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lfunc_lfunctions • Show schema
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{'Lhash': '393013810116452972918233716054', 'a10': [-0.7071067811865476, -1.224744871391589], 'a2': [-0.5, 0.8660254037844386], 'a3': [0.0, 0.0], 'a4': [-0.5, -0.8660254037844386], 'a5': [-0.7071067811865476, 1.224744871391589], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [1.0, -3.9689140359382235e-80], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.8803506822846163, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.5, -0.8660254037844386]]], [3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '1764.667', 'coefficient_field': 'CDF', 'conductor': 1764, 'conductor_radical': 42, 'conjugate': '2422537626795054369821015429991', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.7071067811865476, -1.224744871391589], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [0.5, 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1.6848240607900165, 2.992587663588416, 4.18839257971107, 5.211511723205744], 'positive_zeros': ['0.31003323001282393933179788416571', '1.71010602305280053563800764311059', '2.93786377108900925863387528571091', '3.93631867236240465507806718378401', '4.83802481538778707204668618847457', '5.34344098036039832425231811150013', '7.11447671973884288167442989894938', '7.65654831200167262863158970697121', '8.351754668431760920939286560386427', '9.276259184125496606630298156790634'], 'prelabel': '2-42e2-28.23-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9382700476326719, 'root_angle': 0.856451189731629, 'root_number': '-0.90002393947020927090529184082558 + 0.43584046207359531761932793395659*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.42822559486581446', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31003323001282393933179788417', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.71010602305280053563800764311', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.93786377108900925863387528571', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.8803506822846163, 'bad_primes': [2, 3, 7], 'central_character': '28.23', 'conductor': 1764, 'conductor_radical': 42, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1764/1/y/b/667/1'], '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': '2-42e2-28.23-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-42e2-28.23-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9382700476326719, 'root_angle': 0.4282255948658145, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31003323001282393933179788417', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '393013810116452972918233716054', 'Lhash_array': ['393013810116452972918233716054'], 'label': '2-42e2-28.23-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1764/1/y/b/667/1'}