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lfunc_lfunctions • Show schema
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{'A10': 2, 'A2': -2, 'A3': 0, 'A4': 2, 'A5': -1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 0, 'Lhash': '323525754311786641', 'a10': [0.6324555320336759, 0], 'a2': [-1.414213562373095, 0], 'a3': [0.0, 0], 'a4': [1.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1349.9908217727775, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 1]], [13, [1, 1]], [17, [1]]], 'bad_primes': [3, 5, 13, 17], 'central_character': '169065.1', 'coefficient_field': '1.1.1.1', 'conductor': 169065, 'conductor_radical': 3315, 'degree': 2, 'euler_factors': [[1, 2, 2], [1], [1, 1], [1, -1, 7], [1, -5, 11], [1, 1], [1], [1, 6, 19], [1, -3, 23], [1, -2, 29], [1, 2, 31], [1, 7, 37], [1, -9, 41], [1, 8, 43], [1, 10, 47], [1, 5, 53], [1, 0, 59], [1, 5, 61], [1, 4, 67], [1, -9, 71], [1, -6, 73], [1, -3, 79], [1, -4, 83], [1, 11, 89], [1, -11, 97]], 'gamma_factors': [[], [0]], 'index': 2, 'label': '2-169065-1.1-c1-0-2', 'leading_term': '0.540345848918', '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/169065/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.5403458489182488, 0.1317442333394839, -0.7480815318991544, -1.245433429492137, -0.7412258417715334, 0.2451517624938583, 0.3739023242347967, -0.6752659816800505, -1.122039481462611, 0.8917495418964917, 4.012912547150233, 4.188580244181988, -0.06986016827940864, -4.456339738597386, -3.702738870491833, 0.8998129127364058, 2.68823360239496, -0.6683260935677267, -3.330871317983591, -0.5415852019823426, 2.779906779558352, -1.084253173578459, -9.803445931115292, -13.09228642785083, -7.596946894767338, -1.150674760920481, -0.1301306974295087, -1.213662787101411, 0.2802616349033209, 2.135248537182419, 0.9826335860537344, -0.8298038344016382, -0.2515826086875797, 0.7375956560282991, -0.0750553012688267, -0.6954288777113531, 0.09393731468570692, -0.07233940597623081, -1.391076646560675, -0.8308435384359335, 0.909534742444753, 0.01898170059544415, -2.180013996689086, -1.415167760423491, 0.5451437271450931, 0.0136551832836458, 0.2104350964252171, 3.912662025397847, 5.113339241712733, 1.107843885998873, 0.830804002147501, 7.112691835302106, 7.464308392697588, -2.447245510749177, -7.377051633716925, 0.1402889089701771, 5.764769345014966, 0.8871828939768368, -3.243510032581544, -0.5825612126469607, -0.4709605070210005, -4.882118127104431, -4.288370970025995, 0.9035181375478464, 1.402663213094989, -1.690459049484642, -1.408799033841239, 0.3381846976984722, -0.2029364447708918, -0.2633700382271396, 0.7587889171388384, -0.2129513236267621, -1.07957625216893, 0.7718247701832337, 1.373719526770576, -0.7587066782390438, -1.140533481058167, 0.126130473350169, -0.1088490370135259, 0.2207170607546494, 1.014432352491592, -2.186484300389447, -5.126150023984249, -1.263556213437552, 1.513559336296804, -3.000826566664692, -3.045846693399505, 5.20624362292642, 5.971427645709852, -2.275756007103281, -2.719783345600973, 2.970011095165133, 0.9020517462290971, -1.350822012315686, 6.686304937124011, 11.5865434689692, 4.548650123470471, -0.591427003206303, 1.444493967097471, 0.5885016376023241, -2.164820953090679, -0.1737346210984836, 1.458831680467738, -0.09784966102622943, 1.019858551220108, 3.16676476333015, 1.271320516561383, -0.6718586143053134, -0.05342700038510188, -0.4049416129242998, -0.9034870301524024, -0.006232679009340322, -0.05605361036906516, 0.8919116482842196, 3.751558214361714, 2.096167255372266, -2.435855325637464, -1.343716694740063, 0.8530954590775974, -1.426325185952532, -0.2732772582989789], 'positive_zeros': ['0.2913037367247719', '1.180504422641399', '1.608686666761158', '2.172231173706090', '2.996771924523271', '3.700723360249858', '4.211802636451167', '4.779232439569671', '5.212918875336158', '6.368551656927016', '6.467305374906319', '6.971714004308585', '7.609088112506001', '8.043718447818127', '8.484977284042933', '8.971474856835731', '9.233638816995945', '9.854698474447139', '10.25200702985302', '10.90466547092126', '11.25288535011090', '11.47407121123791', '12.34803790340648', '12.42672648453859', '13.19443304543441', '13.74639742870907', '14.28222565908691', '14.80361263741661', '14.95875173703209', '15.69986123125761', '16.10803668190178', '16.67217737630228', '16.95046951259543', '17.30774332807415', '17.71944493038935', '18.16528603474929', '18.66556973144749', '19.21147491038562', '19.45549257181502', '19.70232438843448'], 'prelabel': '2-169065-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 36.74222124168295, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 323525754311786641, 'z1': {'__RealLiteral__': 0, 'data': '0.2913037367247719', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.180504422641399', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.608686666761158', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1349.9908217727775, 'bad_primes': [3, 5, 13, 17], 'central_character': '1.1', 'conductor': 169065, 'conductor_radical': 3315, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 2, -1, 0, 1, 0, 0, 2, 5, 0, -1, -2, 0, -4, 0, 0, -6, -2, 0, -10, 3, 0, 1, 2, 0, 2, 2, 0, -2, 8, 0, 0, -1, 0, -7, 12, 0, 0, 9, 0, -8, 10, 0, -6, -10, 0, -6, -2, 0, -2, -5, 0, -5, 0, 0, -4, 0, 0, -5, 4, 0, -8, 1, 0, -4, 0, 0, 2, 9, 0, 6, 14, 0, -12, 5, 0, 3, 4, 0, -18, 4, 0, 0, 16, 0, 0, -11, 0, -1, 6, 0, 20, 6, 0, 11, 12, 0, 2], 'euler11': [1, -5, 11], 'euler13': [1, 1, 0], 'euler17': [1, 0, 0], 'euler19': [1, 6, 19], 'euler2': [1, 2, 2], 'euler23': [1, -3, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, 7, 37], 'euler41': [1, -9, 41], 'euler43': [1, 8, 43], 'euler47': [1, 10, 47], 'euler5': [1, 1, 0], 'euler53': [1, 5, 53], 'euler59': [1, 0, 59], 'euler61': [1, 5, 61], 'euler67': [1, 4, 67], 'euler7': [1, -1, 7], 'euler71': [1, -9, 71], 'euler73': [1, -6, 73], 'euler79': [1, -3, 79], 'euler83': [1, -4, 83], 'euler89': [1, 11, 89], 'euler97': [1, -11, 97], 'euler_factors': [[1, 2, 2], [1, 0, 0], [1, 1, 0], [1, -1, 7], [1, -5, 11], [1, 1, 0], [1, 0, 0], [1, 6, 19], [1, -3, 23], [1, -2, 29], [1, 2, 31], [1, 7, 37], [1, -9, 41], [1, 8, 43], [1, 10, 47], [1, 5, 53], [1, 0, 59], [1, 5, 61], [1, 4, 67], [1, -9, 71], [1, -6, 73], [1, -3, 79], [1, -4, 83], [1, 11, 89], [1, -11, 97]], 'index': 2, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/169065/a'], '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': '2-169065-1.1-c1-0-2', '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': '2-169065-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 36.74222124168295, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 323525754311786641, 'z1': {'__RealLiteral__': 0, 'data': '0.2913037367247719', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '323525754311786641', 'Lhash_array': ['323525754311786641'], 'label': '2-169065-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/169065/a'}