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lfunc_lfunctions • Show schema
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{'Lhash': '553922637323659681062877859791', 'a10': [-12.57571471437145, 0.0], 'a2': [-4.123105625617661, 0.0], 'a3': [0.0, 0.0], 'a4': [9.0, 0.0], 'a5': [3.050058828528689, 0.0], 'a6': [0.0, 0.0], 'a7': [-6.683242006404669, 0.0], 'a8': [-4.123105625617661, 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], [4.123105625617661, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.050058828528689, 0], [125.0, 0]], [[1.0, 0], [6.683242006404669, 0], [343.0, 0]], [[1.0, 0], [32.24996133332876, 0], [1331.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-28.85857157145715, 0], [4913.0, 0]], [[1.0, 0], [101.1938305106074, 0], [6859.0, 0]], [[1.0, 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'2.59231736481393849662359922981049', '3.88254955175204368082873557903276', '5.11461393272137153443034943743651', '6.01937795329651416388540407110635', '7.05675908518743857300184197537451', '7.58300543859358617563331709750483', '8.518471152298397939358354235427338', '9.030149940915905097031796152417519'], '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': '0.43696791310155239604860135844', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.72010638527191251343467174974', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.59231736481393849662359922981', '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': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1521/4/a/z/1/1'], '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': '2-39e2-1.1-c3-0-25', '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': '0.43696791310155239604860135844', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '553922637323659681062877859791', 'Lhash_array': ['553922637323659681062877859791'], 'label': '2-39e2-1.1-c3-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1521/4/a/z/1/1'}