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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': -3, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '265599059385665792', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [-1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1433.6021777292601, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]], [229, [1, 1]]], 'bad_primes': [2, 7, 229], 'central_character': '179536.1', 'coefficient_field': '1.1.1.1', 'conductor': 179536, 'conductor_radical': 3206, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1, 3, 5], [1], [1, 6, 11], [1, 0, 13], [1, -5, 17], [1, 2, 19], [1, 8, 23], [1, -4, 29], [1, -3, 31], [1, 1, 37], [1, 0, 41], [1, -6, 43], [1, 8, 47], [1, -1, 53], [1, -12, 59], [1, -1, 61], [1, 7, 67], [1, 8, 71], [1, -10, 73], [1, 0, 79], [1, 0, 83], [1, 0, 89], [1, 18, 97]], 'gamma_factors': [[], [0]], 'index': 10, 'label': '2-179536-1.1-c1-0-10', 'leading_term': '0.710649217578', '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/179536/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.7106492175782111, 0.3770795765544876, -0.158857645614428, 0.2009445063051111, 2.085916647634669, 4.332511237460371, 4.378183386301871, 1.030077731954263, -3.265773991101926, -4.338122193169905, -1.223137038513042, 2.141497991476113, 1.706026957427744, -1.249063706159646, -1.962661262369299, 0.805854207487341, 3.041870299137853, 1.863136821469322, -0.1050918849424729, 0.503399242471055, 2.100698087349118, 1.425866878776473, -0.2774960206466262, 0.224331349675353, 1.511825903317861, -0.1572499363705384, -3.144951418381489, -2.456362058996288, 1.067340085636407, 1.775052705729082, -0.6489625536006794, -1.160828789223238, 0.4977486742640676, 0.1153632722609526, -0.3872167568818329, 4.949653791301178, 12.56644041791564, 11.81458717680954, 2.708427003975141, -3.239816029090627, -1.658886510510443, 0.2482613100458484, -0.9777685631996035, -0.902333978725185, 1.066865003962279, 0.7402260587043396, -0.9998948205463898, -0.5982492700746458, 0.004909494899843811, -1.182796606379179, -0.780152929485372, 0.9856799944796392, -1.395727673208635, -5.165077645795115, -1.430385394410423, 5.984394124351362, 5.151940178837725, -0.9241679130893174, 0.1038268206371171, 5.745995933350252, 4.941410886390146, 0.03980737768597834, -0.5320100969912921, 0.8553515254570369, -0.16490696859462, -0.414376321087497, 0.3329120176603958, -1.899093304129287, -3.51740895551258, 0.1302745381345077, 3.067535420693274, 0.8717493925310593, -0.3875359841009692, 0.7766697567534885, -1.436184684865611, -4.254400139829957, -1.853079845122169, 0.1633341528361895, -1.90761139891857, -0.06439995221505798, 5.567029647982118, 4.260842670550636, -1.320352708493298, -0.4485381149796786, 2.160157325858211, -0.9097512666929393, -1.828491805967021, 3.215952163780822, 4.250613685842862, -0.02715927757226764, -0.818615517096524, 0.8265541281071092, -0.2102593775846903, -0.8900555868711055, -0.004749833950843122, -0.03779345422742524, 1.321356198069704, 2.343029210049745, -2.882632448277536, -6.03535679250883, 2.981884303003016, 11.04316495575031, 5.452778776085957, -1.062548748608479, 0.4043091016982687, -0.7952556788733243, -5.348409496955561, -3.233983099548673, 0.7251119605593966, -0.9546763437263082, -1.907342000852482, 0.1190068293512811, -0.3160088218078446, -0.8197512325125437, 0.4268341866608718, -1.209066405752518, -2.318039596047282, 1.055777994859436, 1.271999337113935, -1.944057356115261, 0.2942317683042509], 'positive_zeros': ['0.4069228870173896', '0.6976149633839411', '1.805851667612700', '2.574555186642774', '3.144290304247787', '3.690377929915698', '4.474923465254447', '4.665640477017693', '5.441531577633858', '5.712819750480237', '6.237490959646675', '6.920474680274067', '7.434474311069760', '7.917273761410798', '8.268586166223245', '8.540083162134690', '9.578150647696745', '10.16278419966021', '10.34079650781623', '10.86114476699949', '11.34370838892705', '11.89919895489871', '12.00236267141282', '12.59095771769007', '12.91451573369406', '13.54454604383175', '14.20068765366920', '14.49510257020865', '15.25293721001151', '15.57326266021746', '15.97143670113954', '16.34178498033079', '16.57666654562434', '17.24334747359860', '17.83451228171035', '18.07952875011175', '18.39676421264667', '19.15556036956549', '19.28735343754531', '19.75299542902935'], 'prelabel': '2-179536-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 37.86293936990709, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 265599059385665792, 'z1': {'__RealLiteral__': 0, 'data': '0.4069228870173896', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.6976149633839411', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.805851667612700', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1433.6021777292601, 'bad_primes': [2, 7, 229], 'central_character': '1.1', 'conductor': 179536, 'conductor_radical': 3206, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, -3, 0, 0, 0, 1, 0, -6, 0, 0, 0, 6, 0, 5, 0, -2, 0, 0, 0, -8, 0, 4, 0, 4, 0, 4, 0, 3, 0, 12, 0, 0, 0, -1, 0, 0, 0, 0, 0, 6, 0, -3, 0, -8, 0, 0, 0, -10, 0, 1, 0, 18, 0, 4, 0, 12, 0, 1, 0, 0, 0, 0, 0, -7, 0, 16, 0, -8, 0, 10, 0, -8, 0, 0, 0, 0, 0, -11, 0, 0, 0, -15, 0, -8, 0, 0, 0, 0, 0, -6, 0, 6, 0, -18, 0, -6, 0], 'euler11': [1, 6, 11], 'euler13': [1, 0, 13], 'euler17': [1, -5, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -4, 29], 'euler3': [1, 2, 3], 'euler31': [1, -3, 31], 'euler37': [1, 1, 37], 'euler41': [1, 0, 41], 'euler43': [1, -6, 43], 'euler47': [1, 8, 47], 'euler5': [1, 3, 5], 'euler53': [1, -1, 53], 'euler59': [1, -12, 59], 'euler61': [1, -1, 61], 'euler67': [1, 7, 67], 'euler7': [1, 0, 0], 'euler71': [1, 8, 71], 'euler73': [1, -10, 73], 'euler79': [1, 0, 79], 'euler83': [1, 0, 83], 'euler89': [1, 0, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 3, 5], [1, 0, 0], [1, 6, 11], [1, 0, 13], [1, -5, 17], [1, 2, 19], [1, 8, 23], [1, -4, 29], [1, -3, 31], [1, 1, 37], [1, 0, 41], [1, -6, 43], [1, 8, 47], [1, -1, 53], [1, -12, 59], [1, -1, 61], [1, 7, 67], [1, 8, 71], [1, -10, 73], [1, 0, 79], [1, 0, 83], [1, 0, 89], [1, 18, 97]], 'index': 10, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/179536/e'], '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': '2-179536-1.1-c1-0-10', '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': '2-179536-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 37.86293936990709, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 265599059385665792, 'z1': {'__RealLiteral__': 0, 'data': '0.4069228870173896', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '265599059385665792', 'Lhash_array': ['265599059385665792'], 'factors': ['2-179536-1.1-c1-0-10'], 'label': '2-179536-1.1-c1-0-10', 'type': 'ECQ', 'url': 'EllipticCurve/Q/179536/e'}