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lfunc_lfunctions • Show schema
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{'Lhash': '1217675507325633084198606786224', 'a10': [-3.0453166369505142, 0.0], 'a2': [-0.8185439686653839, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.3299857713615229, 0.0], 'a5': [3.7204069097422208, 0.0], 'a6': [-0.8185439686653839, 0.0], 'a7': [0.0, 0.0], 'a8': [2.725739768889521, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.997420923394913, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [3, 7, 23], 'central_character': '3381.1', 'coefficient_field': 'CDF', 'conductor': 3381, 'conductor_radical': 483, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8185439686653839, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-3.7204069097422208, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.700040938791874, 0], [11.0, 0]], [[1.0, 0], [6.907349206135581, 0], [13.0, 0]], [[1.0, 0], [3.217717170644236, 0], [17.0, 0]], 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'4.01406488376367009788096586279954', '4.83952467829695351262017731547123', '5.51914198952956595250925072967678', '6.46579731751539223495254830182094', '7.29824709176916678486608893894982', '7.899749891220175872767941663982766', '9.044537559042582373020933837376167'], 'prelabel': '2-3381-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.195904245017888, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.960576602974353706778534829437', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.98549291678652335157863152148', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.70118135464532415031873530675', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.997420923394913, 'bad_primes': [3, 7, 23], 'central_character': '1.1', 'conductor': 3381, 'conductor_radical': 483, 'degree': 2, 'index': 57, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3381/2/a/bf/1/4'], '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': '2-3381-1.1-c1-0-57', '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': '2-3381-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.195904245017888, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.960576602974353706778534829437', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1217675507325633084198606786224', 'Lhash_array': ['1217675507325633084198606786224'], 'label': '2-3381-1.1-c1-0-57', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3381/2/a/bf/1/4'}