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lfunc_lfunctions • Show schema
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{'Lhash': '1779762305314881934252562725301', 'a10': [534.5427712873579, -4.797429599018474e-59], 'a2': [3.34129678453352, -5.7872957939785765], 'a3': [13.3973174719799, -7.969434393668231], 'a4': [-6.328528404668083, -10.961332734027934], 'a5': [39.99515799985915, 69.2736457125009], 'a6': [-1.3570603563631765, -104.16248457029947], 'a7': [-78.38633583831881, 135.76911629112533], 'a8': [129.26102777275923, 0.0], 'a9': [115.97623089003575, -213.53808528817785], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.877998161485086, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-13.3973174719799, 7.969434393668231]]], [11, [[1.0, 0], [-60.5, 104.78907385791707]]]], 'bad_primes': [3, 11], 'central_character': '99.34', 'coefficient_field': 'CDF', 'conductor': 99, 'conductor_radical': 33, 'conjugate': '2379694602865670668819988901316', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.34129678453352, 5.7872957939785765], 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['1.40398490324893255292400926021294', '3.74005081299912542494712243743163', '4.85300311109759975986892917853192', '5.98035038334679176191636774034513', '7.46298215511106888174926776322282', '8.445087407759392529303617925439845', '9.782077290286604776504953474802444', '10.43569531153317679581982137120837', '12.72930067708337820814032023662788', '13.33284046017361574627095924397255'], 'prelabel': '2-99-9.7-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9847205876303406, 'root_angle': 0.2139286164829129, 'root_number': '0.7825304560018346 + 0.6226123074832048*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.106964308241', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40398490324893255292400926021', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.74005081299912542494712243743', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.85300311109759975986892917853', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.877998161485086, 'bad_primes': [3, 11], 'central_character': '9.7', 'conductor': 99, 'conductor_radical': 33, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/99/6/e/a/34/19'], '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': '2-99-9.7-c5-0-31', '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': '2-99-9.7-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.9847205876303406, 'root_angle': 0.10696430824145645, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40398490324893255292400926021', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1779762305314881934252562725301', 'Lhash_array': ['1779762305314881934252562725301'], 'label': '2-99-9.7-c5-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/99/6/e/a/34/19'}