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lfunc_lfunctions • Show schema
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{'Lhash': '2158223590290228084716719126290', 'a10': 0, 'a2': 0, 'a3': 4, 'a4': 0, 'a5': 25, 'a6': 0, 'a7': -49, 'a8': 0, 'a9': -227, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 44.907469547634584, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, -25]], [7, [1, 49]]], 'bad_primes': [2, 5, 7], 'central_character': '280.1', 'coefficient_field': '1.1.1.1', 'conductor': 280, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, -4, 243], [1, -25], [1, 49], [1, -124, 161051], [1, -766, 371293], [1, 1102, 1419857], [1, 764, 2476099], [1, -168, 6436343], [1, 6866, 20511149], [1, 4096, 28629151], [1, 4682, 69343957], [1, -13130, 115856201], [1, -18220, 147008443], [1, 7104, 229345007], [1, 20026, 418195493], [1, 38964, 714924299], [1, 56274, 844596301], [1, 24060, 1350125107], [1, 31896, 1804229351], [1, 23670, 2073071593], [1, -37744, 3077056399], [1, 68204, 3939040643], [1, 19078, 5584059449], [1, 115646, 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'9.224262926035852895831946015059789', '10.76683165766082367173587364490277'], 'prelabel': '2-280-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.70130357077148, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c5-0', 'trace_hash': 563322126767889701, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70253821510569143173827380385', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.00391131981547898238559190865', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.15206788173510201102169121147', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 44.907469547634584, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 280, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, 4, 0, 25, 0, -49, 0, -227, 0, 124, 0, 766, 0, 100, 0, -1102, 0, -764, 0, -196, 0, 168, 0, 625, 0, -1880, 0, -6866, 0, -4096, 0, 496, 0, -1225, 0, -4682, 0, 3064, 0, 13130, 0, 18220, 0, -5675, 0, -7104, 0, 2401, 0, -4408, 0, -20026, 0, 3100, 0, -3056, 0, -38964, 0, -56274, 0, 11123, 0, 19150, 0, -24060, 0, 672, 0, -31896, 0, -23670, 0, 2500, 0, -6076, 0, 37744, 0, 47641, 0, -68204, 0, -27550, 0, -27464, 0, -19078, 0, -37534, 0, -16384, 0, -19100, 0, -115646, 0, -28148, 0], 'euler11': [1, -124, 161051], 'euler13': [1, -766, 371293], 'euler17': [1, 1102, 1419857], 'euler19': [1, 764, 2476099], 'euler2': [1, 0, 0], 'euler23': [1, -168, 6436343], 'euler29': [1, 6866, 20511149], 'euler3': [1, -4, 243], 'euler31': [1, 4096, 28629151], 'euler37': [1, 4682, 69343957], 'euler41': [1, -13130, 115856201], 'euler43': [1, -18220, 147008443], 'euler47': [1, 7104, 229345007], 'euler5': [1, -25, 0], 'euler53': [1, 20026, 418195493], 'euler59': [1, 38964, 714924299], 'euler61': [1, 56274, 844596301], 'euler67': [1, 24060, 1350125107], 'euler7': [1, 49, 0], 'euler71': [1, 31896, 1804229351], 'euler73': [1, 23670, 2073071593], 'euler79': [1, -37744, 3077056399], 'euler83': [1, 68204, 3939040643], 'euler89': [1, 19078, 5584059449], 'euler97': [1, 115646, 8587340257], 'euler_factors': [[1, 0, 0], [1, -4, 243], [1, -25, 0], [1, 49, 0], [1, -124, 161051], [1, -766, 371293], [1, 1102, 1419857], [1, 764, 2476099], [1, -168, 6436343], [1, 6866, 20511149], [1, 4096, 28629151], [1, 4682, 69343957], [1, -13130, 115856201], [1, -18220, 147008443], [1, 7104, 229345007], [1, 20026, 418195493], [1, 38964, 714924299], [1, 56274, 844596301], [1, 24060, 1350125107], [1, 31896, 1804229351], [1, 23670, 2073071593], [1, -37744, 3077056399], [1, 68204, 3939040643], [1, 19078, 5584059449], [1, 115646, 8587340257]], 'index': 23, 'instance_types': ['CMF', 'CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/280/6/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/280/6/a/b'], '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': '2-280-1.1-c5-0-23', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-280-1.1-c5-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 6.70130357077148, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'trace_hash': 563322126767889701, 'z1': {'__RealLiteral__': 0, 'data': '1.70253821510569143173827380385', 'prec': 103}}
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lfunc_instances • Show schema
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id: 20431627
{'Lhash': '2158223590290228084716719126290', 'Lhash_array': ['2158223590290228084716719126290'], 'label': '2-280-1.1-c5-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/280/6/a/b'}
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id: 24571201
{'Lhash': '2158223590290228084716719126290', 'Lhash_array': ['2158223590290228084716719126290'], 'label': '2-280-1.1-c5-0-23', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/280/6/a/b/1/1'}