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lfunc_lfunctions • Show schema
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{'Lhash': '1696382952702829338990254740695', 'a10': [32.59922959120287, 0.0], 'a2': [-4.030246302409503, 0.0], 'a3': [3.0, 0.0], 'a4': [8.242885258085467, 0.0], 'a5': [-8.088644500886524, 0.0], 'a6': [-12.090738907228507, 0.0], 'a7': [-5.950779842869, 0.0], 'a8': [-0.9788874133087311, 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], [4.030246302409503, 0], [8.0, 0]], [[1.0, 0], [-3.0, 0]], [[1.0, 0], [8.088644500886524, 0], [125.0, 0]], [[1.0, 0], [5.950779842869, 0], [343.0, 0]], [[1.0, 0], [17.2358680276508, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-92.92994420050178, 0], [4913.0, 0]], [[1.0, 0], 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'3.97017568211379918568550628464574', '5.41094768324995984441411885311001', '6.97592881170867078943900571295407', '7.65601465803357551848010980379775', '8.209503492055228736877888454286280', '9.308794630191387338265787500615435', '9.659118468522740944389873996107413'], 'prelabel': '2-507-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33821019167064680746293540103', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.82321121770087945833686076265', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.97017568211379918568550628465', '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': 45, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/507/4/a/o/1/3'], '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-c3-0-45', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-507-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.469366359361064, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33821019167064680746293540103', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1696382952702829338990254740695', 'Lhash_array': ['1696382952702829338990254740695'], 'label': '2-507-1.1-c3-0-45', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/507/4/a/o/1/3'}