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lfunc_lfunctions • Show schema
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{'Lhash': '1346254254732514038339118842435', 'a10': [0.46519832343100553, 0.0], 'a2': [-0.9825046383470822, 0.0], 'a3': [-2.7435126114132777, 0.0], 'a4': [-1.034684635626469, 0.0], 'a5': [-0.4734820633657592, 0.0], 'a6': [2.6955138660772615, 0.0], 'a7': [0.7344263342609104, 0.0], 'a8': [2.9815917304236312, 0.0], 'a9': [4.526861448983702, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 73.86960690988651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[11, [[1.0, 0], [-1.0, 0]]], [29, [[1.0, 0], [0, 0]]]], 'bad_primes': [11, 29], 'central_character': '9251.1', 'coefficient_field': 'CDF', 'conductor': 9251, 'conductor_radical': 319, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9825046383470822, 0], [2.0, 0]], [[1.0, 0], [2.7435126114132777, 0], [3.0, 0]], [[1.0, 0], [0.4734820633657592, 0], [5.0, 0]], [[1.0, 0], [-0.7344263342609104, 0], [7.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-4.261994644523453, 0], [13.0, 0]], [[1.0, 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'4.13774470683384198344069224522178', '4.61251861602774632611829687279887', '5.43946911354216081539802466265854', '5.98417492522062035539142515110303', '6.55997140533829636196000554496716', '7.51632016247171362859316449140772'], 'prelabel': '2-9251-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.594742981025465, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06200735004592964059105603955', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.47500077223886141645448570123', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.18319224208754261461106627363', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 73.86960690988651, 'bad_primes': [11, 29], 'central_character': '1.1', 'conductor': 9251, 'conductor_radical': 319, 'degree': 2, 'index': 425, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/14'], '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': '2-9251-1.1-c1-0-425', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-9251-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.594742981025465, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06200735004592964059105603955', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1346254254732514038339118842435', 'Lhash_array': ['1346254254732514038339118842435'], 'label': '2-9251-1.1-c1-0-425', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9251/2/a/ba/1/14'}