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lfunc_lfunctions • Show schema
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{'Lhash': '225387535527327232835295010358', 'a10': [2.3008461214837563, -2.1693563850260187], 'a2': [-1.3603819403064172, 0.3864724783062145], 'a3': [0.7071067811865476, -0.7071067811865476], 'a4': [1.7012780470237052, -1.0515003598264756], 'a5': [-1.9842130247704914, 1.0309697727533707], 'a6': [-0.6886579848420856, 1.2352126051466759], 'a7': [-3.91926785947153, 0.0], 'a8': [-1.9080119806088058, 2.0879392428548447], 'a9': [0.0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3603819403064172, -0.3864724783062145]]], [3, [[1.0, 0], [-0.7071067811865476, 0.7071067811865476]]], [5, [[1.0, 0], [1.9842130247704914, -1.0309697727533707]]]], 'bad_primes': [2, 3, 5], 'central_character': '240.109', 'coefficient_field': 'CDF', 'conductor': 240, 'conductor_radical': 30, 'conjugate': '3024765950655333315098576480358', 'degree': 2, 'euler_factors': 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-0.8799626935830344, 'root_number': '-0.9297333347286861 - 0.3682335214157953*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.439981346792', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.17779941530162031926979124300', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.87855356431618703637531534917', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.69364430471320310713302760047', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.9164096485107303, 'bad_primes': [2, 3, 5], 'central_character': '80.29', 'conductor': 240, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/240/2/bl/a/109/3'], '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': '2-240-80.29-c1-0-1', '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': '2-240-80.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.384344483324411, 'root_angle': -0.4399813467915172, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.17779941530162031926979124300', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '225387535527327232835295010358', 'Lhash_array': ['225387535527327232835295010358'], 'label': '2-240-80.29-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/240/2/bl/a/109/3'}