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lfunc_lfunctions • Show schema
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{'Lhash': '5372132436724809616383789918899', 'a10': [-1.449489742783178, -0.6515307716504657], 'a2': [0.22474487139158905, 0.22474487139158905], 'a3': [-1.224744871391589, 1.224744871391589], 'a4': [0.0, -3.898979485566356], 'a5': [-4.674234614174767, 1.775255128608411], 'a6': [-0.5505102572168219, -1.3985907682907961e-61], 'a7': [3.449489742783178, 3.449489742783178], 'a8': [1.775255128608411, -1.775255128608411], 'a9': [0.0, -3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4087203965404454, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.224744871391589, -1.224744871391589]]], [5, [[1.0, 0], [4.674234614174767, -1.775255128608411]]]], 'bad_primes': [3, 5], 'central_character': '15.7', 'coefficient_field': 'CDF', 'conductor': 15, 'conductor_radical': 15, 'conjugate': '5965968173513255553688825667155', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.22474487139158905, -0.22474487139158905], [0, 4.0]], 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'0.9914128330590283 - 0.13076924120706412*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0208723502004', 'prec': 54}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.23786525700189323868467818503', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '7.17061287013729177032608512564', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '8.502508879335912284238454206158', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4087203965404454, 'bad_primes': [3, 5], 'central_character': '5.2', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/15/3/f/a/7/2'], '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': '2-15-5.2-c2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-15-5.2-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6393124404705772, 'root_angle': -0.020872350200364587, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '4.23786525700189323868467818503', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5372132436724809616383789918899', 'Lhash_array': ['5372132436724809616383789918899'], 'label': '2-15-5.2-c2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/3/f/a/7/2'}