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lfunc_lfunctions • Show schema
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{'Lhash': '1058625619418434158164059591631', 'a10': [10.381821999003327, 0.0], 'a2': [-2.6847892606476975, 0.0], 'a3': [0.23803879558459043, 0.0], 'a4': [5.208093374089209, 0.0], 'a5': [-3.8669038762836614, 0.0], 'a6': [-0.6390840020030208, 0.0], 'a7': [2.1131429901092047, 0.0], 'a8': [-8.613054637909745, 0.0], 'a9': [-2.9433375317966375, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 47.918226252970385, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [-1.0, 0]]], [353, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [17, 353], 'central_character': '6001.1', 'coefficient_field': 'CDF', 'conductor': 6001, 'conductor_radical': 6001, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.6847892606476975, 0], [2.0, 0]], [[1.0, 0], [-0.23803879558459043, 0], [3.0, 0]], [[1.0, 0], [3.8669038762836614, 0], [5.0, 0]], [[1.0, 0], [-2.1131429901092047, 0], [7.0, 0]], [[1.0, 0], [3.075202078448246, 0], [11.0, 0]], [[1.0, 0], 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'2.19036333288640682238136947098976', '2.89069888383423881967628640845912', '3.75019279391933343715881760351177', '4.94877407111245630572416360347221', '5.71660928666433651339770736266399', '6.85294992053664300918401391062596', '7.54110539141609740192560116746780', '7.83350867889899834702459824122257'], 'prelabel': '2-6001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.922299202791684, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.835108364424580303094990778952', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.19036333288640682238136947099', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89069888383423881967628640846', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 47.918226252970385, 'bad_primes': [17, 353], 'central_character': '1.1', 'conductor': 6001, 'conductor_radical': 6001, 'degree': 2, 'index': 180, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6001/2/a/b/1/6'], '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': '2-6001-1.1-c1-0-180', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6001-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.922299202791684, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.835108364424580303094990778952', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1058625619418434158164059591631', 'Lhash_array': ['1058625619418434158164059591631'], 'label': '2-6001-1.1-c1-0-180', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6001/2/a/b/1/6'}