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lfunc_lfunctions • Show schema
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{'Lhash': '615417728089422015157218657138', 'a10': [7.5706377253761366, 0.0], 'a2': [-2.457789457497516, 0.0], 'a3': [0.0, 0.0], 'a4': [4.040729017385934, 0.0], 'a5': [-3.0802629176725516, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.658667133598251, 0.0], 'a8': [-5.015682264540414, 0.0], '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': '729.1', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '615417728089422015157218657138', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.457789457497516, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.0802629176725516, 0], [5.0, 0]], [[1.0, 0], [2.658667133598251, 0], [7.0, 0]], [[1.0, 0], [3.4343407024075385, 0], [11.0, 0]], [[1.0, 0], [3.343956128470459, 0], [13.0, 0]], [[1.0, 0], [-2.5728179036238905, 0], [17.0, 0]], [[1.0, 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'6.56347137029154164452782626195534', '7.20867393831700188346477089300117', '8.036374731427001601549789773838917', '8.481588974756659488327918806146251', '9.645253141535126853668558564246945', '10.19571869089360836878347155500980'], 'prelabel': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.48547898606967995497127464637', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.47218886353780892352747749780', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.50562728692983538953911062359', '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': '1.1', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/a/e/1/1'], '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': '2-3e6-1.1-c1-0-0', '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': '2-3e6-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.48547898606967995497127464637', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '615417728089422015157218657138', 'Lhash_array': ['615417728089422015157218657138'], 'label': '2-3e6-1.1-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/a/e/1/1'}