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lfunc_lfunctions • Show schema
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{'Lhash': '3799320987915655070682158958299', 'a10': [-46.980041871302205, -22.372499894430288], 'a2': [3.7652962189585226, -2.735647833611152], 'a3': [0.0, 0.0], 'a4': [4.221550591962379, -12.99259675823506], 'a5': [-5.340902688221366, -9.822156508371764], 'a6': [0.0, 0.0], 'a7': [-26.044513640038623, 0.0], 'a8': [-8.142059269145442, -25.0586817713541], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.275429751291645, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [5.340902688221366, 9.822156508371764]]]], 'bad_primes': [3, 5], 'central_character': '225.136', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '697974239195291482893953569473', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.7652962189585226, 2.735647833611152], [2.4721359549995796, -7.608452130361228]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.340902688221366, 9.822156508371764]], 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'data': '3.69398992555173655866878260353', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.07829453762690129069119112227', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 13.275429751291645, 'bad_primes': [3, 5], 'central_character': '25.11', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/4/h/a/136/7'], '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': '2-15e2-25.11-c3-0-36', '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': '2-15e2-25.11-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.6435463152389933, 'root_angle': -0.47853116509329013, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '2.99713579375233251360407797753', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3799320987915655070682158958299', 'Lhash_array': ['3799320987915655070682158958299'], 'label': '2-15e2-25.11-c3-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/4/h/a/136/7'}