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lfunc_lfunctions • Show schema
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{'Lhash': '1207638549276665375546002782021', 'a10': [-3.114302225351345e-62, -2.8055710828670826], 'a2': [-0.8660254037844386, -0.5], 'a3': [-1.6759515454841711, 0.43724869032304553], 'a4': [0.5, 0.8660254037844386], 'a5': [1.4027855414335413, 2.42969582988591], 'a6': [1.670040959062606, 0.45930729915085305], 'a7': [1.4256869050680008, -2.228770254808159], 'a8': [0.0, -1.0], 'a9': [2.617627165621563, -1.4656152366156758], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.8660254037844386, 0.5]]], [3, [[1.0, 0], [1.6759515454841711, -0.43724869032304553]]], [7, [[1.0, 0], [-1.4256869050680008, 2.228770254808159]]], [13, [[1.0, 0], [-0.591454996246779, 3.5567092919459586]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.185', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': 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'4.64064174975348053657102425191610', '5.22677278982602334020764479419388', '6.22717832923138185105772582549453', '6.87797978014105141900047421108935', '8.514870215705643797066214903066812', '8.691302863691480253477267022381711', '9.723086348228748564568138828161449', '10.87799927484244633912573802286817'], 'prelabel': '2-546-273.185-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.1400246582093216, 'root_number': '0.9047940663115517 - 0.4258493836644682*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0700123291047', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.952658839162179719595821170062', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.16851992395523006126471414853', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.64064174975348053657102425192', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '273.185', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/u/a/185/1'], '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': '2-546-273.185-c1-0-10', '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': '2-546-273.185-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': -0.0700123291046608, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.952658839162179719595821170062', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1207638549276665375546002782021', 'Lhash_array': ['1207638549276665375546002782021'], 'label': '2-546-273.185-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/u/a/185/1'}