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lfunc_lfunctions • Show schema
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{'Lhash': '2334206418682539243767933151896', 'a10': [-0.6149295366877088, 3.1019125817645214], 'a2': [0.005220991639966664, 1.4142039249154612], 'a3': [-0.21270041276549917, -0.21270041276549917], 'a4': [-1.9999454824925909, 0.014767093738383334], 'a5': [2.1917632029529113, 0.44291541199375195], 'a6': [0.29969125148724146, -0.30191226564097373], 'a7': [2.6508756202138843, -2.6508756202138843], 'a8': [-0.03132538056889916, -2.828253652085013], 'a9': [0.0, -2.9095170688187726], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.034315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.005220991639966664, -1.4142039249154612]]], [5, [[1.0, 0], [-2.1917632029529113, -0.44291541199375195]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '380.267', 'coefficient_field': 'CDF', 'conductor': 380, 'conductor_radical': 190, 'conjugate': '1495047696332512934601261538681', 'degree': 2, 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-0.11508860120131936, 'root_number': '0.935345605264932 - 0.3537352098838592*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0575443006007', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.84136418841460399033346053627', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48211652558656640106902862573', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.57208243150057167315974954831', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.034315276808656, 'bad_primes': [2, 5, 19], 'central_character': '20.7', 'conductor': 380, 'conductor_radical': 190, 'degree': 2, 'index': 34, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/380/2/k/d/267/13'], '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': '2-380-20.7-c1-0-34', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-380-20.7-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': -0.05754430060065968, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.84136418841460399033346053627', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2334206418682539243767933151896', 'Lhash_array': ['2334206418682539243767933151896'], 'label': '2-380-20.7-c1-0-34', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/380/2/k/d/267/13'}