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lfunc_lfunctions • Show schema
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{'Lhash': '588160563728669886745826382534', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [3.449489742783178, 0.0], 'a4': [0.0, 0.0], 'a5': [-9.696938456699069, 0.0], 'a6': [0.0, 0.0], 'a7': [-27.595917942265423, 0.0], 'a8': [0.0, 0.0], 'a9': [-15.101020514433644, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 109.50754497065464, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [29, [[1.0, 0], [29.0, 0]]]], 'bad_primes': [2, 29], 'central_character': '1856.1', 'coefficient_field': 'CDF', 'conductor': 1856, 'conductor_radical': 58, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-3.449489742783178, 0], [27.0, 0]], [[1.0, 0], [9.696938456699069, 0], [125.0, 0]], [[1.0, 0], [27.595917942265423, 0], [343.0, 0]], [[1.0, 0], [-52.348469228349536, 0], [1331.0, 0]], [[1.0, 0], [-5.404082057734575, 0], [2197.0, 0]], [[1.0, 0], [-17.19183588453085, 0], [4913.0, 0]], [[1.0, 0], [44.202041028867285, 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'3.22588952422120851375556921165259', '3.65226383290654908420890471325410', '4.45592025332053249081284439595942', '6.10804389688195153774177041288001', '6.31928024839069932214993420526185', '7.39741431500271757074391105961279', '8.244756372905439831809539320693914', '8.769479737751325647048835913565725'], 'prelabel': '2-1856-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.464585274661134, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46397687471829912936621347208', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01156523622587117318376398948', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.22588952422120851375556921165', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 109.50754497065464, 'bad_primes': [2, 29], 'central_character': '1.1', 'conductor': 1856, 'conductor_radical': 58, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1856/4/a/l/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': '2-1856-1.1-c3-0-30', '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': '2-1856-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.464585274661134, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46397687471829912936621347208', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '588160563728669886745826382534', 'Lhash_array': ['588160563728669886745826382534'], 'label': '2-1856-1.1-c3-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1856/4/a/l/1/2'}