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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '930790114562502611810999183124', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792515, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16.38966710909192, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 2, 3]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '257049.1', 'coefficient_field': '1.1.1.1', 'conductor': 257049, 'conductor_radical': 39, 'degree': 4, 'euler_factors': [[1, 0, -1, 0, 4], [1, 2, 3], [1, 0, 2, 0, 25], [1, 0, -4, 0, 49], [1, 0, -22, 0, 121], [1], [1, -6, 34, -102, 289], [1, 0, -16, 0, 361], [1, -6, 46, -138, 529], [1, 0, 22, 0, 841], [1, 0, 44, 0, 961], [1, 0, -34, 0, 1369], [1, 0, 62, 0, 1681], [1, -14, 126, -602, 1849], [1, 0, 62, 0, 2209], [1, 18, 178, 954, 2809], [1, 0, 38, 0, 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-5.293505453208823, -6.004300628938224, -6.188707873422222, -5.784892262484611, -4.806327999830904, -3.3429270724683477], 'positive_zeros': ['0.73426393234454509309693687055524', '1.64706713671509607318053571788291', '2.66425180231818102315444142037930', '3.12951718765850005954972981452795', '3.95291048716905267129276524078175', '4.63514044980194004917391793963538', '5.05490617752337781949443792468705', '5.68088478474610308995663356944320', '5.95303991829253836051682144011571', '6.48478974329924352959280020551070', '7.01073579549101950820309060680036', '7.39002474056279655909055763247335', '7.86681440859899557940278830496829', '8.436528347276759765453416330773489', '8.980886673486165546826452260551749'], 'prelabel': '4-507e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1e2-0', 'st_group': 'SU(2)', 'symmetry_type': 'symplectic', 'trace_hash': 1147721762199811106, 'z1': {'__RealLiteral__': 0, 'data': '0.73426393234454509309693687055524', 'prec': 113}, 'z2': {'__RealLiteral__': 0, 'data': '1.64706713671509607318053571788291', 'prec': 113}, 'z3': {'__RealLiteral__': 0, 'data': '2.66425180231818102315444142037930', 'prec': 113}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16.38966710909192, 'bad_primes': [3, 13], 'central_character': '1.1', 'conductor': 257049, 'conductor_radical': 39, 'degree': 4, 'dirichlet_coefficients': [1, 0, -2, 1, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 6, 0, -2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 6, 4, 0, -12, 0, -18, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -7, 0, 0, 0, 6, -12, 0, 0, 0, 0, 0, 4, 0, 0, 0, -2, 0, -11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -2], 'euler11': [1, 0, -22, 0, 121], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, -6, 34, -102, 289], 'euler19': [1, 0, -16, 0, 361], 'euler2': [1, 0, -1, 0, 4], 'euler23': [1, -6, 46, -138, 529], 'euler29': [1, 0, 22, 0, 841], 'euler3': [1, 2, 3, 0, 0], 'euler31': [1, 0, 44, 0, 961], 'euler37': [1, 0, -34, 0, 1369], 'euler41': [1, 0, 62, 0, 1681], 'euler43': [1, -14, 126, -602, 1849], 'euler47': [1, 0, 62, 0, 2209], 'euler5': [1, 0, 2, 0, 25], 'euler53': [1, 18, 178, 954, 2809], 'euler59': [1, 0, 38, 0, 3481], 'euler61': [1, -4, 90, -244, 3721], 'euler67': [1, 0, 80, 0, 4489], 'euler7': [1, 0, -4, 0, 49], 'euler71': [1, 0, -94, 0, 5041], 'euler73': [1, 0, 110, 0, 5329], 'euler79': [1, 2, 78, 158, 6241], 'euler83': [1, 0, -46, 0, 6889], 'euler89': [1, 0, 122, 0, 7921], 'euler97': [1, 0, 158, 0, 9409], 'euler_factors': [[1, 0, -1, 0, 4], [1, 2, 3, 0, 0], [1, 0, 2, 0, 25], [1, 0, -4, 0, 49], [1, 0, -22, 0, 121], [1, 0, 0, 0, 0], [1, -6, 34, -102, 289], [1, 0, -16, 0, 361], [1, -6, 46, -138, 529], [1, 0, 22, 0, 841], [1, 0, 44, 0, 961], [1, 0, -34, 0, 1369], [1, 0, 62, 0, 1681], [1, -14, 126, -602, 1849], [1, 0, 62, 0, 2209], [1, 18, 178, 954, 2809], [1, 0, 38, 0, 3481], [1, -4, 90, -244, 3721], [1, 0, 80, 0, 4489], [1, 0, -94, 0, 5041], [1, 0, 110, 0, 5329], [1, 2, 78, 158, 6241], [1, 0, -46, 0, 6889], [1, 0, 122, 0, 7921], [1, 0, 158, 0, 9409]], 'index': 3, 'instance_types': ['HMF', 'ECNF', 'HMF', 'ECNF'], 'instance_urls': ['ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-1521.2-g', 'EllipticCurve/2.2.13.1/1521.3/g', 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-1521.3-g', 'EllipticCurve/2.2.13.1/1521.2/g'], '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': '4-507e2-1.1-c1e2-0-3', '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': '4-507e2-1.1-c1e2-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 2.0120674398436345, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1147721762199811106, 'z1': {'__RealLiteral__': 0, 'data': '0.73426393234454509309693687055524', 'prec': 113}}
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lfunc_instances • Show schema
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id: 9522835
{'Lhash': '930790114562502611810999183124', 'Lhash_array': ['930790114562502611810999183124'], 'label': '4-507e2-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/1521.2/g'}
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id: 9522156
{'Lhash': '930790114562502611810999183124', 'Lhash_array': ['930790114562502611810999183124'], 'label': '4-507e2-1.1-c1e2-0-3', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-1521.3-g'}
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id: 9522154
{'Lhash': '930790114562502611810999183124', 'Lhash_array': ['930790114562502611810999183124'], 'label': '4-507e2-1.1-c1e2-0-3', 'type': 'ECNF', 'url': 'EllipticCurve/2.2.13.1/1521.3/g'}
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id: 9522142
{'Lhash': '930790114562502611810999183124', 'Lhash_array': ['930790114562502611810999183124'], 'label': '4-507e2-1.1-c1e2-0-3', 'type': 'HMF', 'url': 'ModularForm/GL2/TotallyReal/2.2.13.1/holomorphic/2.2.13.1-1521.2-g'}