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lfunc_lfunctions • Show schema
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{'Lhash': '339507533487399275226124969343,2342509068698339175947120173018', 'a10': -18, 'a2': 2, 'a3': 1, 'a4': 0, 'a5': -9, 'a6': 2, 'a7': 0, 'a8': -8, 'a9': 9, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 114.08859661601497, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 4]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '392.1', 'coefficient_field': '1.1.1.1', 'conductor': 153664, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1, -2, 4], [1, -1, -8, -9, 81], [1, 9, 52, 225, 625], [1], [1, 17, 168, 2057, 14641], [1, 0, -146, 0, 28561], [1, 25, 336, 7225, 83521], [1, 7, -312, 2527, 130321], [1, 9, 556, 4761, 279841], [1, 0, -1490, 0, 707281], [1, -57, 2044, -54777, 923521], [1, 15, 1444, 20535, 1874161], [1, 52, 4038, 87412, 2825761], [1, -28, 3894, -51772, 3418801], [1, 87, 4732, 192183, 4879681], [1, 159, 11236, 446631, 7890481], [1, 55, -456, 191455, 12117361], [1, -39, 4228, -145119, 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{'algebraic': True, 'analytic_conductor': 114.08859661601497, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 153664, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 2, 1, 0, -9, 2, 0, -8, 9, -18, -17, 0, 0, 0, -9, -16, -25, 18, -7, 0, 0, -34, -9, -8, 29, 0, 26, 0, 0, -18, 57, 0, -17, -50, 0, 0, -15, -14, 0, 72, -52, 0, 28, 0, -81, -18, -87, -16, 0, 58, -25, 0, -159, 52, 153, 0, -7, 0, -55, 0, 39, 114, 0, 64, 0, -34, -17, 0, -9, 0, 0, -72, 119, -30, 29, 0, 0, 0, -129, 144, 26, -104, -220, 0, 225, 56, 0, 136, 71, -162, 0, 0, 57, -174, 63, 0, 44, 0, -153, 0], 'euler11': [1, 17, 168, 2057, 14641], 'euler13': [1, 0, -146, 0, 28561], 'euler17': [1, 25, 336, 7225, 83521], 'euler19': [1, 7, -312, 2527, 130321], 'euler2': [1, -2, 4, 0, 0], 'euler23': [1, 9, 556, 4761, 279841], 'euler29': [1, 0, -1490, 0, 707281], 'euler3': [1, -1, -8, -9, 81], 'euler31': [1, -57, 2044, -54777, 923521], 'euler37': [1, 15, 1444, 20535, 1874161], 'euler41': [1, 52, 4038, 87412, 2825761], 'euler43': [1, -28, 3894, -51772, 3418801], 'euler47': [1, 87, 4732, 192183, 4879681], 'euler5': [1, 9, 52, 225, 625], 'euler53': [1, 159, 11236, 446631, 7890481], 'euler59': [1, 55, -456, 191455, 12117361], 'euler61': [1, -39, 4228, -145119, 13845841], 'euler67': [1, 17, -4200, 76313, 20151121], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, -10082, 0, 25411681], 'euler73': [1, -119, 8832, -634151, 28398241], 'euler79': [1, 129, 11788, 805089, 38950081], 'euler83': [1, 220, 25878, 1515580, 47458321], 'euler89': [1, -71, -2880, -562391, 62742241], 'euler97': [1, -44, 19302, -413996, 88529281], 'euler_factors': [[1, -2, 4, 0, 0], [1, -1, -8, -9, 81], [1, 9, 52, 225, 625], [1, 0, 0, 0, 0], [1, 17, 168, 2057, 14641], [1, 0, -146, 0, 28561], [1, 25, 336, 7225, 83521], [1, 7, -312, 2527, 130321], [1, 9, 556, 4761, 279841], [1, 0, -1490, 0, 707281], [1, -57, 2044, -54777, 923521], [1, 15, 1444, 20535, 1874161], [1, 52, 4038, 87412, 2825761], [1, -28, 3894, -51772, 3418801], [1, 87, 4732, 192183, 4879681], [1, 159, 11236, 446631, 7890481], [1, 55, -456, 191455, 12117361], [1, -39, 4228, -145119, 13845841], [1, 17, -4200, 76313, 20151121], [1, 0, -10082, 0, 25411681], [1, -119, 8832, -634151, 28398241], [1, 129, 11788, 805089, 38950081], [1, 220, 25878, 1515580, 47458321], [1, -71, -2880, -562391, 62742241], [1, -44, 19302, -413996, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/392/3/k/c'], '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': '4-392e2-1.1-c2e2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-392e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.2682145527678625, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 1508396191551364581, 'z1': {'__RealLiteral__': 0, 'data': '0.26782422019622277127815803120', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '339507533487399275226124969343,2342509068698339175947120173018', 'Lhash_array': ['339507533487399275226124969343', '2342509068698339175947120173018'], 'label': '4-392e2-1.1-c2e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/392/3/k/c'}