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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': -1, 'A8': 1, 'A9': 0, 'Lhash': '1268389921598987414', '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': [-0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 276.68164300373667, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '34650.1', 'coefficient_field': '1.1.1.1', 'conductor': 34650, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1, -1], [1], [1], [1, 1], [1, -1], [1, -4, 13], [1, 0, 17], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, 10, 31], [1, 2, 37], [1, -12, 41], [1, -4, 43], [1, -6, 47], [1, 6, 53], [1, -6, 59], [1, 4, 61], [1, -4, 67], [1, 12, 71], [1, -4, 73], [1, -8, 79], [1, -12, 83], [1, 18, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 40, 'label': '2-34650-1.1-c1-0-40', 'leading_term': '3.82810304962', '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/34650/dm', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.828103049618496, 3.186875599462115, 1.427690722643179, -0.8071358070650508, -2.374454808639673, -2.253584003760714, -0.4894494065296239, 1.531045830158919, 2.080395690842667, 0.6989181472974079, -1.207928741772567, -1.685304895858649, -0.3027161116324115, 1.335274212436201, 1.450667400512064, 0.2547410918481791, -0.34856073087619, 0.6443422778562914, 1.795254309568731, 1.050214503897159, -1.285551303198548, -2.637616746098621, -1.570536680651556, 0.164644325841945, 0.135072084502733, -1.142970352150404, -1.020136455570145, 0.8891575938323606, 1.569017987830076, -0.7987006812308213, -3.260457767733442, -1.850675631150362, 2.14691382865431, 3.322172047289309, -0.01001855232310807, -2.980878834843941, -1.421392251782295, 1.5335548307439, 0.1323095483209851, -4.839584310558794, -6.886476338844608, -3.589246467413579, 0.08248323965688117, -0.04562222744868898, -1.274316376593614, 0.3334313161896493, 2.83973179707953, 2.045352775617706, -0.9451460920093172, -1.635789435735731, 0.168301696281284, 0.6940898556049921, -0.561194080953029, -0.273548047900431, 1.883346250705109, 2.336665875253666, 0.5045446589801015, 0.06672339486613195, 1.778365552757273, 1.737931972756019, -0.9949221263005856, -2.070232840466496, 0.06633700085755276, 1.103834717109358, -0.7611338644322762, -1.288287644246687, 0.9026624010085113, 0.5526642100243289, -3.951359536956041, -5.770226712647184, -1.545177896994698, 1.482697986800553, -1.941434033868231, -5.197605387019673, -1.647246596044105, 3.285525976288231, 2.237086275073702, -1.089818252581516, -0.1209280150517196, 2.086852899780189, -0.06209917548456576, -3.282463451215624, -2.24046422852466, 0.05156123468640069, -0.9743603085344079, -2.311520665254741, -0.4105676615194766, 1.209575449373185, -0.3504823937355114, -1.218691643445975, 0.8330928936943057, 1.702499605363444, -0.08286517519159353, -0.4037035871267756, 1.164946816056326, 0.653476262605065, -0.6432342031717879, 1.732248650617118, 4.84197354922528, 2.994150749967897, -0.6937010259590317, -0.5893962142138419, 0.1612754482022005, -2.267590365343908, -2.829637053806407, 0.9489616517951692, 0.9866383410290808, -5.494881578957147, -7.999824920073291, -2.000196923841084, 2.182351796542657, -0.5867296210866153, -1.717202818369105, 2.006519642815466, 2.396263563362548, -1.934763959172848, -2.841262239292078, 0.1044750453969019, 0.02863446560054355, -1.914999732334652, -0.3122534406598538], 'positive_zeros': ['0.6585681453153803', '1.555076575074961', '2.335160706137482', '3.039944981409309', '3.805541923145240', '4.128217712839053', '4.869033378646049', '5.716306537379260', '6.029971041189450', '6.642446924242284', '7.186670248727971', '7.866250736101080', '8.499411191731756', '9.102028840465362', '9.508014642068758', '10.48964553836762', '10.74267107598515', '11.22016400250661', '11.91608588515713', '12.47676092733315', '12.89181150214366', '13.28744567104585', '14.09275999660240', '14.23274439277464', '14.91555443007619', '15.49328030826100', '15.91400875927047', '16.40302054459445', '16.79028706132100', '17.57884830132357', '17.89962659992706', '18.56820203419245', '19.14590890308352', '19.51044244054457', '19.99603473839971'], 'prelabel': '2-34650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.63375011847108, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1268389921598987414, 'z1': {'__RealLiteral__': 0, 'data': '0.6585681453153803', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.555076575074961', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.335160706137482', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 276.68164300373667, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 34650, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, -1, 1, 0, 0, 1, 0, 4, -1, 0, 1, 0, 0, -4, 0, 0, 1, 0, 0, 0, 4, 0, -1, 6, 0, -10, 1, 0, 0, 0, 0, -2, -4, 0, 0, 12, 0, 4, 1, 0, 0, 6, 0, 1, 0, 0, 4, -6, 0, 0, -1, 0, 6, 6, 0, -4, -10, 0, 1, 0, 0, 4, 0, 0, 0, -12, 0, 4, -2, 0, -4, -1, 0, 8, 0, 0, 12, 12, 0, 0, 4, 0, 1, -18, 0, -4, 0, 0, 6, 0, 0, 10, 1, 0, 0], 'euler11': [1, -1, 0], 'euler13': [1, -4, 13], 'euler17': [1, 0, 17], 'euler19': [1, 4, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 10, 31], 'euler37': [1, 2, 37], 'euler41': [1, -12, 41], 'euler43': [1, -4, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -6, 59], 'euler61': [1, 4, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 12, 71], 'euler73': [1, -4, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 18, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -4, 13], [1, 0, 17], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, 10, 31], [1, 2, 37], [1, -12, 41], [1, -4, 43], [1, -6, 47], [1, 6, 53], [1, -6, 59], [1, 4, 61], [1, -4, 67], [1, 12, 71], [1, -4, 73], [1, -8, 79], [1, -12, 83], [1, 18, 89], [1, -10, 97]], 'index': 40, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/34650/dm'], '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': '2-34650-1.1-c1-0-40', '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': '2-34650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.63375011847108, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1268389921598987414, 'z1': {'__RealLiteral__': 0, 'data': '0.6585681453153803', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1268389921598987414', 'Lhash_array': ['1268389921598987414'], 'label': '2-34650-1.1-c1-0-40', 'type': 'ECQ', 'url': 'EllipticCurve/Q/34650/dm'}