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lfunc_lfunctions • Show schema
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{'Lhash': '2362492268265782866341791461899', 'a10': [1.0, 2.0], 'a2': [-0.7071067811865476, 0.7071067811865476], 'a3': [0.0, 0.0], 'a4': [0.0, -1.0], 'a5': [0.7071067811865476, -2.1213203435596424], 'a6': [0.0, 0.0], 'a7': [-2.1213203435596424, 2.1213203435596424], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.905189800106762, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, -0.7071067811865476]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-0.7071067811865476, 2.1213203435596424]]], [11, [[1.0, 0], [-1.4142135623730951, 3.0]]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '990.307', 'coefficient_field': 'CDF', 'conductor': 990, 'conductor_radical': 330, 'conjugate': '164359047878500626420914914155', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [0, 0]], [[1.0, 0], 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.905189800106762, 'bad_primes': [2, 3, 5, 11], 'central_character': '55.32', 'conductor': 990, 'conductor_radical': 330, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/990/2/m/d/307/1'], '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': '2-990-55.32-c1-0-23', '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': '2-990-55.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.81161693694336, 'root_angle': 0.40821354508927754, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.86367778932178693395655009509', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2362492268265782866341791461899', 'Lhash_array': ['2362492268265782866341791461899'], 'factors': ['2-990-55.32-c1-0-23'], 'label': '2-990-55.32-c1-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/990/2/m/d/307/1'}