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lfunc_lfunctions • Show schema
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{'Lhash': '1594605039384736914458748290334', 'a10': [-56.739928127785234, -46.94939712674987], 'a2': [0, 1.3174114418220608], 'a3': [0, -9.0], 'a4': [30.264427092956318, 0], 'a5': [-35.637611482875826, 43.06925408914806], 'a6': [11.856702976398548, 0], 'a7': [0, -87.47862468321817], 'a8': [0, 82.02786867075618], 'a9': [-81.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.46333026914181, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 9.0]]], [5, [[1.0, 0], [35.637611482875826, -43.06925408914806]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '165.34', 'coefficient_field': 'CDF', 'conductor': 165, 'conductor_radical': 165, 'conjugate': '1017480392753016659443752506933', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -1.3174114418220608], [-32.0, 0]], [[1.0, 0], [0, 9.0]], [[1.0, 0], [35.637611482875826, -43.06925408914806]], [[1.0, 0], [0, 87.47862468321817], [-16807.0, 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64}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.25792157483903074419989700145', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86302567658525896242458274010', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.17837098935044067764280194371', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.46333026914181, 'bad_primes': [3, 5, 11], 'central_character': '5.4', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/165/6/c/b/34/15'], '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': '2-165-5.4-c5-0-32', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-165-5.4-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.144252158394047, 'root_angle': 0.11001672873003863, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25792157483903074419989700145', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1594605039384736914458748290334', 'Lhash_array': ['1594605039384736914458748290334'], 'label': '2-165-5.4-c5-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/165/6/c/b/34/15'}