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lfunc_lfunctions • Show schema
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{'Lhash': '502269223184609303909309742871', 'a10': [-7.093569705358613, -1.68120690395158], 'a2': [1.8304687789196572, 0.5095458103580319], 'a3': [0.0, 0.0], 'a4': [1.3786452186856646, 0.832016652275662], 'a5': [-3.8338615764124215, 0.14877128904800724], 'a6': [0.0, 0.0], 'a7': [0.36515667412600633, 0.05710946170302828], 'a8': [-0.5081931280032754, -0.5386532465242921], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.685', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '2899811124751634809193912917980', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.8304687789196572, -0.5095458103580319], [1.712333799060533, 1.0333987423037259]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.8338615764124215, -0.14877128904800724], [4.98496470583896, 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0.536788053316173*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.409818738251', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.39622055406606530537209505881', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96393967374781155001160036200', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.35725616403862270483301814402', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '243.103', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/i/a/685/21'], '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': '2-3e6-243.103-c1-0-2', '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': '2-3e6-243.103-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': -0.40981873825057913, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.39622055406606530537209505881', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '502269223184609303909309742871', 'Lhash_array': ['502269223184609303909309742871'], 'label': '2-3e6-243.103-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/i/a/685/21'}