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lfunc_lfunctions • Show schema
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{'Lhash': '2000929124571738492150969152129', 'a10': [2.7659773239392584, 1.532765293009278], 'a2': [0.4568555122654128, 1.338388225035138], 'a3': [-0.7071067811865476, -0.7071067811865476], 'a4': [-1.5825660818254146, 1.2229000763168492], 'a5': [1.6575435035744683, -1.500849603977053], 'a6': [0.6233377590372458, -1.2694290205279004], 'a7': [2.5897749658634908, 0.0], 'a8': [-2.3597191005432596, -1.5593991684399828], 'a9': [0.0, 1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.4568555122654128, -1.338388225035138]]], [3, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [-1.6575435035744683, 1.500849603977053]]]], 'bad_primes': [2, 3, 5], 'central_character': '240.229', 'coefficient_field': 'CDF', 'conductor': 240, 'conductor_radical': 30, 'conjugate': '2173243775948815106508996568102', 'degree': 2, 'euler_factors': 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-0.2780479127116788, 'root_number': '0.6421372716699633 - 0.7665896714228909*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.139023956356', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57845476049274832266405837581', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.26215502631623561500228519336', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.46131006306247884532694875343', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'bad_primes': [2, 3, 5], 'central_character': '80.69', 'conductor': 240, 'conductor_radical': 30, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/240/2/bl/a/229/15'], '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': '2-240-80.69-c1-0-9', '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': '2-240-80.69-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.384344483324411, 'root_angle': -0.1390239563558394, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57845476049274832266405837581', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2000929124571738492150969152129', 'Lhash_array': ['2000929124571738492150969152129'], 'label': '2-240-80.69-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/240/2/bl/a/229/15'}