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lfunc_lfunctions • Show schema
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{'Lhash': '1149200396780791304828038781158', 'a10': [14.717478624890845, 0.0], 'a2': [0.8073717385384811, 0.0], 'a3': [0.0, 0.0], 'a4': [-7.348150875809351, 0.0], 'a5': [18.22887515425384, 0.0], 'a6': [0.0, 0.0], 'a7': [-7.0, 0.0], 'a8': [-12.391663255953107, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.45408297325494, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [7.0, 0]]]], 'bad_primes': [3, 7], 'central_character': '567.1', 'coefficient_field': 'CDF', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8073717385384811, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-18.22887515425384, 0], [125.0, 0]], [[1.0, 0], [7.0, 0]], [[1.0, 0], [49.42930794788409, 0], [1331.0, 0]], [[1.0, 0], [-44.48595518906411, 0], [2197.0, 0]], [[1.0, 0], [-47.23009508361075, 0], [4913.0, 0]], [[1.0, 0], [-56.75446792166304, 0], [6859.0, 0]], 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'2.43796025571670008641189145755920', '3.54521156394464639328599815002901', '5.00118678792501349202734527756404', '5.63565389972906301315918629927619', '6.32564299820104854278790889700118', '7.80739951212169852179757687181601', '8.718437056256337295642065422118864', '9.702268294250300235283971760278361', '10.01112299547976561420205120755679'], 'prelabel': '2-567-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.783950464280874, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.906559265284840969815175048477', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.43796025571670008641189145756', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54521156394464639328599815003', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.45408297325494, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 567, 'conductor_radical': 21, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/567/4/a/i/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': '2-567-1.1-c3-0-22', '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': '2-567-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.783950464280874, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.906559265284840969815175048477', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1149200396780791304828038781158', 'Lhash_array': ['1149200396780791304828038781158'], 'label': '2-567-1.1-c3-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/567/4/a/i/1/4'}