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lfunc_lfunctions • Show schema
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{'Lhash': '1389576052036895063780080669678', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-2.6620774281109743, 0.0], 'a6': [0.0, 0.0], 'a7': [-1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 34.878655602895286, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.0, 0]]], [7, [[1.0, 0], [1.0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '4368.1', 'coefficient_field': 'CDF', 'conductor': 4368, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.6620774281109743, 0], [5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [1.5754211948530352, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.759024029403918, 0], [17.0, 0]], [[1.0, 0], [-2.2374986229640097, 0], [19.0, 0]], [[1.0, 0], [5.8456802626618565, 0], [23.0, 0]], 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 39, 'label': '2-4368-1.1-c1-0-39', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4368/2/a/br/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-3.050736005357708e-61, 0.11643009808388595, 0.23187639337514235, 0.34532647139843325, 0.45571273539021534, 0.5618897796850046, 0.6626173512700241, 0.7565501956589068, 0.8422356843532882, 0.9181197097156151, 0.982560941119913, 1.0338531859345985, 1.0702553015913538, 1.0900278626858324, 1.0914755950813462, 1.0729944391788653, 1.033121987959568, 0.9705899544199873, 0.8843772522781739, 0.7737622207230005, 0.6383724884349528, 0.47823095608436333, 0.29379638335489705, 0.08599710030825175, -0.14374357222592296, -0.39349150881416856, -0.6607967501629728, 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'7.41507359338878937961642364442524', '7.891101562585154362139018717759346'], 'prelabel': '2-4368-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.905815405419923, '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': '1.09618222228326484542116341695', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.55137885659551782993702748081', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.62096671539881266056804701561', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 34.878655602895286, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 4368, 'conductor_radical': 546, 'degree': 2, 'index': 39, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4368/2/a/br/1/2'], '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': '2-4368-1.1-c1-0-39', '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': '2-4368-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.905815405419923, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09618222228326484542116341695', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1389576052036895063780080669678', 'Lhash_array': ['1389576052036895063780080669678'], 'label': '2-4368-1.1-c1-0-39', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4368/2/a/br/1/2'}