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lfunc_lfunctions • Show schema
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{'A10': -1, 'A2': 1, 'A3': 0, 'A4': -1, 'A5': -1, 'A6': 0, 'A7': -1, 'A8': -3, 'A9': -3, 'Lhash': '144236563770334289', 'a10': [-0.31622776601683794, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [-0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-1.0606601717798212, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 469.7998402922034, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, 1]], [7, [1, 1]], [41, [1]]], 'bad_primes': [5, 7, 41], 'central_character': '58835.1', 'coefficient_field': '1.1.1.1', 'conductor': 58835, 'conductor_radical': 1435, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, 0, 3], [1, 1], [1, 1], [1, 2, 11], [1, 2, 13], [1, 2, 17], [1, 2, 19], [1, -4, 23], [1, 8, 29], [1, 0, 31], [1, -2, 37], [1], [1, -8, 43], [1, 4, 47], [1, 6, 53], [1, -12, 59], [1, 2, 61], [1, 4, 67], [1, 10, 71], [1, 10, 73], [1, 2, 79], [1, -4, 83], [1, 16, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 4, 'label': '2-58835-1.1-c1-0-4', 'leading_term': '3.90394730456', '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': 1, 'origin': 'EllipticCurve/Q/58835/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.8019013495642215, 0.6099080077372759, -1.174511185358954, -4.093546518944193, -6.425598172476841, -6.23721687781814, -3.180672329626251, 0.7584330311629892, 2.798767562993674, 2.010297734970434, 0.2047381973308548, -0.2127773560398368, 0.9314233584624004, 1.611878843039764, 0.5447493477790624, -0.9374232644522711, -0.8244644667752613, 0.5216644699583642, 0.8436422173452278, -0.4934171884438163, -1.400722784906476, -0.4643651553812708, 0.4535560806026336, -0.8561882653079547, -2.728582893699304, -1.542139765439201, 2.224377279829767, 3.661978582664417, 0.6617088487241882, -2.2942932744043, -0.6789078323695148, 2.953061119976318, 3.007154395338326, -0.1513513037728594, -1.204201590789286, 0.746319971253672, 0.7775443684447534, -2.491560522342854, -3.480219446355737, 0.7652541914215063, 4.420762297574032, 1.88660832653062, -2.913584105392826, -3.148337590764794, -0.1726242839641355, -0.003271064718115785, -2.376251650532978, -2.134847046406406, 0.7948746464873511, 1.764674652253069, 0.3303677636153501, 0.1427619788436597, 1.06001916887248, -0.100010489367456, -2.161146354047583, -1.426223334911986, 0.7065595787774891, 0.3867057633117514, -0.9401074127899572, -0.06954505275216795, 0.4499079101354591, -2.341736512986027, -4.014249856584051, -0.4913725530582963, 2.655676479175423, -0.2953754995216045, -3.950960773036794, -1.839764429172675, 1.182470741515655, -0.9080582933609332, -2.966567106878806, 0.451960703699911, 3.245592788302011, -0.1989027350872878, -3.560593730554752, -1.401221102635959, 0.3740299999379123, -2.146395817021218, -2.398977005055583, 2.273281124435567, 4.189825075237562, 0.7762641915654114, -0.7045186946108264, 1.355696115478576, 0.3412274583943799, -3.713435571458525, -4.041653748115855, -0.9431445686509923, 0.1452528351755617, -0.06555577742672913, 1.247412695998353, 1.603871820855104, -0.09734545251395686, -0.3259437165536242, 0.2383090792074201, -1.974189102001408, -3.433310894837555, -0.2347754005193358, 1.258803950175843, -3.30409098300042, -5.286691568652163, 0.1627777878023936, 3.611474979740611, 0.5229053857786832, -0.6432175876241069, 2.034248459875112, 0.8767843821700989, -2.389374339178149, -0.1753056390301143, 2.925277002897154, 0.01785350876907605, -2.225060993312111, 1.371854770033685, 2.578918383218438, -1.367734879309778, -1.274049537333712, 3.001627713818307, 2.122321433864926, -1.615244548643979, 0.3612987466808178], 'positive_zeros': ['0.6137128915292472', '1.947028589645532', '2.790854985418813', '3.066195899020672', '3.829751565611626', '4.404173471363618', '4.922854378612476', '5.583482121302314', '5.888955319116836', '6.606978450648725', '7.290916996932379', '7.794520721636328', '8.487308531550421', '8.913060605354546', '9.323014913786199', '9.964583888626469', '10.58895622509766', '11.26997589971109', '11.49956589750063', '12.18147704197733', '12.83516395967149', '12.95129902291237', '13.48901697009273', '14.15059487252242', '14.55845799994486', '15.01117975595287', '15.31447059888511', '16.02533741596703', '16.48499194920627', '17.11452143425646', '17.43571004336068', '17.97651962634599', '18.49024576470313', '19.11841680358905', '19.31432371947009', '19.89008215976263'], 'prelabel': '2-58835-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 21.674866557656205, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 144236563770334289, 'z1': {'__RealLiteral__': 0, 'data': '0.6137128915292472', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.947028589645532', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.790854985418813', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 469.7998402922034, 'bad_primes': [5, 7, 41], 'central_character': '1.1', 'conductor': 58835, 'conductor_radical': 1435, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, -1, -1, 0, -1, -3, -3, -1, -2, 0, -2, -1, 0, -1, -2, -3, -2, 1, 0, -2, 4, 0, 1, -2, 0, 1, -8, 0, 0, 5, 0, -2, 1, 3, 2, -2, 0, 3, 0, 0, 8, 2, 3, 4, -4, 0, 1, 1, 0, 2, -6, 0, 2, 3, 0, -8, 12, 0, -2, 0, 3, 7, 2, 0, -4, 2, 0, 1, -10, 9, -10, 2, 0, 2, 2, 0, -2, 1, 9, 0, 4, 0, 2, 8, 0, 6, -16, 3, 2, -4, 0, -4, 2, 0, 10, 1, 6, -1], 'euler11': [1, 2, 11], 'euler13': [1, 2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 2, 19], 'euler2': [1, -1, 2], 'euler23': [1, -4, 23], 'euler29': [1, 8, 29], 'euler3': [1, 0, 3], 'euler31': [1, 0, 31], 'euler37': [1, -2, 37], 'euler41': [1, 0, 0], 'euler43': [1, -8, 43], 'euler47': [1, 4, 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, 10, 71], 'euler73': [1, 10, 73], 'euler79': [1, 2, 79], 'euler83': [1, -4, 83], 'euler89': [1, 16, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, -1, 2], [1, 0, 3], [1, 1, 0], [1, 1, 0], [1, 2, 11], [1, 2, 13], [1, 2, 17], [1, 2, 19], [1, -4, 23], [1, 8, 29], [1, 0, 31], [1, -2, 37], [1, 0, 0], [1, -8, 43], [1, 4, 47], [1, 6, 53], [1, -12, 59], [1, 2, 61], [1, 4, 67], [1, 10, 71], [1, 10, 73], [1, 2, 79], [1, -4, 83], [1, 16, 89], [1, -10, 97]], 'index': 4, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/58835/i'], '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': '2-58835-1.1-c1-0-4', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-58835-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 21.674866557656205, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 144236563770334289, 'z1': {'__RealLiteral__': 0, 'data': '0.6137128915292472', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '144236563770334289', 'Lhash_array': ['144236563770334289'], 'label': '2-58835-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/58835/i'}