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lfunc_lfunctions • Show schema
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{'Lhash': '448909732828425878591021483300', 'a10': [-7.10577965862533, 6.730952024266433], 'a2': [2.0010891211845094, -0.21763155707342524], 'a3': [1.9421588543454829, 2.2864861653829096], 'a4': [-3.8559702693919053, 0.8487632391160387], 'a5': [-3.87098847654292, 2.9426489367037867], 'a6': [4.3840444994420436, 4.152787535731478], 'a7': [5.750411546119805, 14.432444692996283], 'a8': [-22.791585835805453, 7.679379389946029], 'a9': [-1.4560379689748826, 8.881438702873735], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.443338071016093, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.9421588543454829, -2.2864861653829096]]], [59, [[1.0, 0], [-37.15565695527931, -451.661883665449]]]], 'bad_primes': [3, 59], 'central_character': '177.133', 'coefficient_field': 'CDF', 'conductor': 177, 'conductor_radical': 177, 'conjugate': '3423132089739135263757902375604', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'rational': False, 'root_analytic_conductor': 3.231615396518604, 'root_angle': -0.8554348300907977, 'root_number': '-0.898627720532166 - 0.438712001079482*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.427717415045', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35412733820155459883004045117', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.54831821668756117957489907674', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.26133024612860127742465009351', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.443338071016093, 'bad_primes': [3, 59], 'central_character': '59.15', 'conductor': 177, 'conductor_radical': 177, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/177/4/e/b/133/10'], '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': '2-177-59.15-c3-0-3', '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': '2-177-59.15-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.231615396518604, 'root_angle': -0.42771741504539884, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.35412733820155459883004045117', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '448909732828425878591021483300', 'Lhash_array': ['448909732828425878591021483300'], 'label': '2-177-59.15-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/177/4/e/b/133/10'}