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  • lfunc_lfunctions • Show schema
    {'Lhash': '1345764281873055727741035081157,1579176236564341113054296139732,1836474459866294004823360549293,2722892229888797090383045991315', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 27.96909274743008, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1, 2, 1, 6, 9]]], 'bad_primes': [2, 3], 'central_character': '288.1', 'coefficient_field': '1.1.1.1', 'conductor': 6879707136, 'conductor_radical': 6, 'degree': 8, 'euler_factors': [[1], [1, 2, 1, 6, 9], [1, 0, -10, 0, 75, 0, -250, 0, 625], [1, 0, 14, 0, 147, 0, 686, 0, 2401], [1, -18, 155, -846, 3276, -9306, 18755, -23958, 14641], [1, 0, 26, 0, 507, 0, 4394, 0, 28561], [1, 0, 2, 0, -285, 0, 578, 0, 83521], [1, -4, -26, -16, 1099, -304, -9386, -27436, 130321], [1, 0, -46, 0, 1587, 0, -24334, 0, 279841], [1, 0, -58, 0, 2523, 0, -48778, 0, 707281], [1, 0, 62, 0, 2883, 0, 59582, 0, 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'11.15509175516008389067823390551494', '11.58975277535010450734568043171068', '11.63595754724090456211164852419466', '11.97148632948201170523318652616183', '11.99313925735939708058797026571210'], 'prelabel': '8-288e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5164734017492283, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e4-0', 'trace_hash': 1355415585971985125, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06162082961248363009660896400', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.24575039547965681227910336117', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.44872290482539340360860925926', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 27.96909274743008, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 6879707136, 'conductor_radical': 6, 'degree': 8, 'dirichlet_coefficients': [1, 0, -2, 0, 0, 0, 0, 0, 3, 0, 18, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 10, 0, -10, 0, 0, 0, 0, 0, -36, 0, 0, 0, 0, 0, 0, 0, 18, 0, 10, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 0, 0, -8, 0, -18, 0, 0, 0, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, -4, 0, -20, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 54, 0], 'euler11': [1, -18, 155, -846, 3276, -9306, 18755, -23958, 14641], 'euler13': [1, 0, 26, 0, 507, 0, 4394, 0, 28561], 'euler17': [1, 0, 2, 0, -285, 0, 578, 0, 83521], 'euler19': [1, -4, -26, -16, 1099, -304, -9386, -27436, 130321], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -46, 0, 1587, 0, -24334, 0, 279841], 'euler29': [1, 0, -58, 0, 2523, 0, -48778, 0, 707281], 'euler3': [1, 2, 1, 6, 9, 0, 0, 0, 0], 'euler31': [1, 0, 62, 0, 2883, 0, 59582, 0, 923521], 'euler37': [1, 0, -148, 0, 8214, 0, -202612, 0, 1874161], 'euler41': [1, -18, 185, -1386, 8676, -56826, 310985, -1240578, 2825761], 'euler43': [1, -10, 43, 290, -2900, 12470, 79507, -795070, 3418801], 'euler47': [1, 0, -94, 0, 6627, 0, -207646, 0, 4879681], 'euler5': [1, 0, -10, 0, 75, 0, -250, 0, 625], 'euler53': [1, 0, 212, 0, 16854, 0, 595508, 0, 7890481], 'euler59': [1, 18, 203, 1710, 11916, 100890, 706643, 3696822, 12117361], 'euler61': [1, 0, 122, 0, 11163, 0, 453962, 0, 13845841], 'euler67': [1, 14, 67, -70, -980, -4690, 300763, 4210682, 20151121], 'euler7': [1, 0, 14, 0, 147, 0, 686, 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, 158, 0, 18723, 0, 986078, 0, 38950081], 'euler83': [1, 0, 158, 0, 18075, 0, 1088462, 0, 47458321], 'euler89': [1, 0, -292, 0, 37158, 0, -2312932, 0, 62742241], 'euler97': [1, 10, 97, -1910, -19100, -185270, 912673, 9126730, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 1, 6, 9, 0, 0, 0, 0], [1, 0, -10, 0, 75, 0, -250, 0, 625], [1, 0, 14, 0, 147, 0, 686, 0, 2401], [1, -18, 155, -846, 3276, -9306, 18755, -23958, 14641], [1, 0, 26, 0, 507, 0, 4394, 0, 28561], [1, 0, 2, 0, -285, 0, 578, 0, 83521], [1, -4, -26, -16, 1099, -304, -9386, -27436, 130321], [1, 0, -46, 0, 1587, 0, -24334, 0, 279841], [1, 0, -58, 0, 2523, 0, -48778, 0, 707281], [1, 0, 62, 0, 2883, 0, 59582, 0, 923521], [1, 0, -148, 0, 8214, 0, -202612, 0, 1874161], [1, -18, 185, -1386, 8676, -56826, 310985, -1240578, 2825761], [1, -10, 43, 290, -2900, 12470, 79507, -795070, 3418801], [1, 0, -94, 0, 6627, 0, -207646, 0, 4879681], [1, 0, 212, 0, 16854, 0, 595508, 0, 7890481], [1, 18, 203, 1710, 11916, 100890, 706643, 3696822, 12117361], [1, 0, 122, 0, 11163, 0, 453962, 0, 13845841], [1, 14, 67, -70, -980, -4690, 300763, 4210682, 20151121], [1, 0, 284, 0, 30246, 0, 1431644, 0, 25411681], [1, 4, -134, 16, 16003, 1168, -714086, 1556068, 28398241], [1, 0, 158, 0, 18723, 0, 986078, 0, 38950081], [1, 0, 158, 0, 18075, 0, 1088462, 0, 47458321], [1, 0, -292, 0, 37158, 0, -2312932, 0, 62742241], [1, 10, 97, -1910, -19100, -185270, 912673, 9126730, 88529281]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/288/2/p/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': '8-288e4-1.1-c1e4-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0, 0, 0], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '8-288e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.5164734017492283, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 1355415585971985125, 'z1': {'__RealLiteral__': 0, 'data': '1.06162082961248363009660896400', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1345764281873055727741035081157,1579176236564341113054296139732,1836474459866294004823360549293,2722892229888797090383045991315', 'Lhash_array': ['1345764281873055727741035081157', '1579176236564341113054296139732', '1836474459866294004823360549293', '2722892229888797090383045991315'], 'factors': ['2-288-72.11-c1-0-0', '2-288-72.11-c1-0-2', '2-288-72.59-c1-0-3', '2-288-72.59-c1-0-7'], 'label': '8-288e4-1.1-c1e4-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/288/2/p/a'}