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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': 4, 'A8': 1, 'A9': 0, 'Lhash': '832135768532129723', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 412.9383690128496, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [13, [1]], [17, [1, -1]]], 'bad_primes': [2, 3, 13, 17], 'central_character': '51714.1', 'coefficient_field': '1.1.1.1', 'conductor': 51714, 'conductor_radical': 1326, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 0, 5], [1, -4, 7], [1, -6, 11], [1], [1, -1], [1, -4, 19], [1, 0, 23], [1, 0, 29], [1, -4, 31], [1, -4, 37], [1, -6, 41], [1, -8, 43], [1, 0, 47], [1, -6, 53], [1, 0, 59], [1, 4, 61], [1, 8, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, 0, 83], [1, 6, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 19, 'label': '2-51714-1.1-c1-0-19', 'leading_term': '7.16416584774', '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/51714/v', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [7.164165847741281, 6.397328821701984, 4.298767919585882, 1.63876413737656, -0.2890542179796207, -0.5006403817058498, 0.6509520313475404, 1.524631036591321, 0.7171044380494912, -1.297772603196498, -2.402210013823337, -1.120027778250483, 1.481008207339781, 2.765218440539596, 1.56173540852701, -0.454710029709759, -0.9949846220629307, -0.1671202989220558, -0.07545760014801157, -1.471796565787295, -2.422623372284624, -1.271696396890944, 0.4886605381850198, 0.255417341463957, -1.439280893626022, -1.355572482645509, 1.306409648862281, 3.074421795403459, 1.350907142923978, -1.211295992061524, -0.6704021620901925, 1.68196506999082, 1.225435471066286, -1.984342442512314, -2.508275840183294, 1.613789848288695, 4.843038335722304, 2.700596174049213, -0.5577172027483565, 1.477742358990399, 6.646556420009113, 7.265837476475113, 2.27481685531313, -1.518705002032343, -0.5354690529747098, 1.171993983017614, 0.3146184405904927, -0.6549210221051575, 0.01771036169772503, -0.5597510811464745, -3.361877725030857, -3.897706789869709, 0.04105697296649802, 3.573899137248671, 2.623511709222725, 0.2592924308096204, 0.1868239596732681, 0.5499905374248801, -0.6492666650000783, -0.9864634993096087, 0.3616849276475514, -0.3598731147559526, -3.407466684565536, -3.103056817202862, 1.488301505397765, 3.304189533776244, -0.08852617627280275, -1.759562294832269, 1.314266384276594, 2.739674974332515, -0.007441326765183217, -0.6702144989112945, 1.786815146588379, -0.4395029589308993, -7.756261400417281, -9.645101473839475, -3.23827802383019, 1.378633795836515, -0.3890204872671718, -1.184783018094752, 2.104002003248481, 3.172225858828691, 0.4527608471079053, -0.2910499348074773, 1.296603062994022, 0.3653455353359958, -1.822231299762118, -1.017993019196677, 0.2405310492691404, -1.388507395008865, -2.095002704835936, 0.4712714811746216, 1.346465786498573, -0.9348596976506772, -0.78025562073713, 2.27548107611086, 2.492046723309897, 0.1619827769958354, -0.1733316452574787, -0.2179375617078999, -2.159833453833593, -1.320082420941545, 2.477351523679229, 0.6784895539912316, -6.196712229278221, -6.106042042503123, 1.603128993977339, 4.217506309115155, -0.02567066712205905, -1.186389126035351, 0.631627987339951, -1.302096262952027, -2.731607262720403, 1.532317064123235, 3.324968638825755, -2.458385223242561, -5.805403669313298, -1.458979995040479, 1.528172712281667, -0.6758052611416293, -1.341552697028978], 'positive_zeros': ['0.9461148615051682', '1.377172860502349', '2.094661375296494', '2.858762875302694', '3.684307143648342', '4.310844597627686', '4.472598939392835', '5.412819194784533', '5.791355941370739', '6.391902802941246', '7.112698560734044', '7.569083117090960', '8.101041661697443', '8.668466024680720', '9.429787550699291', '9.656500119335563', '10.61262977672523', '11.05721054820635', '11.55083159740838', '11.99365458106343', '12.15779391196609', '12.99789783606899', '13.81615958767369', '13.92977469383552', '14.38683524824508', '14.92883414445688', '15.21074025676572', '15.92353928675849', '16.49438349057490', '16.91188623843421', '17.49935236478058', '17.82218128121128', '18.23097695944186', '19.12814561069961', '19.46595991596846', '19.85692082631008'], 'prelabel': '2-51714-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.32088504501833, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 832135768532129723, 'z1': {'__RealLiteral__': 0, 'data': '0.9461148615051682', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.377172860502349', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.094661375296494', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 412.9383690128496, 'bad_primes': [2, 3, 13, 17], 'central_character': '1.1', 'conductor': 51714, 'conductor_radical': 1326, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 4, 1, 0, 0, 6, 0, 0, 4, 0, 1, 1, 0, 4, 0, 0, 6, 0, 0, -5, 0, 0, 4, 0, 0, 4, 1, 0, 1, 0, 0, 4, 4, 0, 0, 6, 0, 8, 6, 0, 0, 0, 0, 9, -5, 0, 0, 6, 0, 0, 4, 0, 0, 0, 0, -4, 4, 0, 1, 0, 0, -8, 1, 0, 0, 0, 0, -2, 4, 0, 4, 24, 0, 8, 0, 0, 6, 0, 0, 0, 8, 0, 6, -6, 0, 0, 0, 0, 0, 0, 0, -14, 9, 0, -5], 'euler11': [1, -6, 11], 'euler13': [1, 0, 0], 'euler17': [1, -1, 0], 'euler19': [1, -4, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -4, 37], 'euler41': [1, -6, 41], 'euler43': [1, -8, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 5], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 4, 61], 'euler67': [1, 8, 67], 'euler7': [1, -4, 7], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 0, 83], 'euler89': [1, 6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 0, 5], [1, -4, 7], [1, -6, 11], [1, 0, 0], [1, -1, 0], [1, -4, 19], [1, 0, 23], [1, 0, 29], [1, -4, 31], [1, -4, 37], [1, -6, 41], [1, -8, 43], [1, 0, 47], [1, -6, 53], [1, 0, 59], [1, 4, 61], [1, 8, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, 0, 83], [1, 6, 89], [1, 14, 97]], 'index': 19, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/51714/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': '2-51714-1.1-c1-0-19', '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': '2-51714-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.32088504501833, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 832135768532129723, 'z1': {'__RealLiteral__': 0, 'data': '0.9461148615051682', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '832135768532129723', 'Lhash_array': ['832135768532129723'], 'factors': ['2-51714-1.1-c1-0-19'], 'label': '2-51714-1.1-c1-0-19', 'type': 'ECQ', 'url': 'EllipticCurve/Q/51714/v'}