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lfunc_lfunctions • Show schema
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{'Lhash': '2566567993994717190671986431627', 'a10': [0.0, 0.0], 'a2': [1.8793852415718169, 0.0], 'a3': [-1.532088886237956, 0.0], 'a4': [2.5320888862379562, 0.0], 'a5': [0.0, 0.0], 'a6': [-2.879385241571817, 0.0], 'a7': [0.0, 0.0], 'a8': [2.879385241571817, 0.0], 'a9': [1.3472963553338606, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.2869623822639764, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 23], 'central_character': '575.551', 'coefficient_field': 'CDF', 'conductor': 575, 'conductor_radical': 115, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8793852415718169, 0], [1.0, 0]], [[1.0, 0], [1.532088886237956, 0], [1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.3472963553338607, 0], [1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'root_analytic_conductor': 0.5356886990258208, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.02466515105394899431729173924', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.65652723499038769190938768506', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.53258870454623338382412597617', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.2869623822639764, 'bad_primes': [5, 23], 'central_character': '23.22', 'conductor': 575, 'conductor_radical': 115, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/575/1/d/c/551/3'], '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': '2-575-23.22-c0-0-4', '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': '2-575-23.22-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5356886990258208, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.02466515105394899431729173924', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2566567993994717190671986431627', 'Lhash_array': ['2566567993994717190671986431627'], 'label': '2-575-23.22-c0-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/575/1/d/c/551/3'}