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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '330889636256594934', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 124.56662715319746, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '15600.1', 'coefficient_field': '1.1.1.1', 'conductor': 15600, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, 4, 7], [1, 4, 11], [1, 1], [1, -4, 17], [1, 7, 19], [1, -4, 23], [1, -5, 29], [1, 4, 31], [1, 9, 37], [1, 5, 41], [1, 10, 43], [1, -3, 47], [1, 9, 53], [1, -6, 59], [1, -4, 61], [1, 7, 67], [1, -15, 71], [1, 12, 73], [1, 7, 79], [1, -6, 83], [1, -14, 89], [1, -16, 97]], 'gamma_factors': [[], [0]], 'index': 2, 'label': '2-15600-1.1-c1-0-2', 'leading_term': '1.08272395338', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/15600/bo', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.082723953383503, 0.6733621962947455, -0.4805848275456228, -2.047227126353262, -3.337642564395075, -3.554479513283623, -2.356139635803459, -0.2916538040183687, 1.400298920141197, 1.675697455669883, 0.5968862786498924, -0.6417850844575897, -0.8152424288420931, 0.03891094543745878, 0.5348458655113582, -0.5841258908005886, -2.81542672768504, -4.05405909675919, -2.755847399404436, 0.09760633938849907, 1.679572271929269, 0.3125485675401201, -2.488846032522579, -3.543126001791373, -1.631165822861016, 1.050464334453762, 1.567066095864434, -0.1184251869624619, -1.19470419297723, 0.1994318736544404, 2.39741658764684, 2.422804233384219, 0.1167977050255081, -1.553357167974747, -0.6011164797166086, 1.184779045331973, 0.8519767410661928, -1.367963023755059, -2.385070419900845, -0.87399467013206, 0.7899579148195198, 0.4302465868825912, -0.1603321659676964, 2.104535129659261, 6.055103035275014, 6.695757456574552, 2.025114362655622, -3.518995419874443, -4.580560572596379, -1.724845762511593, 0.2336447277527276, -0.5381800503429699, -1.225484819921593, -0.1064720525717403, 0.3191713971148887, -1.959347390946418, -4.200137610268516, -2.897187387812998, 0.2804182164439831, 0.8162541167656507, -1.497999415348172, -2.475085950274821, -0.6922827607958226, 0.3452538772061311, -1.266478839456926, -2.215928051643252, -0.01223881928460223, 1.939737593811, -0.03955948128039302, -2.766589814511739, -0.6267880992676008, 4.900378896657365, 6.80344146474321, 3.203241750101186, -0.3456711432744098, -0.1496565089209015, 0.8707642612178721, 0.02171295210652536, -0.2652218791813274, 1.848972718469928, 3.015101614183759, 0.66019950246497, -1.664575902481744, -0.3405199983565115, 1.666842753034745, 0.3174489579926018, -1.791387103454455, -0.2969351041077626, 2.2147699632222, 0.4301224867156266, -3.705328843699351, -3.949392680966175, -0.6625677724070836, 0.4664989306056099, -0.7242639416699066, 0.8287271830058559, 4.54490263992452, 3.992185695022408, -1.394639474457828, -4.495977427939046, -2.283458370514621, 0.2528126143994473, 0.009784898598680683, -0.05148886789319496, 1.131036940743598, 0.3178782050668823, -2.108909729536565, -1.589184523377456, 1.129900400923768, 0.1661350617830869, -3.941444808874515, -3.880363763911109, 1.147694897160645, 3.476740304788675, 0.6862421642521827, -0.8666415483273886, 1.227796246911878, 1.657081645985871, -1.001457555650132, -1.549249753161507, 0.3962971255408914], 'positive_zeros': ['0.4114706710331682', '1.785166696074903', '2.606746320426566', '3.239965473671610', '3.663583571312512', '4.741060638988591', '5.279210826590815', '6.140133890903392', '6.734735931882752', '7.228202414086625', '8.011452938240019', '8.574395657733950', '9.104165128621246', '9.854984586922741', '10.35273739415126', '10.54672474138258', '11.58095445718065', '12.43141565960364', '12.64329937314357', '13.26960679916003', '13.55917652491025', '14.47305602126669', '14.85305539108820', '15.59298901444096', '15.83702996379411', '16.50101635600457', '16.99712742480746', '17.53081603340878', '18.45767850250692', '18.77602466350092', '19.25443910926326', '19.54887112545415'], 'prelabel': '2-15600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.160942036996584, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 330889636256594934, 'z1': {'__RealLiteral__': 0, 'data': '0.4114706710331682', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.785166696074903', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.606746320426566', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 124.56662715319746, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 15600, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -4, 0, 1, 0, -4, 0, -1, 0, 0, 0, 4, 0, -7, 0, -4, 0, 4, 0, 0, 0, 1, 0, 5, 0, -4, 0, -4, 0, 0, 0, -9, 0, -1, 0, -5, 0, -10, 0, 0, 0, 3, 0, 9, 0, 4, 0, -9, 0, 0, 0, -7, 0, 6, 0, 4, 0, -4, 0, 0, 0, -7, 0, 4, 0, 15, 0, -12, 0, 0, 0, 16, 0, -7, 0, 1, 0, 6, 0, 0, 0, 5, 0, 14, 0, 4, 0, -4, 0, 0, 0, 16, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 1, 0], 'euler17': [1, -4, 17], 'euler19': [1, 7, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -5, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 9, 37], 'euler41': [1, 5, 41], 'euler43': [1, 10, 43], 'euler47': [1, -3, 47], 'euler5': [1, 0, 0], 'euler53': [1, 9, 53], 'euler59': [1, -6, 59], 'euler61': [1, -4, 61], 'euler67': [1, 7, 67], 'euler7': [1, 4, 7], 'euler71': [1, -15, 71], 'euler73': [1, 12, 73], 'euler79': [1, 7, 79], 'euler83': [1, -6, 83], 'euler89': [1, -14, 89], 'euler97': [1, -16, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 4, 7], [1, 4, 11], [1, 1, 0], [1, -4, 17], [1, 7, 19], [1, -4, 23], [1, -5, 29], [1, 4, 31], [1, 9, 37], [1, 5, 41], [1, 10, 43], [1, -3, 47], [1, 9, 53], [1, -6, 59], [1, -4, 61], [1, 7, 67], [1, -15, 71], [1, 12, 73], [1, 7, 79], [1, -6, 83], [1, -14, 89], [1, -16, 97]], 'index': 2, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/15600/bo'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-15600-1.1-c1-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-15600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.160942036996584, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 330889636256594934, 'z1': {'__RealLiteral__': 0, 'data': '0.4114706710331682', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '330889636256594934', 'Lhash_array': ['330889636256594934'], 'label': '2-15600-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/15600/bo'}