474], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.0183451964044, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.5623816969241155, 0.6589385701780474]]]], 'bad_primes': [2, 3, 7], 'central_character': '378.37', 'coefficient_field': 'CDF', 'conductor': 378, 'conductor_radical': 42, 'conjugate': '1183074720159352893767466176848', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.5909716680261965, 2.7556437624239773], [-2.5, 4.330127018922194]], [[1.0, 0], [2.5623816969241155, 0.6589385701780474]], [[1.0, 0], 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'2-378-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.4541652875448099, 'root_number': '0.14349690979212015 + 0.9896507651086378*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.227082643772', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.36429474107570020497919387375', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.55586632460255318295741375386', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.33193110203303504909978094090', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.0183451964044, 'bad_primes': [2, 3, 7], 'central_character': '63.58', 'conductor': 378, 'conductor_radical': 42, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/378/2/e/d/37/1'], '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': '2-378-63.58-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-378-63.58-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.737338538225754, 'root_angle': 0.22708264377240495, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.36429474107570020497919387375', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2997099647641057583979508031354', 'Lhash_array': ['2997099647641057583979508031354'], 'label': '2-378-63.58-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/378/2/e/d/37/1'}