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lfunc_lfunctions • Show schema
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{'Lhash': '2282096568550324151218988534039,4002358157514215596771001714004', 'a10': 0, 'a2': -2, 'a3': 6, 'a4': 2, 'a5': 0, 'a6': -12, 'a7': -6, 'a8': 0, 'a9': 18, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.8561373616464327, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 2]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '50.1', 'coefficient_field': '1.1.1.1', 'conductor': 2500, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1, 2, 2], [1, -6, 18, -54, 81], [1], [1, 6, 18, 294, 2401], [1, -24, 386, -2904, 14641], [1, 24, 288, 4056, 28561], [1, -24, 288, -6936, 83521], [1, 0, -322, 0, 130321], [1, -6, 18, -3174, 279841], [1, 0, -782, 0, 707281], [1, 16, 1986, 15376, 923521], [1, 96, 4608, 131424, 1874161], [1, 96, 5666, 161376, 2825761], [1, 54, 1458, 99846, 3418801], [1, -54, 1458, -119286, 4879681], [1, 24, 288, 67416, 7890481], [1, 0, -3362, 0, 12117361], [1, -64, 8466, -238144, 13845841], [1, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.8561373616464327, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 2500, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, -2, 6, 2, 0, -12, -6, 0, 18, 0, 24, 12, -24, 12, 0, -4, 24, -36, 0, 0, -36, -48, 6, 0, 0, 48, 54, -12, 0, 0, -16, 8, 144, -48, 0, 36, -96, 0, -144, 0, -96, 72, -54, 48, 0, -12, 54, -24, 18, 0, 144, -48, -24, -108, 0, 0, 0, 0, 0, 0, 64, 32, -108, -8, 0, -288, -6, 48, 36, 0, -96, 0, -24, 192, 0, 0, -144, 288, 0, 0, 243, 192, 186, -72, 0, 108, 0, 0, 0, 0, 144, 12, -96, -108, 0, 48, 24, -36, 432, 0], 'euler11': [1, -24, 386, -2904, 14641], 'euler13': [1, 24, 288, 4056, 28561], 'euler17': [1, -24, 288, -6936, 83521], 'euler19': [1, 0, -322, 0, 130321], 'euler2': [1, 2, 2, 0, 0], 'euler23': [1, -6, 18, -3174, 279841], 'euler29': [1, 0, -782, 0, 707281], 'euler3': [1, -6, 18, -54, 81], 'euler31': [1, 16, 1986, 15376, 923521], 'euler37': [1, 96, 4608, 131424, 1874161], 'euler41': [1, 96, 5666, 161376, 2825761], 'euler43': [1, 54, 1458, 99846, 3418801], 'euler47': [1, -54, 1458, -119286, 4879681], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 24, 288, 67416, 7890481], 'euler59': [1, 0, -3362, 0, 12117361], 'euler61': [1, -64, 8466, -238144, 13845841], 'euler67': [1, 6, 18, 26934, 20151121], 'euler7': [1, 6, 18, 294, 2401], 'euler71': [1, 96, 12386, 483936, 25411681], 'euler73': [1, 24, 288, 127896, 28398241], 'euler79': [1, 0, -10882, 0, 38950081], 'euler83': [1, -186, 17298, -1281354, 47458321], 'euler89': [1, 0, -14942, 0, 62742241], 'euler97': [1, -24, 288, -225816, 88529281], 'euler_factors': [[1, 2, 2, 0, 0], [1, -6, 18, -54, 81], [1, 0, 0, 0, 0], [1, 6, 18, 294, 2401], [1, -24, 386, -2904, 14641], [1, 24, 288, 4056, 28561], [1, -24, 288, -6936, 83521], [1, 0, -322, 0, 130321], [1, -6, 18, -3174, 279841], [1, 0, -782, 0, 707281], [1, 16, 1986, 15376, 923521], [1, 96, 4608, 131424, 1874161], [1, 96, 5666, 161376, 2825761], [1, 54, 1458, 99846, 3418801], [1, -54, 1458, -119286, 4879681], [1, 24, 288, 67416, 7890481], [1, 0, -3362, 0, 12117361], [1, -64, 8466, -238144, 13845841], [1, 6, 18, 26934, 20151121], [1, 96, 12386, 483936, 25411681], [1, 24, 288, 127896, 28398241], [1, 0, -10882, 0, 38950081], [1, -186, 17298, -1281354, 47458321], [1, 0, -14942, 0, 62742241], [1, -24, 288, -225816, 88529281]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/50/3/c/a'], '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': '4-50e2-1.1-c2e2-0-1', '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': '4-50e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.1672194831313796, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 1230467108045195713, 'z1': {'__RealLiteral__': 0, 'data': '1.80025676486837353071318586815', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2282096568550324151218988534039,4002358157514215596771001714004', 'Lhash_array': ['2282096568550324151218988534039', '4002358157514215596771001714004'], 'label': '4-50e2-1.1-c2e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/50/3/c/a'}