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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': 1, 'A3': 1, 'A4': 1, 'A5': 1, 'A6': 1, 'A7': -1, 'A8': 1, 'A9': 1, 'Lhash': '1054123320429876504', 'a10': [0.31622776601683794, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.4082482904638631, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 283.3890767735242, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, -1]], [5, [1, -1]], [7, [1, 1]], [13, [1]]], 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '35490.1', 'coefficient_field': '1.1.1.1', 'conductor': 35490, 'conductor_radical': 2730, 'degree': 2, 'euler_factors': [[1, -1], [1, -1], [1, -1], [1, 1], [1, -5, 11], [1], [1, -3, 17], [1, -3, 19], [1, 2, 23], [1, -3, 29], [1, 2, 31], [1, -6, 37], [1, 11, 41], [1, 2, 43], [1, 11, 47], [1, -9, 53], [1, -2, 59], [1, -7, 61], [1, -2, 67], [1, -12, 71], [1, -16, 73], [1, 5, 79], [1, 0, 83], [1, -11, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 47, 'label': '2-35490-1.1-c1-0-47', 'leading_term': '6.72152970007', '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/35490/dq', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [6.721529700065466, 6.007232858238579, 3.996740356487901, 1.282713656901632, -0.9746137785664946, -1.634001961977083, -0.5526292517415069, 1.054126483943618, 1.527730585706884, 0.3271435774684683, -1.352043903115484, -1.788079859417972, -0.6475496972196157, 0.6168467417441651, 0.565544266647495, -0.3240487481546704, -0.218612258030936, 1.492415066678092, 3.010172204905529, 2.32009216583662, 0.1213169480228136, -0.7296244302985969, 0.9957311131147882, 3.022348908133961, 2.616377220875669, 0.4933345809445717, -0.266289183726528, 0.9732096789665018, 1.193052848796098, -1.490218713896845, -4.1794996729254, -3.01171047382333, 0.685635907999975, 1.681924519603784, -1.496664965275954, -4.118020603043393, -2.29479187365872, 1.182141305890355, 1.546507596604617, -0.2285081138627341, 0.5330663924508484, 3.651062004519545, 3.618065812319298, -1.263708922865714, -5.218908554433473, -3.510556273519645, 0.4989379683604823, 1.213969574837367, -0.4770559463450241, 0.01602280717778256, 2.488532068055695, 2.755148170658786, 0.4883682492561864, -0.4295937750737557, 0.9038442857851618, 1.329221085634334, 0.05492112000851637, -0.212821180087044, 0.7829344542154548, 0.3292423745077079, -0.9901736560396069, 0.4397806910877228, 3.617008664881184, 3.30313207827208, -0.4106705651360183, -1.523121450258967, 0.8676445877906013, 0.7397904672534596, -2.749680395162845, -2.389690708827761, 3.359464420114384, 5.556365951307897, -0.03583998833893898, -4.816766437273229, -2.09203331951137, 1.726152394789562, -0.5098391095474766, -4.335316140271065, -3.271427816954558, -0.2886906017576564, -0.114990522578227, -0.006823404863318823, 2.818282550024105, 4.201325242595236, 1.481381651196005, -0.7337330346303813, 0.2843464474342628, 0.5996013445473886, -1.213227532749962, -1.102674110717993, 1.008377825151005, 0.5909850265388669, -1.171649257433293, 1.00120352323622, 4.886239467903976, 3.982233256582927, 0.2096882953512209, 0.007452375938053763, 1.855814275828983, 0.7622783063400178, -1.07458879748978, -0.2024453600220407, 0.1897283238022945, -1.286325203251886, 0.4508726638099931, 4.82866270581563, 3.718565101863171, -2.190289089254296, -3.035113894742177, 0.596152059638184, -1.530029042992269, -7.748971029410786, -6.764096533169752, -0.3501350988065684, -0.005068320132165356, -4.459199194548003, -3.699065668901185, 0.790471196371897, 1.08686988379256, -0.7991932127403497, 0.3961940378074218], 'positive_zeros': ['0.8764581841918619', '1.581519789825330', '2.295735426985873', '3.108638113580931', '3.654657929120107', '4.045892967356836', '5.015520038672589', '5.390104399680085', '6.326370160312184', '6.577650869711188', '7.136977807881607', '7.950089811244893', '8.404049163098924', '9.152204455102263', '9.708071438278064', '9.940627115389212', '10.69499845574523', '11.46101306101652', '11.92176179722954', '12.24808084648292', '13.06192448067886', '13.35365447315993', '14.01156564545816', '14.30876322460861', '14.80282683634466', '15.21208239636349', '15.97097863009258', '16.41438818428069', '16.81000926736132', '17.36512338309085', '17.99875264478520', '18.60493075790664', '18.97124807693062', '19.80233993314406', '19.96162369190409'], 'prelabel': '2-35490-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.834163976079246, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1054123320429876504, 'z1': {'__RealLiteral__': 0, 'data': '0.8764581841918619', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.581519789825330', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.295735426985873', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 283.3890767735242, 'bad_primes': [2, 3, 5, 7, 13], 'central_character': '1.1', 'conductor': 35490, 'conductor_radical': 2730, 'degree': 2, 'dirichlet_coefficients': [1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 5, 1, 0, -1, 1, 1, 3, 1, 3, 1, -1, 5, -2, 1, 1, 0, 1, -1, 3, 1, -2, 1, 5, 3, -1, 1, 6, 3, 0, 1, -11, -1, -2, 5, 1, -2, -11, 1, 1, 1, 3, 0, 9, 1, 5, -1, 3, 3, 2, 1, 7, -2, -1, 1, 0, 5, 2, 3, -2, -1, 12, 1, 16, 6, 1, 3, -5, 0, -5, 1, 1, -11, 0, -1, 3, -2, 3, 5, 11, 1, 0, -2, -2, -11, 3, 1, 14, 1, 5, 1], 'euler11': [1, -5, 11], 'euler13': [1, 0, 0], 'euler17': [1, -3, 17], 'euler19': [1, -3, 19], 'euler2': [1, -1, 0], 'euler23': [1, 2, 23], 'euler29': [1, -3, 29], 'euler3': [1, -1, 0], 'euler31': [1, 2, 31], 'euler37': [1, -6, 37], 'euler41': [1, 11, 41], 'euler43': [1, 2, 43], 'euler47': [1, 11, 47], 'euler5': [1, -1, 0], 'euler53': [1, -9, 53], 'euler59': [1, -2, 59], 'euler61': [1, -7, 61], 'euler67': [1, -2, 67], 'euler7': [1, 1, 0], 'euler71': [1, -12, 71], 'euler73': [1, -16, 73], 'euler79': [1, 5, 79], 'euler83': [1, 0, 83], 'euler89': [1, -11, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, -1, 0], [1, -1, 0], [1, -1, 0], [1, 1, 0], [1, -5, 11], [1, 0, 0], [1, -3, 17], [1, -3, 19], [1, 2, 23], [1, -3, 29], [1, 2, 31], [1, -6, 37], [1, 11, 41], [1, 2, 43], [1, 11, 47], [1, -9, 53], [1, -2, 59], [1, -7, 61], [1, -2, 67], [1, -12, 71], [1, -16, 73], [1, 5, 79], [1, 0, 83], [1, -11, 89], [1, -14, 97]], 'index': 47, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/35490/dq'], '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': '2-35490-1.1-c1-0-47', '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': '2-35490-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.834163976079246, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1054123320429876504, 'z1': {'__RealLiteral__': 0, 'data': '0.8764581841918619', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1054123320429876504', 'Lhash_array': ['1054123320429876504'], 'label': '2-35490-1.1-c1-0-47', 'type': 'ECQ', 'url': 'EllipticCurve/Q/35490/dq'}