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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': -1, 'A8': 0, 'A9': 1, 'Lhash': '1369128937043926185', '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': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, 1]], [11, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '369600.1', 'coefficient_field': '1.1.1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 1], [1, 1], [1, 4, 13], [1, 4, 17], [1, 4, 19], [1, 2, 23], [1, 10, 29], [1, 4, 31], [1, -4, 37], [1, 6, 41], [1, 0, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, -14, 61], [1, -2, 67], [1, -12, 71], [1, 6, 73], [1, 0, 79], [1, 0, 83], [1, 4, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 121, 'label': '2-369600-1.1-c1-0-121', 'leading_term': '2.85321745015', '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/369600/s', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.4437741053956932, -0.4508432778689959, -2.666946808154471, -4.290099525056735, -3.242822872241392, -0.1713463300971908, 1.639515722403103, 0.4755638835916415, -1.009410350403112, 0.4692352831221222, 3.2552406864503, 2.618534494022529, -1.595416411436172, -3.922986442253161, -1.739787089112087, 0.4983679336204791, -1.011704327023882, -2.976281912221403, -1.484265517975529, 0.6290509883013584, -0.4390840088467199, -1.826120635092857, 0.1459035306331266, 2.245247793017583, 0.8048643037164993, -0.6160333942106923, 1.284100460207859, 2.372581792036625, 0.1145290596114142, -0.246322820751304, 2.962202785375215, 2.859528207866516, -1.72728731011604, -2.234041791747205, 2.753456663408348, 4.186692637671611, 0.5355020172836519, -0.3759562211712876, 1.470789870048291, -0.2796311372331463, -3.038043940932901, -1.172919560671323, 1.077197996221364, -0.3888193140633636, -0.4338964413094917, 2.150243389215434, 1.044600596513598, -2.343109063889884, -1.356522728721601, 0.8011905442130993, -0.7815155041185451, -1.360662878923579, 0.1911779046224883, -2.633005105920804, -6.204926767158191, -1.794181353007918, 3.845310751374342, 1.35480810641393, -1.934148896287084, 0.05223116991469223, -0.2553044871161487, -3.605843909084981, -2.126602823904909, 0.6422944037264225, -1.667890665311588, -2.905416014940458, -0.04421975117248923, 0.3983999533289789, -0.330604087002985, 1.940067014450189, 1.410431282059408, -2.545931936014128, -1.516245090730255, 1.722736482329935, 0.4403633818060788, 0.9805383431006311, 5.060475564456044, 3.207110334671385, -1.542074703620742, -0.5381495866476818, -0.5580617694664343, -4.507270974573827, -1.87407057205767, 4.167717357371493, 2.0746036759925, -1.774614010411832, 0.07808508848309453, 0.7094705727123215, -0.5140210753283686, 0.9910749795362026, -0.1192824033279754, -3.652681452587452, -1.637748934527458, 1.068120425152653, -1.110773968517336, -1.027256345438277, 0.5625304421065851, -2.043796851409923, -1.194412167512764, 3.906783832134737, 1.924506895137156, -1.93858255041241, 1.358552142175631, 1.788183639305399, -3.025884491822518, -2.155869910791867, 0.03348813002111092, -2.297082127194809, -0.5029769148251604, 3.302096487722146, 0.6318937222058294, -1.174135247306166, 0.711906281699975, -1.43262315419944, -3.075387390368734, -0.215250633022999, -0.1128598818639896, -0.5073674047018965, 1.917812643169856, 0.06523636214351732], 'positive_zeros': ['0.4241539145650760', '1.514325464867429', '2.057907111246929', '2.457042114291156', '3.161853137111387', '3.901789828523036', '4.146147331481811', '4.891862137568460', '5.197445240809387', '5.737983083601686', '6.336936032024227', '6.619982843795109', '7.262137693118459', '7.526267382907660', '8.157546523509262', '8.621406990718498', '9.293618596023836', '9.550295038745400', '9.980143181274653', '10.58928629766992', '10.95188359834005', '11.29537886442156', '11.81841605242210', '12.36582609751932', '12.66605254003604', '13.18783194744445', '13.31876981797568', '14.06004542385567', '14.56835681942587', '14.99450388533045', '15.22820713998971', '15.89628214875130', '16.12183529563261', '16.75434154611889', '17.06894289133166', '17.30732408680205', '17.83615386279495', '18.34283352791963', '18.82296396721687', '18.89390966830975', '19.64410275340692'], 'prelabel': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1369128937043926185, 'z1': {'__RealLiteral__': 0, 'data': '0.4241539145650760', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.514325464867429', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.057907111246929', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2951.2708587065245, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 369600, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -1, 0, 1, 0, -1, 0, -4, 0, 0, 0, -4, 0, -4, 0, 1, 0, -2, 0, 0, 0, -1, 0, -10, 0, -4, 0, 1, 0, 0, 0, 4, 0, 4, 0, -6, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, -6, 0, 0, 0, 4, 0, -12, 0, 14, 0, -1, 0, 0, 0, 2, 0, 2, 0, 12, 0, -6, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 10, 0, -4, 0, 4, 0, 4, 0, 0, 0, 10, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, 4, 13], 'euler17': [1, 4, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, 10, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -4, 37], 'euler41': [1, 6, 41], 'euler43': [1, 0, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, 12, 59], 'euler61': [1, -14, 61], 'euler67': [1, -2, 67], 'euler7': [1, 1, 0], 'euler71': [1, -12, 71], 'euler73': [1, 6, 73], 'euler79': [1, 0, 79], 'euler83': [1, 0, 83], 'euler89': [1, 4, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 4, 13], [1, 4, 17], [1, 4, 19], [1, 2, 23], [1, 10, 29], [1, 4, 31], [1, -4, 37], [1, 6, 41], [1, 0, 43], [1, 0, 47], [1, 6, 53], [1, 12, 59], [1, -14, 61], [1, -2, 67], [1, -12, 71], [1, 6, 73], [1, 0, 79], [1, 0, 83], [1, 4, 89], [1, -10, 97]], 'index': 121, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/369600/s'], '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': '2-369600-1.1-c1-0-121', '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': '2-369600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 54.32560039895118, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1369128937043926185, 'z1': {'__RealLiteral__': 0, 'data': '0.4241539145650760', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1369128937043926185', 'Lhash_array': ['1369128937043926185'], 'label': '2-369600-1.1-c1-0-121', 'type': 'ECQ', 'url': 'EllipticCurve/Q/369600/s'}