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lfunc_lfunctions • Show schema
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{'Lhash': '1352402834803552222755214507322', 'a10': [3.2779726325672023, 0.0], 'a2': [0.21369989565587372, 0.0], 'a3': [0.0, 0.0], 'a4': [-7.954332354596668, 0.0], 'a5': [15.33914007073641, 0.0], 'a6': [0.0, 0.0], 'a7': [32.39277706513322, 0.0], 'a8': [-3.409439159436438, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 89.74190511873151, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 13], 'central_character': '1521.1', 'coefficient_field': 'CDF', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.21369989565587372, 0], [8.0, 0]], [[1.0, 0], [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], [10.660039025781405, 0], 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'1.63142224958817948584729707365690', '2.97761245250613712616401650287266', '4.35537467964435227219021203252870', '4.90153532496053492661102101352486', '5.67797860377020575198481124879659', '6.43820826532599153833083329551219', '7.79046174030806708274407894107761', '8.329252722739139057664825604389054', '9.158997625477842219994222433924767'], 'prelabel': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06685772448659269582131288574', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.63142224958817948584729707366', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.97761245250613712616401650287', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.74190511873151, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 1521, 'conductor_radical': 39, 'degree': 2, 'index': 108, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/bf/1/6'], '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': '2-39e2-1.1-c3-0-108', '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': '2-39e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.473220419621383, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06685772448659269582131288574', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1352402834803552222755214507322', 'Lhash_array': ['1352402834803552222755214507322'], 'label': '2-39e2-1.1-c3-0-108', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/bf/1/6'}