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lfunc_lfunctions • Show schema
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{'Lhash': '1147758410600490229749233706698', 'a10': [7.0, 0], 'a2': [0, -1.0], 'a3': [3.0, 0], 'a4': [7.0, 0], 'a5': [0, 7.0], 'a6': [0, -3.0], 'a7': [0, 10.0], 'a8': [0, -15.0], 'a9': [9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.913968372910507, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-3.0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '507.337', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'conjugate': '1906922274608817499031812874819', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.0], [-8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [0, -7.0], [-125.0, 0]], [[1.0, 0], [0, -10.0], [-343.0, 0]], [[1.0, 0], [0, -22.0], [-1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [37.0, 0], [4913.0, 0]], [[1.0, 0], [0, -30.0], [-6859.0, 0]], [[1.0, 0], [-162.0, 0], [12167.0, 0]], [[1.0, 0], [113.0, 0], [24389.0, 0]], [[1.0, 0], [0, -196.0], [-29791.0, 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'2-507-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': -0.1871670418109988, 'root_number': '0.83205029433784368302751260018549906451952997857967220293 - 0.5547001962252291220183417334569993763463533190531148020*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0935835209054994', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.905421738761332474586948828172', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.29676760800215134062938286735', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46349867047418674221993607443', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.913968372910507, 'bad_primes': [3, 13], 'central_character': '13.12', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/4/b/d/337/1'], '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': '2-507-13.12-c3-0-36', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-507-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': -0.0935835209054994, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.905421738761332474586948828172', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1147758410600490229749233706698', 'Lhash_array': ['1147758410600490229749233706698'], 'label': '2-507-13.12-c3-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/4/b/d/337/1'}