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lfunc_lfunctions • Show schema
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{'Lhash': '1448152044022381376791158779424', 'a10': [-2.23606797749979, -3.872983346207417], 'a2': [-1.118033988749895, 1.9364916731037085], 'a3': [-0.6180339887498949, -1.0704662693192697], 'a4': [-1.5, -2.598076211353316], 'a5': [-1.0, 1.7320508075688772], 'a6': [2.76393202250021, -4.842269503452787e-61], 'a7': [0.0, 0.0], 'a8': [2.23606797749979, 0.0], 'a9': [0.7360679774997897, -1.274907134854101], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.303936668947014, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-0.5, -0.8660254037844386]]]], 'bad_primes': [7, 11], 'central_character': '539.177', 'coefficient_field': 'CDF', 'conductor': 539, 'conductor_radical': 77, 'conjugate': '745616914968031626761139476299', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.118033988749895, -1.9364916731037085], [-1.0, -1.7320508075688772]], [[1.0, 0], [0.6180339887498949, 1.0704662693192697], [-1.5, 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'prelabel': '2-539-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0745931333509744, 'root_angle': -0.0806918122157845, 'root_number': '0.9680403732843879 - 0.25079440921085727*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0403459061079', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.14239053234515431091069104261', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61154015120235771882239822792', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.00674898605575350253888151167', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.303936668947014, 'bad_primes': [7, 11], 'central_character': '7.2', 'conductor': 539, 'conductor_radical': 77, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/539/2/e/j/177/1'], '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': '2-539-7.2-c1-0-11', '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': '2-539-7.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0745931333509744, 'root_angle': -0.04034590610789225, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.14239053234515431091069104261', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1448152044022381376791158779424', 'Lhash_array': ['1448152044022381376791158779424'], 'label': '2-539-7.2-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/539/2/e/j/177/1'}