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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': '1144105918009302996', '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': 3117.2798445087665, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, -1]], [5, [1, -1]], [7, [1, 1]], [11, [1, -1]], [13, [1]]], 'bad_primes': [2, 3, 5, 7, 11, 13], 'central_character': '390390.1', 'coefficient_field': '1.1.1.1', 'conductor': 390390, 'conductor_radical': 30030, 'degree': 2, 'euler_factors': [[1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1], [1, -6, 17], [1, -4, 19], [1, 0, 23], [1, -6, 29], [1, 8, 31], [1, -10, 37], [1, -6, 41], [1, -8, 43], [1, 0, 47], [1, -6, 53], [1, 12, 59], [1, -2, 61], [1, -4, 67], [1, 12, 71], [1, -10, 73], [1, 4, 79], [1, -12, 83], [1, 6, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 62, 'label': '2-390390-1.1-c1-0-62', 'leading_term': '3.96945459055', '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/390390/ce', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.969454590548411, 3.053533203014412, 1.012090196710056, -0.4413548692230475, -0.1117601110545936, 1.044868022089372, 0.8114217484775091, -1.118328397612995, -2.217925035085945, -0.7775350992918444, 1.044421295250175, 0.4232189119769494, -1.147008598264237, -0.1771772162962903, 1.994964185187628, 0.5386711570898959, -3.629196506166854, -3.313598340745475, 2.864103062618539, 6.129415973745382, 1.159492627538974, -4.630209083304476, -3.418520534689341, 0.32980172835615, -0.519993093285115, -2.55977547348883, 0.1475467893985132, 3.75393239562468, 2.455941608448446, -0.3236822269769613, 0.1339176183032831, 0.6750361914174234, -1.270131579511175, -1.498090580495887, 1.207082372211708, 1.816303495436713, -0.2378349870509121, -0.5637532660935167, 0.2153652579637889, -0.5744253990663171, -0.1866338726117941, 2.136374514309015, 1.440741142686662, -0.8795501179364874, 1.818248736630005, 5.427503550596473, 1.811994548102745, -2.806658377072363, -0.07346183399296784, 2.679321000650761, -0.4993327854803492, -0.91462127198003, 3.366667079004264, 1.831491567311151, -3.97000637116176, -3.04040820773038, 0.9630654644320192, -0.1533364416214706, -0.7659841715940853, 2.007466075331426, 0.08714108414964748, -4.399836033852537, -2.094402964542149, 1.881770871338782, -0.003518308075519047, -1.40321707392884, 0.5488399706607981, -0.341867036359113, -1.204293070544166, 2.901347848797405, 4.652944639630627, 1.040409079148423, -0.07697758121129791, 0.8455558118002477, -1.281300777304651, -1.917069610546417, 0.3787072380044178, -0.3204899012994918, -1.454673090589014, 0.8917889028648822, 1.186388040986262, -0.2921121150747851, 1.730935540006526, 1.734462767643341, -2.38634061075603, -1.968389822239784, 0.003147131831467144, -3.001468755191426, -1.193765255712821, 5.831623922387917, 2.664874561518894, -4.078240659547593, 1.371021166863025, 6.351304952483834, 0.5462456163184061, -0.248732741080915, 5.682583878554143, 3.348883946873098, -2.114007227805185, -0.8653841186762823, 0.06451953591502284, -1.197464168223408, 0.2082001299329484, 0.5096966109270522, -0.3489286649636451, 1.507724345155208, 1.03271900352882, -1.678193232994573, -0.08939963583874541, 0.9282317692968118, -1.413663602709268, -0.2189556017106205, 0.4086904585878712, -3.87135004708183, -3.299500831084963, 1.145282591778834, 0.07927966581729347, -0.6961503066188911, 1.182736924651851, -1.197212871532334, -1.203615182809409], 'positive_zeros': ['0.6421024853064671', '1.024493813220823', '1.617866254897141', '2.336152532903145', '2.807328930769400', '3.268410353466391', '3.783859030906239', '4.395375554977274', '5.039442205915302', '5.714181599896481', '5.950506159238874', '6.491843908050262', '7.202002076561601', '7.476948747113066', '7.856453186023182', '8.394605348702471', '8.968337765924691', '9.388485314675121', '9.612475955644735', '10.02256192651900', '10.62339806521517', '10.89486445210280', '11.57203968792082', '12.00376519027747', '12.46742345716090', '12.80830660374614', '13.32356217260716', '13.91406543753129', '14.23486561614043', '14.57367103843656', '15.00429662645570', '15.60033181994975', '15.99973126417373', '16.42331755097310', '16.71299464226607', '17.09792578171233', '17.84755342787561', '18.01611627982271', '18.38193202637226', '18.94859877354985', '19.21245065190082', '19.66795669807890'], 'prelabel': '2-390390-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.83260556797226, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1144105918009302996, 'z1': {'__RealLiteral__': 0, 'data': '0.6421024853064671', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.024493813220823', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.617866254897141', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3117.2798445087665, 'bad_primes': [2, 3, 5, 7, 11, 13], 'central_character': '1.1', 'conductor': 390390, 'conductor_radical': 30030, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 0, 1, 1, 1, 6, -1, 4, 1, -1, -1, 0, -1, 1, 0, 1, -1, 6, -1, -8, -1, 1, -6, -1, 1, 10, -4, 0, -1, 6, 1, 8, 1, 1, 0, 0, 1, 1, -1, 6, 0, 6, -1, 1, 1, 4, -6, -12, 1, 2, 8, -1, 1, 0, -1, 4, 6, 0, 1, -12, -1, 10, -10, 1, 4, -1, 0, -4, 1, 1, -6, 12, -1, 6, -8, 6, -1, -6, -1, 0, 0, -8, 0, 4, -1, 10, -1, 1, 1], 'euler11': [1, -1, 0], 'euler13': [1, 0, 0], 'euler17': [1, -6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 8, 31], 'euler37': [1, -10, 37], 'euler41': [1, -6, 41], 'euler43': [1, -8, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 12, 59], 'euler61': [1, -2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 12, 71], 'euler73': [1, -10, 73], 'euler79': [1, 4, 79], 'euler83': [1, -12, 83], 'euler89': [1, 6, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 1, 0], [1, -1, 0], [1, -1, 0], [1, 1, 0], [1, -1, 0], [1, 0, 0], [1, -6, 17], [1, -4, 19], [1, 0, 23], [1, -6, 29], [1, 8, 31], [1, -10, 37], [1, -6, 41], [1, -8, 43], [1, 0, 47], [1, -6, 53], [1, 12, 59], [1, -2, 61], [1, -4, 67], [1, 12, 71], [1, -10, 73], [1, 4, 79], [1, -12, 83], [1, 6, 89], [1, -10, 97]], 'index': 62, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/390390/ce'], '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': '2-390390-1.1-c1-0-62', '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': '2-390390-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 55.83260556797226, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1144105918009302996, 'z1': {'__RealLiteral__': 0, 'data': '0.6421024853064671', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1144105918009302996', 'Lhash_array': ['1144105918009302996'], 'factors': ['2-390390-1.1-c1-0-62'], 'label': '2-390390-1.1-c1-0-62', 'type': 'ECQ', 'url': 'EllipticCurve/Q/390390/ce'}