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lfunc_lfunctions • Show schema
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{'Lhash': '2453304142402216096835892295089', 'a10': [2093.6949156301016, 5334.647643280585], 'a2': [-2.712199121555198, -11.8829207660898], 'a3': [111.82640725973386, 103.7597426646994], 'a4': [327.4482785078352, -157.6907799015922], 'a5': [-464.9285931957929, 70.07671009259721], 'a6': [929.6733172579663, -1610.2414199318978], 'a7': [-1144.1748747235033, -1981.7690157648628], 'a8': [-6652.8314660767865, -8342.386791614708], 'a9': [268.14873071362575, 3578.1961408585476], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 22.14654095504655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[43, [[1.0, 0], [-21459110.66770711, -6488388.18875242]]]], 'bad_primes': [43], 'central_character': '43.10', 'coefficient_field': 'CDF', 'conductor': 43, 'conductor_radical': 43, 'conjugate': '742741164374184835301356605389', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.712199121555198, 11.8829207660898], [-461.2960603660386, 222.14847442818976]], 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0.6312711813581235, 'root_number': '-0.40080979829345814 + 0.9161612879793368*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.3156355906790618', 'prec': 60}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93531572655787024189191584270177', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '3.07220466655517500346034581685917', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '5.45431726222714364191301473238869', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 22.14654095504655, 'bad_primes': [43], 'central_character': '43.10', 'conductor': 43, 'conductor_radical': 43, 'degree': 2, 'index': 23, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/43/10/g/a/10/13'], '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': '2-43-43.10-c9-0-23', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-43-43.10-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.706011151181705, 'root_angle': 0.3156355906790618, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93531572655787024189191584270177', 'prec': 113}}
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lfunc_instances • Show schema
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{'Lhash': '2453304142402216096835892295089', 'Lhash_array': ['2453304142402216096835892295089'], 'label': '2-43-43.10-c9-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/43/10/g/a/10/13'}