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lfunc_lfunctions • Show schema
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{'Lhash': '3011763200089123285868796305041', 'a10': [597.4963407394706, 126.54763850509417], 'a2': [-6.421810867234986, 8.838864374347542], 'a3': [13.272043976168229, -4.312348497126355], 'a4': [-26.99732479357449, -83.0892220649575], 'a5': [-22.774406409608243, -51.052193025275564], 'a6': [-47.114292735556454, 145.00288311787773], 'a7': [0.0, -134.69964370452422], 'a8': [575.2834144675451, 186.9209122766239], 'a9': [-39.040327888436806, 28.364458518223067], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.0095954953245165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [22.774406409608243, 51.052193025275564]]]], 'bad_primes': [5], 'central_character': '25.9', 'coefficient_field': 'CDF', 'conductor': 25, 'conductor_radical': 5, 'conjugate': '889208808105637273385522863413', 'degree': 2, 'euler_factors': [[[1.0, 0], [6.421810867234986, -8.838864374347542], [-9.888543819998318, -30.433808521444913]], [[1.0, 0], 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'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.37586224433363709827133460408', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.53284331648816300207843037880', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.67373882318510718602415338957', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.0095954953245165, 'bad_primes': [5], 'central_character': '25.9', 'conductor': 25, 'conductor_radical': 5, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/25/6/e/a/9/1'], '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': '2-5e2-25.9-c5-0-7', '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': '2-5e2-25.9-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0023974369052007, 'root_angle': 0.08643515640832111, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.37586224433363709827133460408', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3011763200089123285868796305041', 'Lhash_array': ['3011763200089123285868796305041'], 'label': '2-5e2-25.9-c5-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/25/6/e/a/9/1'}