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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': -2, 'A8': 0, 'A9': 1, 'Lhash': '2115181709123201437', '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': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 623.9829815550937, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [11, [1, -1]], [37, [1, 1]]], 'bad_primes': [2, 3, 11, 37], 'central_character': '78144.1', 'coefficient_field': '1.1.1.1', 'conductor': 78144, 'conductor_radical': 2442, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 0, 5], [1, 2, 7], [1, -1], [1, 4, 13], [1, -2, 17], [1, -8, 19], [1, 2, 23], [1, -2, 29], [1, 8, 31], [1, 1], [1, -6, 41], [1, 12, 43], [1, 10, 47], [1, 12, 53], [1, -4, 59], [1, 0, 61], [1, -12, 67], [1, 14, 71], [1, 14, 73], [1, 10, 79], [1, 12, 83], [1, -6, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 1, 'label': '2-78144-1.1-c1-0-1', 'leading_term': '0.39040448516', '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/78144/v', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.3904044851603331, -0.1420084147839628, -1.417264642790566, -2.50294813999165, -2.326695645510997, -0.7348450079288666, 0.8838907672507306, 0.6025067599266902, -1.912432372769107, -4.506899578653588, -4.532702855934925, -1.96207624804788, 0.2660193427162619, -0.267763317987691, -2.256802142059032, -2.283424772651643, 0.4114342774314813, 2.580148495976027, 1.399683820943773, -1.427356570595586, -2.118259956343744, -0.3802701360893122, 0.4562101784834158, -0.9547958793992947, -1.71832570146354, 0.2815488305795582, 2.450850945170921, 1.701493724489796, -0.1159719779296554, 0.6435504088133762, 2.688866036412795, 1.766410062037945, -1.177160974389717, -0.3429346832752541, 5.127291341721167, 8.490125409198834, 5.541893640755175, 0.9046246111517483, -0.0904628298493727, 0.5967525550204029, -0.5723452708306743, -1.180198156147072, 1.872903958867874, 4.897782544935578, 3.151503572287844, -0.5146572721041722, -0.8263161655197734, 0.6521461201475708, -0.1797782706426646, -1.326385941569086, 0.6465835283209154, 2.596185697072437, 0.8799732283340534, -0.4265448526364455, 2.771393257433966, 5.470488124158423, 2.521491701038331, -1.108101097738186, 0.1032416756482845, 1.29577194559285, -2.782198081045003, -6.604654316385711, -4.159420702161791, -0.08021495678309618, 0.1345519993084881, -0.214624688072482, 1.684276822684602, 1.663668240116688, -1.241897821809561, -1.542120670539107, 1.001649777610066, 0.7836313767109278, -1.089239630962138, 0.8904186687280206, 3.778941569928896, 1.729903208953763, -1.147319639802979, 0.7654051924453626, 2.613881837429672, -0.001680825206242667, -1.36396627516535, 0.8149593151723658, -0.856849144562218, -6.754068319352215, -7.070900101943376, -1.103813163036038, 1.409160341495137, -0.7296405149658886, -0.8371641564813069, 0.2558898665594796, -1.303162066960198, -1.86725711776252, 0.4460138451163748, 0.1406392887460165, -2.537031902394972, -1.087288367020239, 2.05904830734942, 0.2849052118176404, -2.197578343246976, -0.1313106938144158, 0.5187766124694253, -2.91638159739965, -2.360399558436759, 2.442088851577666, 2.056316976721383, -2.013574015597163, -0.9369244372451188, 2.012370711418887, 0.3428166317429534, -0.7093218447364111, 2.130171854186114, 1.851867887215848, -1.777690157264347, -1.093633719570203, 1.861626988796759, 0.7226673199127958, -0.8860551355239712, 0.2368775779900198, -0.3610978859562584, -1.345298283354875, 1.945494211096957], 'positive_zeros': ['0.2126326258001332', '1.346250798368414', '1.827945672717355', '2.948752728724556', '3.209465280061951', '3.967544052922335', '4.619325761825281', '5.304973168484833', '5.611273943028382', '6.224825661704048', '6.972031180877822', '7.156721516360649', '7.890263434042354', '8.271151941332707', '9.352899121387134', '9.528846259516835', '9.915804397074035', '10.37830126261294', '11.20402286711472', '11.62098821781055', '11.97504503251907', '12.44429021764922', '13.08949270349049', '13.31331723152127', '14.14122221293996', '14.49034423225071', '14.86336643170887', '15.75903410778410', '16.03054356273076', '16.29209752386285', '16.89542149927407', '17.39779728111192', '17.83476218387991', '18.18631641011714', '18.86337379197267', '19.19111066547810', '19.74987353338032'], 'prelabel': '2-78144-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.979651349750537, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2115181709123201437, 'z1': {'__RealLiteral__': 0, 'data': '0.2126326258001332', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.346250798368414', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.827945672717355', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 623.9829815550937, 'bad_primes': [2, 3, 11, 37], 'central_character': '1.1', 'conductor': 78144, 'conductor_radical': 2442, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -2, 0, 1, 0, 1, 0, -4, 0, 0, 0, 2, 0, 8, 0, 2, 0, -2, 0, -5, 0, -1, 0, 2, 0, -8, 0, -1, 0, 0, 0, -1, 0, 4, 0, 6, 0, -12, 0, 0, 0, -10, 0, -3, 0, -2, 0, -12, 0, 0, 0, -8, 0, 4, 0, 0, 0, -2, 0, 0, 0, 12, 0, 2, 0, -14, 0, -14, 0, 5, 0, -2, 0, -10, 0, 1, 0, -12, 0, 0, 0, -2, 0, 6, 0, 8, 0, 8, 0, 0, 0, -10, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, 4, 13], 'euler17': [1, -2, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, -2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 1, 0], 'euler41': [1, -6, 41], 'euler43': [1, 12, 43], 'euler47': [1, 10, 47], 'euler5': [1, 0, 5], 'euler53': [1, 12, 53], 'euler59': [1, -4, 59], 'euler61': [1, 0, 61], 'euler67': [1, -12, 67], 'euler7': [1, 2, 7], 'euler71': [1, 14, 71], 'euler73': [1, 14, 73], 'euler79': [1, 10, 79], 'euler83': [1, 12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 5], [1, 2, 7], [1, -1, 0], [1, 4, 13], [1, -2, 17], [1, -8, 19], [1, 2, 23], [1, -2, 29], [1, 8, 31], [1, 1, 0], [1, -6, 41], [1, 12, 43], [1, 10, 47], [1, 12, 53], [1, -4, 59], [1, 0, 61], [1, -12, 67], [1, 14, 71], [1, 14, 73], [1, 10, 79], [1, 12, 83], [1, -6, 89], [1, 10, 97]], 'index': 1, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/78144/v'], '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': '2-78144-1.1-c1-0-1', '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': '2-78144-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.979651349750537, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2115181709123201437, 'z1': {'__RealLiteral__': 0, 'data': '0.2126326258001332', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2115181709123201437', 'Lhash_array': ['2115181709123201437'], 'factors': ['2-78144-1.1-c1-0-1'], 'label': '2-78144-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/78144/v'}