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lfunc_lfunctions • Show schema
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{'Lhash': '310701728953290022414498688507,1513875875655925241795378389178,1530843961614330603874504719550,1975442292497393680517455122873', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 5, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 124410.689690955, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, -5, 0, 9]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '2352.1', 'coefficient_field': '1.1.1.1', 'conductor': 30601961865216, 'conductor_radical': 42, 'degree': 8, 'euler_factors': [[1], [1, 0, -5, 0, 9], [1, 0, 2, 0, 51, 0, 50, 0, 625], [1], [1, 0, 22, 0, 363, 0, 2662, 0, 14641], [1, -16, 148, -880, 3766, -11440, 25012, -35152, 28561], [1, 0, -46, 0, 1107, 0, -13294, 0, 83521], [1, 0, 22, 0, 843, 0, 7942, 0, 130321], [1, 0, 70, 0, 2283, 0, 37030, 0, 279841], [1, 0, -28, 0, 1878, 0, -23548, 0, 707281], [1, 0, -106, 0, 4731, 0, -101866, 0, 923521], [1, 4, 154, 448, 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'1.20762295331120068890166440811', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 124410.689690955, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 30601961865216, 'conductor_radical': 42, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, 0, 0, 0], 'euler11': [1, 0, 22, 0, 363, 0, 2662, 0, 14641], 'euler13': [1, -16, 148, -880, 3766, -11440, 25012, -35152, 28561], 'euler17': [1, 0, -46, 0, 1107, 0, -13294, 0, 83521], 'euler19': [1, 0, 22, 0, 843, 0, 7942, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 70, 0, 2283, 0, 37030, 0, 279841], 'euler29': [1, 0, -28, 0, 1878, 0, -23548, 0, 707281], 'euler3': [1, 0, -5, 0, 9, 0, 0, 0, 0], 'euler31': [1, 0, -106, 0, 4731, 0, -101866, 0, 923521], 'euler37': [1, 4, 154, 448, 8659, 16576, 210826, 202612, 1874161], 'euler41': [1, 0, -76, 0, 4806, 0, -127756, 0, 2825761], 'euler43': [1, 0, -164, 0, 10422, 0, -303236, 0, 3418801], 'euler47': [1, 0, -10, 0, 4443, 0, -22090, 0, 4879681], 'euler5': [1, 0, 2, 0, 51, 0, 50, 0, 625], 'euler53': [1, 0, -190, 0, 14643, 0, -533710, 0, 7890481], 'euler59': [1, 0, 214, 0, 18411, 0, 744934, 0, 12117361], 'euler61': [1, 12, 298, 2304, 28995, 140544, 1108858, 2723772, 13845841], 'euler67': [1, 0, -106, 0, 11787, 0, -475834, 0, 20151121], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, -68, 0, 11238, 0, -342788, 0, 25411681], 'euler73': [1, 28, 586, 7504, 77299, 547792, 3122794, 10892476, 28398241], 'euler79': [1, 0, -154, 0, 18411, 0, -961114, 0, 38950081], 'euler83': [1, 0, -20, 0, 13878, 0, -137780, 0, 47458321], 'euler89': [1, 0, -334, 0, 43731, 0, -2645614, 0, 62742241], 'euler97': [1, 32, 772, 11360, 135046, 1101920, 7263748, 29205536, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -5, 0, 9, 0, 0, 0, 0], [1, 0, 2, 0, 51, 0, 50, 0, 625], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 22, 0, 363, 0, 2662, 0, 14641], [1, -16, 148, -880, 3766, -11440, 25012, -35152, 28561], [1, 0, -46, 0, 1107, 0, -13294, 0, 83521], [1, 0, 22, 0, 843, 0, 7942, 0, 130321], [1, 0, 70, 0, 2283, 0, 37030, 0, 279841], [1, 0, -28, 0, 1878, 0, -23548, 0, 707281], [1, 0, -106, 0, 4731, 0, -101866, 0, 923521], [1, 4, 154, 448, 8659, 16576, 210826, 202612, 1874161], [1, 0, -76, 0, 4806, 0, -127756, 0, 2825761], [1, 0, -164, 0, 10422, 0, -303236, 0, 3418801], [1, 0, -10, 0, 4443, 0, -22090, 0, 4879681], [1, 0, -190, 0, 14643, 0, -533710, 0, 7890481], [1, 0, 214, 0, 18411, 0, 744934, 0, 12117361], [1, 12, 298, 2304, 28995, 140544, 1108858, 2723772, 13845841], [1, 0, -106, 0, 11787, 0, -475834, 0, 20151121], [1, 0, -68, 0, 11238, 0, -342788, 0, 25411681], [1, 28, 586, 7504, 77299, 547792, 3122794, 10892476, 28398241], [1, 0, -154, 0, 18411, 0, -961114, 0, 38950081], [1, 0, -20, 0, 13878, 0, -137780, 0, 47458321], [1, 0, -334, 0, 43731, 0, -2645614, 0, 62742241], [1, 32, 772, 11360, 135046, 1101920, 7263748, 29205536, 88529281]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2352/2/h/j'], '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': '8-2352e4-1.1-c1e4-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-2352e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.33368371658629, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1351847157529291660, 'z1': {'__RealLiteral__': 0, 'data': '0.24510044715582581986988388617', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '310701728953290022414498688507,1513875875655925241795378389178,1530843961614330603874504719550,1975442292497393680517455122873', 'Lhash_array': ['310701728953290022414498688507', '1513875875655925241795378389178', '1530843961614330603874504719550', '1975442292497393680517455122873'], 'label': '8-2352e4-1.1-c1e4-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2352/2/h/j'}