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lfunc_lfunctions • Show schema
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{'Lhash': '807992177088834951491319291794', 'a10': [-25.828238102501157, 0.0], 'a2': [2.0, 0.0], 'a3': [-3.0, 0.0], 'a4': [4.0, 0.0], 'a5': [-12.914119051250578, 0.0], 'a6': [-6.0, 0.0], 'a7': [-7.0, 0.0], 'a8': [8.0, 0.0], 'a9': [9.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.99584506554546, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-2.0, 0]]], [3, [[1.0, 0], [3.0, 0]]], [7, [[1.0, 0], [7.0, 0]]], [23, [[1.0, 0], [-23.0, 0]]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '966.1', 'coefficient_field': 'CDF', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.0, 0]], [[1.0, 0], [3.0, 0]], [[1.0, 0], [12.914119051250578, 0], [125.0, 0]], [[1.0, 0], [7.0, 0]], [[1.0, 0], [-36.529516317074815, 0], [1331.0, 0]], [[1.0, 0], [-0.37342191477511905, 0], [2197.0, 0]], [[1.0, 0], [86.28007508847799, 0], [4913.0, 0]], [[1.0, 0], [68.5097619457007, 0], [6859.0, 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'4.15680061736062795316239024427546', '5.14075322758432194462983512531831', '6.39185213060096416997574452118278', '6.76573810163244608603526646338432', '7.79052827549096836526476018300780', '8.741703993499246367042815723070014', '9.704722566394728441787986214756655'], 'prelabel': '2-966-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.549559262999758, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.63739344022979441504602975398', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.23430879911173480748793234160', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.71650316146138483154393490319', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.99584506554546, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 966, 'conductor_radical': 966, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/966/4/a/p/1/2'], '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': '2-966-1.1-c3-0-10', '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': '2-966-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.549559262999758, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.63739344022979441504602975398', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '807992177088834951491319291794', 'Lhash_array': ['807992177088834951491319291794'], 'label': '2-966-1.1-c3-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/966/4/a/p/1/2'}