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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '929968170480682715001578937301', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.894427190999916, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.381007527240165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 3]], [5, [1, -2, 1]]], 'bad_primes': [2, 3, 5], 'central_character': '460800.1', 'coefficient_field': '1.1.1.1', 'conductor': 460800, 'conductor_radical': 30, 'degree': 4, 'euler_factors': [[1], [1, 0, 3], [1, -2, 1], [1, 0, -2, 0, 49], [1, 0, 22, 0, 121], [1, 0, -26, 0, 169], [1, 0, -18, 0, 289], [1, 0, 22, 0, 361], [1, 0, 30, 0, 529], [1, 4, 62, 116, 841], [1, 0, 46, 0, 961], [1, 0, -10, 0, 1369], [1, 0, -82, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, -50, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, 54, 0, 3481], [1, 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1.689246337994917, 1.1654230626954505, 0.4748133084098189], 'positive_zeros': ['0.73361553279211959590738050197367', '1.85002262761065550940770768931454', '2.36109081293852701197155332036369', '2.98552164392524700166139297507348', '3.61563115039431469539014078391194', '4.17961073870792015197438446766158', '4.94897715264491245217176175610699', '5.37857675108188839245052886761144', '5.69666490725776974011178109689094', '6.24493166094866962383206803304526', '6.62939534411560437700705962812131', '7.17756370139367675925186485216878', '7.66923221369575147422434947665970', '8.232094164874916399482119953312594', '8.553763350172173214830647596267999'], 'prelabel': '4-460800-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3281806270075056, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1869363933105850462, 'z1': {'__RealLiteral__': 0, 'data': '0.73361553279211959590738050197367', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.85002262761065550940770768931454', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.36109081293852701197155332036369', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.381007527240165, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 460800, 'conductor_radical': 30, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 2, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, 0, 22, 0, 121], 'euler13': [1, 0, -26, 0, 169], 'euler17': [1, 0, -18, 0, 289], 'euler19': [1, 0, 22, 0, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, 30, 0, 529], 'euler29': [1, 4, 62, 116, 841], 'euler3': [1, 0, 3, 0, 0], 'euler31': [1, 0, 46, 0, 961], 'euler37': [1, 0, -10, 0, 1369], 'euler41': [1, 0, -82, 0, 1681], 'euler43': [1, 0, 22, 0, 1849], 'euler47': [1, 0, -50, 0, 2209], 'euler5': [1, -2, 1, 0, 0], 'euler53': [1, -12, 142, -636, 2809], 'euler59': [1, 0, 54, 0, 3481], 'euler61': [1, 0, -106, 0, 3721], 'euler67': [1, 0, 134, 0, 4489], 'euler7': [1, 0, -2, 0, 49], 'euler71': [1, 0, 78, 0, 5041], 'euler73': [1, -20, 246, -1460, 5329], 'euler79': [1, 0, 142, 0, 6241], 'euler83': [1, 0, 102, 0, 6889], 'euler89': [1, 0, -114, 0, 7921], 'euler97': [1, -4, 198, -388, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 3, 0, 0], [1, -2, 1, 0, 0], [1, 0, -2, 0, 49], [1, 0, 22, 0, 121], [1, 0, -26, 0, 169], [1, 0, -18, 0, 289], [1, 0, 22, 0, 361], [1, 0, 30, 0, 529], [1, 4, 62, 116, 841], [1, 0, 46, 0, 961], [1, 0, -10, 0, 1369], [1, 0, -82, 0, 1681], [1, 0, 22, 0, 1849], [1, 0, -50, 0, 2209], [1, -12, 142, -636, 2809], [1, 0, 54, 0, 3481], [1, 0, -106, 0, 3721], [1, 0, 134, 0, 4489], [1, 0, 78, 0, 5041], [1, -20, 246, -1460, 5329], [1, 0, 142, 0, 6241], [1, 0, 102, 0, 6889], [1, 0, -114, 0, 7921], [1, -4, 198, -388, 9409]], 'index': 12, 'instance_types': ['ECNF', 'HMF', 'ECNF', 'HMF'], 'instance_urls': ['EllipticCurve/2.2.24.1/800.1/l', 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-800.1-e', 'EllipticCurve/2.2.24.1/800.1/e', 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-800.1-l'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': True, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': True, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-460800-1.1-c1e2-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-460800-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.3281806270075056, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1869363933105850462, 'z1': {'__RealLiteral__': 0, 'data': '0.73361553279211959590738050197367', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9515093
{'Lhash': '929968170480682715001578937301', 'Lhash_array': ['929968170480682715001578937301'], 'label': '4-460800-1.1-c1e2-0-12', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-800.1-l'}
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id: 9515047
{'Lhash': '929968170480682715001578937301', 'Lhash_array': ['929968170480682715001578937301'], 'label': '4-460800-1.1-c1e2-0-12', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/800.1/e'}
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id: 9514858
{'Lhash': '929968170480682715001578937301', 'Lhash_array': ['929968170480682715001578937301'], 'label': '4-460800-1.1-c1e2-0-12', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.24.1/holomorphic/2.2.24.1-800.1-e'}
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id: 9514759
{'Lhash': '929968170480682715001578937301', 'Lhash_array': ['929968170480682715001578937301'], 'label': '4-460800-1.1-c1e2-0-12', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.24.1/800.1/l'}