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lfunc_lfunctions • Show schema
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{'Lhash': '944807685724237531068332669238', 'a10': [3.2779726325672023, 0.0], 'a2': [-0.21369989565587372, 0.0], 'a3': [3.0, 0.0], 'a4': [-7.954332354596668, 0.0], 'a5': [-15.33914007073641, 0.0], 'a6': [-0.6410996869676212, 0.0], 'a7': [32.39277706513322, 0.0], 'a8': [3.409439159436438, 0.0], 'a9': [9.0, 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': '507.1', 'coefficient_field': 'CDF', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.21369989565587372, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [15.33914007073641, 0], [125.0, 0]], [[1.0, 0], [-32.39277706513322, 0], [343.0, 0]], [[1.0, 0], [29.592525961687937, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [78.19578890299314, 0], [4913.0, 0]], [[1.0, 0], 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['0.74532184622019125158232130819770', '2.41534315070755980712694849592098', '4.15119282799731212503161629196789', '4.35136094317743944417155972579178', '5.51982030091184697726478454171028', '7.47237691119821399684602852046238', '7.893246024464252676168383620263880', '8.513372719958250644451414402112957', '9.329497961112365460997579212904617', '10.70395818906654728654116209184731'], 'prelabel': '2-507-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74532184622019125158232130820', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.41534315070755980712694849592', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15119282799731212503161629197', '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': '1.1', 'conductor': 507, 'conductor_radical': 39, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/4/a/p/1/4'], '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': '2-507-1.1-c3-0-14', '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': '2-507-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74532184622019125158232130820', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '944807685724237531068332669238', 'Lhash_array': ['944807685724237531068332669238'], 'label': '2-507-1.1-c3-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/4/a/p/1/4'}