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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 1, 'Lhash': '1538239948439331116', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1694.1061292834854, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [13, [1, 1]], [17, [1, 1]]], 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '212160.1', 'coefficient_field': '1.1.1.1', 'conductor': 212160, 'conductor_radical': 6630, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, 2, 7], [1, 0, 11], [1, 1], [1, 1], [1, 4, 19], [1, 0, 23], [1, 6, 29], [1, 10, 31], [1, -4, 37], [1, 2, 41], [1, 4, 43], [1, 6, 47], [1, -6, 53], [1, -6, 59], [1, 6, 61], [1, -8, 67], [1, -12, 71], [1, 16, 73], [1, -8, 79], [1, 14, 83], [1, 16, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 40, 'label': '2-212160-1.1-c1-0-40', 'leading_term': '3.1246445924', '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': 1, 'origin': 'EllipticCurve/Q/212160/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.5668424603066547, 0.03093263356069453, -1.757119856088287, -3.408918694802229, -3.008506359804945, -0.488430512417561, 1.520776263890536, 0.4678765291103619, -2.50548153331883, -3.396787282681741, -0.6070455324858678, 2.461683447059251, 1.98610861632929, -0.7077608809411485, -1.330331181370573, 0.4348874534057449, 0.5591894831908851, -2.154549259396256, -3.611894988170807, -1.482242466781564, 0.4674680905412742, -1.033734596808216, -2.858098040158819, -1.337663144492718, 0.8421129126084431, -0.07912448756857049, -1.578768801926004, -0.1023853659873971, 1.352345731634151, -0.7276728645620032, -2.24012224405236, 1.119633236066322, 4.38726355829336, 1.841430658172707, -1.830506766885431, -0.2905599960094264, 2.354823512338861, 0.2274802993553185, -2.550347076366625, -0.8889146874676279, 0.7254212505328916, -1.822946028439525, -3.499669942923825, -1.111203153699616, 0.2866776561435232, -0.8239305457708701, 0.6653030756480396, 3.963833628703475, 3.139303684570798, 0.04513791589056426, -0.03408874431664493, 0.06521279210157906, -2.069988707150646, -0.1611955426244178, 6.360717354120532, 7.074378388336168, 0.6097697085724024, -1.789698477607383, 1.499090847229222, 1.388738518605626, -1.379138192845288, 0.152065549877932, 2.322975317661257, -0.05749152063635809, -1.717195532469209, 0.1419958600524065, 0.3597294128689322, -0.05613445483820553, 3.164919424660601, 4.414989962788125, -0.2796388942993882, -2.794586759291482, -0.2759379430550151, -0.3852270557446396, -2.303888294715875, 0.4363167196774626, 2.962128747388029, 0.4739828636644829, -0.2572510196643416, 1.490809284744939, -1.805153394802911, -5.377847759519719, -1.139966379039178, 2.411306442559151, -1.60656628270956, -3.54552718801671, 0.1020109099433589, 0.8094815687249441, -0.5913393507829513, 1.368642145547365, 2.018213389704866, -0.240815535052417, 0.5359075464605719, 1.761010004655659, -0.7159874509631129, -0.9208461485383109, 0.9497089325887623, -2.508200267598962, -5.349544254551866, -0.5586570642041614, 1.88216727980209, -2.027358978014526, -1.581508970882724, 1.795203000049342, -0.4270808441099605, -1.374554306947431, 3.223062924112164, 3.476847137438745, -0.2151860457193793, 0.5840401811223727, 1.44072188592726, -0.783909236919004, 0.7581652657990506, 3.228346090793887, 0.5179393960607596, -0.8936743714432303, 0.8204355466105274, -0.6250430355469618, -0.9088185581504596, 2.591560053806744], 'positive_zeros': ['0.5060396014699739', '1.543929070796321', '2.042569546712105', '2.790107728297388', '3.430122155360985', '3.940535932614739', '4.317236848609114', '5.143586235503054', '5.387687649821239', '6.123941974382743', '6.490513211020171', '7.010521010585127', '7.438885908415779', '7.940206332612462', '8.599443504256487', '9.020265745836946', '9.514790944648676', '10.07991054514978', '10.35796576899188', '11.11750867808000', '11.32848524561632', '11.69618699073246', '12.50608119140027', '12.75808801751058', '13.01046464976294', '13.50728785985738', '14.27564734344506', '14.64318344903008', '15.10790880821674', '15.48853373238214', '15.99572851203576', '16.48141082589675', '16.82539401539069', '17.00944392563289', '17.73700416182702', '18.28309829048584', '18.45343270971659', '18.97455286047672', '19.54333495942447', '19.78304148021322'], 'prelabel': '2-212160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.159520518143616, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1538239948439331116, 'z1': {'__RealLiteral__': 0, 'data': '0.5060396014699739', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.543929070796321', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.042569546712105', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1694.1061292834854, 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '1.1', 'conductor': 212160, 'conductor_radical': 6630, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -2, 0, 1, 0, 0, 0, -1, 0, 1, 0, -1, 0, -4, 0, 2, 0, 0, 0, 1, 0, -1, 0, -6, 0, -10, 0, 0, 0, 2, 0, 4, 0, 1, 0, -2, 0, -4, 0, -1, 0, -6, 0, -3, 0, 1, 0, 6, 0, 0, 0, 4, 0, 6, 0, -6, 0, -2, 0, 1, 0, 8, 0, 0, 0, 12, 0, -16, 0, -1, 0, 0, 0, 8, 0, 1, 0, -14, 0, 1, 0, 6, 0, -16, 0, 2, 0, 10, 0, 4, 0, 12, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 10, 31], 'euler37': [1, -4, 37], 'euler41': [1, 2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 6, 47], 'euler5': [1, 1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -6, 59], 'euler61': [1, 6, 61], 'euler67': [1, -8, 67], 'euler7': [1, 2, 7], 'euler71': [1, -12, 71], 'euler73': [1, 16, 73], 'euler79': [1, -8, 79], 'euler83': [1, 14, 83], 'euler89': [1, 16, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 2, 7], [1, 0, 11], [1, 1, 0], [1, 1, 0], [1, 4, 19], [1, 0, 23], [1, 6, 29], [1, 10, 31], [1, -4, 37], [1, 2, 41], [1, 4, 43], [1, 6, 47], [1, -6, 53], [1, -6, 59], [1, 6, 61], [1, -8, 67], [1, -12, 71], [1, 16, 73], [1, -8, 79], [1, 14, 83], [1, 16, 89], [1, -12, 97]], 'index': 40, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/212160/m'], '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': '2-212160-1.1-c1-0-40', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-212160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.159520518143616, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1538239948439331116, 'z1': {'__RealLiteral__': 0, 'data': '0.5060396014699739', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1538239948439331116', 'Lhash_array': ['1538239948439331116'], 'label': '2-212160-1.1-c1-0-40', 'type': 'ECQ', 'url': 'EllipticCurve/Q/212160/m'}