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lfunc_lfunctions • Show schema
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{'Lhash': '708807133580591101716932254912', 'a10': [-5.310904389043146, 0.0], 'a2': [1.3453358889684006, 0.0], 'a3': [-2.2967408447323265, 0.0], 'a4': [-0.19007134585360347, 0.0], 'a5': [-3.9476419477038784, 0.0], 'a6': [-3.089887886078, 0.0], 'a7': [-5.021596916095509, 0.0], 'a8': [-2.946381580978179, 0.0], 'a9': [2.275018507861761, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.20770826531158, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [1.0, 0]]], [17, [[1.0, 0], [1.0, 0]]], [43, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [11, 17, 43], 'central_character': '8041.1', 'coefficient_field': 'CDF', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.3453358889684006, 0], [2.0, 0]], [[1.0, 0], [2.2967408447323265, 0], [3.0, 0]], [[1.0, 0], [3.9476419477038784, 0], [5.0, 0]], [[1.0, 0], [5.021596916095509, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], 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'3.88290829679228798780242812229376', '4.80859528239009715154148450685608', '5.18052654805796777088838217621321', '6.22379176154723931433862620651273', '6.38830046353099631472854595754103', '7.39848029190125385104886060661326'], 'prelabel': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, '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': '0.55915023702349573121672492896', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.77572202595021638131810588841', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.42921240969012180830811509006', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.20770826531158, 'bad_primes': [11, 17, 43], 'central_character': '1.1', 'conductor': 8041, 'conductor_radical': 8041, 'degree': 2, 'index': 133, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8041/2/a/h/1/53'], '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': '2-8041-1.1-c1-0-133', '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': '2-8041-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.012971250747851, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.55915023702349573121672492896', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '708807133580591101716932254912', 'Lhash_array': ['708807133580591101716932254912'], 'label': '2-8041-1.1-c1-0-133', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8041/2/a/h/1/53'}