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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': -1, 'A8': 0, 'A9': 1, 'Lhash': '1463381959401251485', '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': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 308.54195341022756, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [7, [1, 1]], [23, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '38640.1', 'coefficient_field': '1.1.1.1', 'conductor': 38640, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, 1], [1, 0, 11], [1, -2, 13], [1, 2, 17], [1, -4, 19], [1, -1], [1, 10, 29], [1, -4, 31], [1, 6, 37], [1, -2, 41], [1, -8, 43], [1, 12, 47], [1, 6, 53], [1, 12, 59], [1, -2, 61], [1, -8, 67], [1, 8, 71], [1, -10, 73], [1, -8, 79], [1, -4, 83], [1, -14, 89], [1, 18, 97]], 'gamma_factors': [[], [0]], 'index': 12, 'label': '2-38640-1.1-c1-0-12', 'leading_term': '2.15746634636', '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/38640/bz', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.157466346356956, 1.613340645094476, 0.1671376003045876, -1.527591273987315, -2.432350460222549, -1.788268142304493, 0.05329590767882133, 1.598009960513763, 1.393626530636612, -0.486152507129254, -2.294565782900966, -2.318420044134909, -0.7852551582505616, 0.3444676830398286, -0.2238536097260215, -1.360358494352189, -0.9000434483478345, 1.253395534811861, 2.503217009308636, 0.8458970916087575, -1.993366567653056, -2.25918547314946, 0.8742651718057133, 3.766687231411142, 2.900579454040554, -0.3333896660316492, -1.508907392047151, 0.6689341802795655, 2.742774663306428, 1.819278049353056, -0.2185840990547269, -0.0237507938007744, 1.736476951959907, 1.60657640994298, -0.7413880616204676, -1.824260688504764, -0.2305803911855146, 0.9318652698184775, -0.4487718758926395, -1.406482723973058, 1.108028103409658, 4.296155895003413, 3.445340714645758, -0.1727176454398728, -1.126341088312875, 1.089310869004023, 1.266282846308218, -2.272513881899767, -4.436941363331828, -2.082074948820451, 0.5543891346052592, -0.6626661757627289, -2.774851942464832, -1.636383504699699, 0.467481148798315, -0.4423986864040327, -2.201063554803339, -0.6538668489479703, 2.092311191491117, 1.360490560535416, -1.289420868733631, -1.10205163213303, 0.8621847060212864, 0.3639929490122977, -1.136501657021082, 0.4443448110703938, 2.545914471847959, -0.009216121653127445, -4.138762281986717, -2.733373760361284, 2.264203997237958, 2.774664759284313, -1.103426689867868, -1.986121114363428, 0.9673884302592362, 1.712642250945971, -0.3703106734661134, -0.3420937129292275, 1.457395753128393, 0.5704312374581304, -1.623252777148588, -0.7481797273692758, 1.131389011462754, 0.1803386220857212, -0.2748237447791581, 3.246022775902656, 5.420923350300804, 1.576198655807552, -2.457004673046885, -1.056149709283058, 0.8629839987752699, -1.189393767332258, -2.036075830123114, 1.413625858412409, 2.60939858560348, -1.429925298515473, -3.719821356351763, -1.229989960188338, 0.1012302339770802, -1.079822152554381, 0.7790802477058129, 4.750302502946322, 4.2242117021036, 0.4647981809504486, -0.4141629032767991, 0.170355820522308, -1.434704343935954, -1.50030227991622, 2.227169658763163, 3.530610775770542, 0.2903442979795292, -0.6135999074288755, 1.763069521616681, 0.3070875852278718, -3.799732461499884, -2.515890804674304, 1.684438622892664, 0.5638128683427903, -2.531460397623358, -0.2491808006799051, 2.972266083461187], 'positive_zeros': ['0.5240716158634332', '1.493332709133943', '2.194761410400353', '3.133702793658873', '3.451241599506593', '4.115233510216174', '4.820493476328567', '5.442696341829791', '6.222179157905945', '6.691660386964164', '7.462251474780715', '7.753902679054633', '8.425973265889322', '9.028360037405768', '9.442823128446419', '9.921992273947172', '10.73622406648993', '11.13812802375031', '11.60726238654523', '12.41359726138753', '12.68146158375870', '13.41784826229874', '13.69622413838758', '14.30141828330864', '14.86842182556933', '15.37768145264583', '15.79740641657568', '16.21054349323556', '16.74950666493106', '17.38143327846893', '17.92911655302390', '18.42202994777378', '18.95219590632966', '19.29625675594736', '19.80600602174839'], 'prelabel': '2-38640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.565362319355316, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1463381959401251485, 'z1': {'__RealLiteral__': 0, 'data': '0.5240716158634332', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.493332709133943', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.194761410400353', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 308.54195341022756, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 38640, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 2, 0, -1, 0, -2, 0, 4, 0, -1, 0, 1, 0, 1, 0, 1, 0, -10, 0, 4, 0, 0, 0, 1, 0, -6, 0, 2, 0, 2, 0, 8, 0, -1, 0, -12, 0, 1, 0, -2, 0, -6, 0, 0, 0, 4, 0, -12, 0, 2, 0, -1, 0, -2, 0, 8, 0, 1, 0, -8, 0, 10, 0, 1, 0, 0, 0, 8, 0, 1, 0, 4, 0, 2, 0, -10, 0, 14, 0, -2, 0, 4, 0, -4, 0, -18, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, 2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, 10, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 6, 37], 'euler41': [1, -2, 41], 'euler43': [1, -8, 43], 'euler47': [1, 12, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 12, 59], 'euler61': [1, -2, 61], 'euler67': [1, -8, 67], 'euler7': [1, 1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -10, 73], 'euler79': [1, -8, 79], 'euler83': [1, -4, 83], 'euler89': [1, -14, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, 1, 0], [1, 0, 11], [1, -2, 13], [1, 2, 17], [1, -4, 19], [1, -1, 0], [1, 10, 29], [1, -4, 31], [1, 6, 37], [1, -2, 41], [1, -8, 43], [1, 12, 47], [1, 6, 53], [1, 12, 59], [1, -2, 61], [1, -8, 67], [1, 8, 71], [1, -10, 73], [1, -8, 79], [1, -4, 83], [1, -14, 89], [1, 18, 97]], 'index': 12, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/38640/bz'], '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': '2-38640-1.1-c1-0-12', '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': '2-38640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.565362319355316, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1463381959401251485, 'z1': {'__RealLiteral__': 0, 'data': '0.5240716158634332', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1463381959401251485', 'Lhash_array': ['1463381959401251485'], 'label': '2-38640-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/38640/bz'}