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lfunc_lfunctions • Show schema
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{'Lhash': '1417802771505399807273535471462', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0.9232284979073434, 1.5990786653710156], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [1.7282957200561908, 0], 'a8': [0, 0], 'a9': [-0.20470171869649903, 0.3545537771790083], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.17157638404328, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-2.4150979591018036, 3.628677699650701]]]], 'bad_primes': [2, 5, 19], 'central_character': '1900.501', 'coefficient_field': 'CDF', 'conductor': 1900, 'conductor_radical': 190, 'conjugate': '1493993267648909521442612639091', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.9232284979073434, -1.5990786653710156], [-1.5, 2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.7282957200561908, 0], [7.0, 0]], [[1.0, 0], [-2.663659009982841, 0], [11.0, 0]], [[1.0, 0], 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'2.508141576895542712001395084078536721221472812126821568', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1900/2/i/e/501/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.5081415768955426, 2.4701887009582753, 2.4250914676983757, 2.3728031993727394, 2.3131539076593293, 2.2458829643246734, 2.170677177790941, 2.087212223493859, 1.9951953639343065, 1.8944075279767294, 1.784743052555811, 1.666245674015759, 1.5391396477653325, 1.403855143238087, 1.2610472899091125, 1.1116084353976545, 0.9566733234991379, 0.7976170184339708, 0.6360455034873717, 0.4737789786650986, 0.31282798199437534, 0.15536256887541858, 0.00367490679319488, -0.1398642205379156, -0.2728543564071971, -0.39291896036619617, -0.4977626796433884, -0.5852311776728862, -0.6533722412404858, 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'7.74782530647527938071520749382847', '8.139828792766555499897957342774128', '8.899948333968116928130889336171949'], 'prelabel': '2-1900-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8950707803637252, 'root_angle': -0.24532395906752485, 'root_number': '0.71741766250648505606903197290057810469479507161245289690 - 0.6966433072410378839392236989378630892699640331432169571*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.12266197953376243', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11844917775460905460078765419', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.96074520178096000600771186959', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.00807288499840061083992024838', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.17157638404328, 'bad_primes': [2, 5, 19], 'central_character': '19.7', 'conductor': 1900, 'conductor_radical': 190, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1900/2/i/e/501/6'], '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': '2-1900-19.7-c1-0-15', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-1900-19.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8950707803637252, 'root_angle': -0.12266197953376243, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11844917775460905460078765419', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1417802771505399807273535471462', 'Lhash_array': ['1417802771505399807273535471462'], 'label': '2-1900-19.7-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1900/2/i/e/501/6'}