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lfunc_lfunctions • Show schema
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{'Lhash': '363230262943621380369359923389', 'a10': [-76.26024157132213, 0.0], 'a2': [1.290091188168615, 0.0], 'a3': [0.0, 0.0], 'a4': [-30.335664726209693, 0.0], 'a5': [-59.11228777523818, 0.0], 'a6': [0.0, 0.0], 'a7': [-213.33142572287804, 0.0], 'a8': [-80.41869177191629, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.199450701287, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [529.0, 0]]]], 'bad_primes': [3, 23], 'central_character': '207.1', 'coefficient_field': 'CDF', 'conductor': 207, 'conductor_radical': 69, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.290091188168615, 0], [32.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [59.11228777523818, 0], [3125.0, 0]], [[1.0, 0], [213.33142572287804, 0], [16807.0, 0]], [[1.0, 0], [126.52827629474035, 0], [161051.0, 0]], [[1.0, 0], [884.8249725872421, 0], [371293.0, 0]], [[1.0, 0], [-1179.9768176835032, 0], [1419857.0, 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'positive_zeros': ['0.28653815402937130228886915297647', '2.94139719933452043445025123526444', '3.88163664816850123492767152289791', '4.98482712103859096299220930750176', '6.33336576564512094649636509209559', '7.52315990871588891008226601862215', '8.520397999797927016256298347918755', '9.696759384747092465244397555436780', '10.22924458657577991475564247962191', '11.88985588527675319707324387570319'], 'prelabel': '2-207-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.761896450066332, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.28653815402937130228886915298', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.94139719933452043445025123526', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.88163664816850123492767152290', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.199450701287, 'bad_primes': [3, 23], 'central_character': '1.1', 'conductor': 207, 'conductor_radical': 69, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/207/6/a/c/1/2'], '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': '2-207-1.1-c5-0-1', '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': '2-207-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.761896450066332, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.28653815402937130228886915298', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '363230262943621380369359923389', 'Lhash_array': ['363230262943621380369359923389'], 'label': '2-207-1.1-c5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/207/6/a/c/1/2'}