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lfunc_lfunctions • Show schema
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{'Lhash': '1758346034248045983594264912277', 'a10': [314.32033657500926, -1.8083638921227175e-59], 'a2': [4.333087948762897, -2.5017094936405817], 'a3': [-3.2695845505018095, 5.663086561111384], 'a4': [-3.4828992188571664, 6.032558404702567], 'a5': [54.404677499925, 31.410555199756477], 'a6': [5.6420839134000565e-61, 32.71820284100381], 'a7': [22.909135223133486, -39.67978616393297], 'a8': [0.0, 194.9622157578306], 'a9': [100.11963373423976, 173.41229246289018], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.934201333080285, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[37, [[1.0, 0], [-6066.810772851842, -5704.188289880414]]]], 'bad_primes': [37], 'central_character': '37.11', 'coefficient_field': 'CDF', 'conductor': 37, 'conductor_radical': 37, 'conjugate': '3001666872639894334874769939765', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.333087948762897, 2.5017094936405817], [16.0, -27.712812921102035]], [[1.0, 0], 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'5.81785589564648242635494097818336', '6.76685021958613034088015199031995', '9.043458910785964115325550316717569', '10.04388472920279748588388206667068', '12.23687522376553416137202554611462', '12.80375090162915153256320346525282', '14.32628228487524673583666090230688', '14.74196887311460684346901413997384'], 'prelabel': '2-37-37.11-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4360216199944293, 'root_angle': -0.18678435840637456, 'root_number': '0.8327165730641467 - 0.5536994752971179*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0933921792032', 'prec': 54}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38709044426868978066750072202', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.34409783082056496569318672838', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.81785589564648242635494097818', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.934201333080285, 'bad_primes': [37], 'central_character': '37.11', 'conductor': 37, 'conductor_radical': 37, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/37/6/e/a/11/11'], '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': '2-37-37.11-c5-0-7', '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': '2-37-37.11-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4360216199944293, 'root_angle': -0.09339217920318728, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.38709044426868978066750072202', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1758346034248045983594264912277', 'Lhash_array': ['1758346034248045983594264912277'], 'label': '2-37-37.11-c5-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/37/6/e/a/11/11'}