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lfunc_lfunctions • Show schema
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{'Lhash': '1741987324138248702835876131267', 'a10': [0.4308675151749985, 0.0], 'a2': [0.4308675151749985, 0.0], 'a3': [-1.259212092771661, 0.0], 'a4': [-1.8143531843669225, 0.0], 'a5': [1.0, 0.0], 'a6': [-0.5425535854908352, 0.0], 'a7': [4.345433830058481, 0.0], 'a8': [-1.6434808785480188, 0.0], 'a9': [-1.4143849054176136, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.059936411544086, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-1.0, 0]]], [11, [[1.0, 0], [-1.0, 0]]], [73, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 11, 73], 'central_character': '4015.1', 'coefficient_field': 'CDF', 'conductor': 4015, 'conductor_radical': 4015, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.4308675151749985, 0], [2.0, 0]], [[1.0, 0], [1.259212092771661, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.345433830058481, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.047190993142529, 0], [13.0, 0]], [[1.0, 0], 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'5.25415584464259385823454136818760', '5.58798569073376960138355902706750', '6.30647180327293575716134019139703', '7.39791928644836844832196052691045', '8.202299094646925982481832600147899'], 'prelabel': '2-4015-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.662149451537295, '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': '1.37418569740322698034632566844', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.31706420325243333155503028364', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79698455898855723789704027415', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.059936411544086, 'bad_primes': [5, 11, 73], 'central_character': '1.1', 'conductor': 4015, 'conductor_radical': 4015, 'degree': 2, 'index': 171, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4015/2/a/b/1/15'], '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': '2-4015-1.1-c1-0-171', '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': '2-4015-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.662149451537295, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37418569740322698034632566844', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1741987324138248702835876131267', 'Lhash_array': ['1741987324138248702835876131267'], 'label': '2-4015-1.1-c1-0-171', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4015/2/a/b/1/15'}