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lfunc_lfunctions • Show schema
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{'Lhash': '4606030782759158937396950496407', 'a10': [3.0, -1.0], 'a2': [-1.0, 1.0], 'a3': [0.0, 0.0], 'a4': [0.0, -2.0], 'a5': [-2.0, -1.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [2.0, 2.0], 'a9': [0.0, 3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.15970080404256085, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, -1.0]]], [5, [[1.0, 0], [2.0, 1.0]]]], 'bad_primes': [2, 5], 'central_character': '20.3', 'coefficient_field': 'CDF', 'conductor': 20, 'conductor_radical': 10, 'conjugate': '6457268689446145708595529609989', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, -1.0]], [[1.0, 0], [0, 0], [0, -3.0]], [[1.0, 0], [2.0, 1.0]], [[1.0, 0], [0, 0], [0, 7.0]], [[1.0, 0], [0, 0], [-11.0, 0]], [[1.0, 0], [1.0, 1.0], [0, 13.0]], [[1.0, 0], [-3.0, 3.0], [0, -17.0]], [[1.0, 0], [0, 0], [19.0, 0]], [[1.0, 0], [0, 0], [0, -23.0]], [[1.0, 0], [0, 4.0], [-29.0, 0]], [[1.0, 0], [0, 0], [-31.0, 0]], [[1.0, 0], 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'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0881040955874', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.63351761276323569547339575571', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.08937157793967758816517109516', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.640379848934142593144264292186', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.15970080404256085, 'bad_primes': [2, 5], 'central_character': '20.3', 'conductor': 20, 'conductor_radical': 10, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/20/2/e/a/3/1'], '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': '2-20-20.3-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': '2-20-20.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.399625830049261, 'root_angle': -0.0881040955873917, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.63351761276323569547339575571', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4606030782759158937396950496407', 'Lhash_array': ['4606030782759158937396950496407'], 'label': '2-20-20.3-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/20/2/e/a/3/1'}