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lfunc_lfunctions • Show schema
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{'Lhash': '587326445438699919149879444839,969238758043031182280027317238,1126635982605281020733329853492,1742553633549147240146489255493', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 2, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 426293.1374398732, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '3200.1', 'coefficient_field': '1.1.1.1', 'conductor': 104857600000000, 'conductor_radical': 10, 'degree': 8, 'euler_factors': [[1], [1, 0, -2, 0, -5, 0, -18, 0, 81], [1], [1, 0, 28, 0, 294, 0, 1372, 0, 2401], [1, 0, 14, 0, 75, 0, 1694, 0, 14641], [1, 0, -52, 0, 1014, 0, -8788, 0, 28561], [1, -12, 74, -432, 2163, -7344, 21386, -58956, 83521], [1, 0, -34, 0, 795, 0, -12274, 0, 130321], [1, 0, 92, 0, 3174, 0, 48668, 0, 279841], [1, 0, -116, 0, 5046, 0, -97556, 0, 707281], [1, 0, 124, 0, 5766, 0, 119164, 0, 923521], [1, 0, -148, 0, 8214, 0, 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'prelabel': '8-3200e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.054911339164094, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 1628134908176267300, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46331887140901201831646089021', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.76459456404511481518675418543', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.888759081092566096352428329528', 'prec': 107}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 426293.1374398732, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 104857600000000, 'conductor_radical': 10, 'degree': 8, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 12, 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, -28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0], 'euler11': [1, 0, 14, 0, 75, 0, 1694, 0, 14641], 'euler13': [1, 0, -52, 0, 1014, 0, -8788, 0, 28561], 'euler17': [1, -12, 74, -432, 2163, -7344, 21386, -58956, 83521], 'euler19': [1, 0, -34, 0, 795, 0, -12274, 0, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 92, 0, 3174, 0, 48668, 0, 279841], 'euler29': [1, 0, -116, 0, 5046, 0, -97556, 0, 707281], 'euler3': [1, 0, -2, 0, -5, 0, -18, 0, 81], 'euler31': [1, 0, 124, 0, 5766, 0, 119164, 0, 923521], 'euler37': [1, 0, -148, 0, 8214, 0, -202612, 0, 1874161], 'euler41': [1, -12, 26, -432, 6339, -17712, 43706, -827052, 2825761], 'euler43': [1, 0, -28, 0, 3894, 0, -51772, 0, 3418801], 'euler47': [1, 0, 188, 0, 13254, 0, 415292, 0, 4879681], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -212, 0, 16854, 0, -595508, 0, 7890481], 'euler59': [1, 0, 164, 0, 13686, 0, 570884, 0, 12117361], 'euler61': [1, 0, -244, 0, 22326, 0, -907924, 0, 13845841], 'euler67': [1, 0, 62, 0, -645, 0, 278318, 0, 20151121], 'euler7': [1, 0, 28, 0, 294, 0, 1372, 0, 2401], 'euler71': [1, 0, 284, 0, 30246, 0, 1431644, 0, 25411681], 'euler73': [1, 4, -134, 16, 16003, 1168, -714086, 1556068, 28398241], 'euler79': [1, 0, 316, 0, 37446, 0, 1972156, 0, 38950081], 'euler83': [1, 0, 158, 0, 18075, 0, 1088462, 0, 47458321], 'euler89': [1, -36, 794, -11664, 128739, -1038096, 6289274, -25378884, 62742241], 'euler97': [1, -40, 988, -15640, 182854, -1517080, 9296092, -36506920, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -2, 0, -5, 0, -18, 0, 81], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 28, 0, 294, 0, 1372, 0, 2401], [1, 0, 14, 0, 75, 0, 1694, 0, 14641], [1, 0, -52, 0, 1014, 0, -8788, 0, 28561], [1, -12, 74, -432, 2163, -7344, 21386, -58956, 83521], [1, 0, -34, 0, 795, 0, -12274, 0, 130321], [1, 0, 92, 0, 3174, 0, 48668, 0, 279841], [1, 0, -116, 0, 5046, 0, -97556, 0, 707281], [1, 0, 124, 0, 5766, 0, 119164, 0, 923521], [1, 0, -148, 0, 8214, 0, -202612, 0, 1874161], [1, -12, 26, -432, 6339, -17712, 43706, -827052, 2825761], [1, 0, -28, 0, 3894, 0, -51772, 0, 3418801], [1, 0, 188, 0, 13254, 0, 415292, 0, 4879681], [1, 0, -212, 0, 16854, 0, -595508, 0, 7890481], [1, 0, 164, 0, 13686, 0, 570884, 0, 12117361], [1, 0, -244, 0, 22326, 0, -907924, 0, 13845841], [1, 0, 62, 0, -645, 0, 278318, 0, 20151121], [1, 0, 284, 0, 30246, 0, 1431644, 0, 25411681], [1, 4, -134, 16, 16003, 1168, -714086, 1556068, 28398241], [1, 0, 316, 0, 37446, 0, 1972156, 0, 38950081], [1, 0, 158, 0, 18075, 0, 1088462, 0, 47458321], [1, -36, 794, -11664, 128739, -1038096, 6289274, -25378884, 62742241], [1, -40, 988, -15640, 182854, -1517080, 9296092, -36506920, 88529281]], 'index': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/2/d/q'], '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': '8-3200e4-1.1-c1e4-0-25', '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': '8-3200e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.054911339164094, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1628134908176267300, 'z1': {'__RealLiteral__': 0, 'data': '0.46331887140901201831646089021', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '587326445438699919149879444839,969238758043031182280027317238,1126635982605281020733329853492,1742553633549147240146489255493', 'Lhash_array': ['587326445438699919149879444839', '969238758043031182280027317238', '1126635982605281020733329853492', '1742553633549147240146489255493'], 'label': '8-3200e4-1.1-c1e4-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/2/d/q'}