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lfunc_lfunctions • Show schema
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{'Lhash': '1666611487477475485928576403645', 'a10': [0.0, 0.0], 'a2': [1.0, 0.0], 'a3': [0.0, 0.0], 'a4': [1.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [4.358898943540674, 0.0], 'a8': [1.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.779804272872857, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1350.1', 'coefficient_field': 'CDF', 'conductor': 1350, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-4.358898943540674, 0], [7.0, 0]], [[1.0, 0], [4.358898943540674, 0], [11.0, 0]], [[1.0, 0], [0, 0], [13.0, 0]], [[1.0, 0], [-4.0, 0], [17.0, 0]], [[1.0, 0], [-6.0, 0], [19.0, 0]], [[1.0, 0], [2.0, 0], [23.0, 0]], [[1.0, 0], [0, 0], [29.0, 0]], [[1.0, 0], [-7.0, 0], [31.0, 0]], [[1.0, 0], 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'rational': False, 'root_analytic_conductor': 3.2832612251955915, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.31472464666321829271225485775', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.48726936281705293448809254923', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.53307271168479685023107989173', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 10.779804272872857, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1350, 'conductor_radical': 30, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1350/2/a/x/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': '2-1350-1.1-c1-0-13', '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': '2-1350-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.2832612251955915, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.31472464666321829271225485775', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1666611487477475485928576403645', 'Lhash_array': ['1666611487477475485928576403645'], 'label': '2-1350-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1350/2/a/x/1/2'}