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lfunc_lfunctions • Show schema
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{'Lhash': '949700929661090762468865964194', 'a10': [0.0, 0.0], 'a2': [-2.2856963133808335, -1.6606555777762442], 'a3': [0.0, 0.0], 'a4': [1.8485967002534862, 5.689395631246652], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [3.476679319005886, -10.700118704142087], 'a9': [2.4270509831248424, 1.7633557568774194], '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], [3.173167590627137, 0.9648872689561054]]]], 'bad_primes': [7, 11], 'central_character': '539.246', 'coefficient_field': 'CDF', 'conductor': 539, 'conductor_radical': 77, 'conjugate': '1488585517160007971995791647649', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.2856963133808335, 1.6606555777762442], [0.6180339887498949, 1.902113032590307]], [[1.0, 0], [0, 0], [-2.4270509831248424, -1.7633557568774194]], [[1.0, 0], [0, 0], [1.545084971874737, 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'root_analytic_conductor': 2.0745931333509744, 'root_angle': 0.04319767974765098, 'root_number': '0.9633914271218528 + 0.268098784309291*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0431976797477', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74918193506168451923392434774', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.31141733878217379427440428490', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.63466935211992110298635119771', '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': '11.4', 'conductor': 539, 'conductor_radical': 77, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/539/2/f/c/246/1'], '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': '2-539-11.4-c1-0-9', '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': '2-539-11.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0745931333509744, 'root_angle': 0.04319767974765098, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74918193506168451923392434774', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '949700929661090762468865964194', 'Lhash_array': ['949700929661090762468865964194'], 'factors': ['2-539-11.4-c1-0-9'], 'label': '2-539-11.4-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/539/2/f/c/246/1'}