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lfunc_lfunctions • Show schema
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{'Lhash': '1299516636489803363399860701920', 'a10': [0, -78.42615723576017], 'a2': [0, 6.103236694173747], 'a3': [-5.196152422706632, 0], 'a4': [-21.24949814510888, 0], 'a5': [-12.849928843596565, 0], 'a6': [0, -31.71334813478293], 'a7': [4.616084648888791, 0], 'a8': [0, -32.03892970522555], 'a9': [27.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.296483465840453, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [5.196152422706632, 0]]], [59, [[1.0, 0], [-2040.0652582217765, 2820.5486597817307]]]], 'bad_primes': [3, 59], 'central_character': '177.58', 'coefficient_field': 'CDF', 'conductor': 177, 'conductor_radical': 177, 'conjugate': '757498126960042865146922970500', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -6.103236694173747], [-16.0, 0]], [[1.0, 0], [5.196152422706632, 0]], [[1.0, 0], [12.849928843596565, 0], [625.0, 0]], [[1.0, 0], [-4.616084648888791, 0], [2401.0, 0]], [[1.0, 0], [0, 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.02513787021111082251684641593', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.40534371194816987493166760142', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98987761799690426641290555889', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.296483465840453, 'bad_primes': [3, 59], 'central_character': '59.58', 'conductor': 177, 'conductor_radical': 177, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/177/5/c/a/58/35'], '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': '2-177-59.58-c4-0-16', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-177-59.58-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.277438890953377, 'root_angle': -0.15033968208146825, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.02513787021111082251684641593', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1299516636489803363399860701920', 'Lhash_array': ['1299516636489803363399860701920'], 'label': '2-177-59.58-c4-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/177/5/c/a/58/35'}