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lfunc_lfunctions • Show schema
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{'Lhash': '648694683457303878458737806343', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.224744871391589, -1.224744871391589], 'a4': [0.0, 0.0], 'a5': [0.7071067811865476, -0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [1.7320508075688772, 1.7320508075688772], 'a8': [0.0, 0.0], 'a9': [0.0, 3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.515792804936482, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.224744871391589, 1.224744871391589]]], [17, [[1.0, 0], [3.5355339059327378, -2.1213203435596424]]]], 'bad_primes': [2, 3, 17], 'central_character': '816.47', 'coefficient_field': 'CDF', 'conductor': 816, 'conductor_radical': 102, 'conjugate': '2026925024280660425370087176846', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.224744871391589, 1.224744871391589]], [[1.0, 0], [-0.7071067811865476, 0.7071067811865476], [0, -5.0]], [[1.0, 0], [-1.7320508075688772, 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'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.86170683878712086202333433152', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.515792804936482, 'bad_primes': [2, 3, 17], 'central_character': '204.47', 'conductor': 816, 'conductor_radical': 102, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/816/2/bf/b/47/2'], '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': '2-816-204.47-c1-0-8', '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': '2-816-204.47-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5526051016435116, 'root_angle': -0.188838550738991, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.51172987520418644957285841301', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '648694683457303878458737806343', 'Lhash_array': ['648694683457303878458737806343'], 'label': '2-816-204.47-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/816/2/bf/b/47/2'}