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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': -1, 'A7': 0, 'A8': 1, 'A9': 1, 'Lhash': '787133501758140480', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1115.110864227181, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [5, [1]], [7, [1]], [19, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '139650.1', 'coefficient_field': '1.1.1.1', 'conductor': 139650, 'conductor_radical': 3990, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1], [1], [1, -6, 11], [1, 0, 13], [1, -7, 17], [1, 1], [1, -6, 23], [1, 4, 29], [1, -8, 31], [1, -8, 37], [1, 10, 41], [1, 4, 43], [1, 0, 47], [1, -11, 53], [1, -5, 59], [1, 6, 61], [1, 13, 67], [1, 10, 71], [1, -2, 73], [1, 17, 79], [1, -7, 83], [1, -17, 89], [1, 1, 97]], 'gamma_factors': [[], [0]], 'index': 105, 'label': '2-139650-1.1-c1-0-105', 'leading_term': '5.37912859683', '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/139650/gu', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.379128596829138, 4.423091247760232, 2.046213103005771, -0.319358363807791, -1.049180149584883, 0.062786595568455, 1.115333933916449, -0.07453460497382693, -3.131119960646871, -4.949458500712805, -3.241545333074671, 0.3303736438560591, 1.974636760288941, 0.6468568124469044, -0.7652080977319189, 0.1212932407543698, 1.693183784813411, 1.249010687139876, -0.3827948522883534, -0.272413170435017, 1.426926398113144, 1.612351791362037, -0.2582453352459359, -1.10997319243105, 0.1343886832495538, 0.5871532798440782, -0.8568258927668349, -1.009855906016522, 1.182491385291945, 1.553659843260931, -1.303403601574095, -1.452200494281138, 4.386377364884139, 8.971909924554321, 5.469930979191102, -0.2289984795305443, 1.060947793050061, 6.033117242860867, 5.229247690058889, -0.002450497941221238, -1.066639665814966, 1.542573750966328, 0.3722236862039269, -3.883362270721832, -4.155834423810423, -0.7428825873915543, 0.4792406290319232, -0.3867184754254764, 0.06456372877486283, -0.02631446573849093, -2.57297511547632, -3.433497671801376, -0.848178545988248, -0.04224233476823507, -2.310784762702837, -1.919234112666699, 1.495756948131073, 1.83039637319032, -0.6122361120266578, -0.619257648905716, -0.03842750420961071, -2.455808959319537, -2.84336914124638, 2.228042804892509, 5.328748273046338, 2.15565153278965, -0.5536426339844205, 0.1036911823532199, -0.6016545259174721, -0.9958960572807461, 3.135998237375686, 4.676651962118908, -2.149358884161949, -6.84138233816291, -1.779334435839904, 2.787280975343503, 0.5875150473940522, 0.606264269179313, 4.714432104020557, 3.632550659628933, -0.6601260207763021, 1.288580184554899, 5.163438996599436, 2.798201991422764, -0.370391517393795, 1.019833549634956, 1.354063192069875, -0.954060016527118, -0.5858927655850337, 0.8905676645252162, -0.4522400588422392, -1.175655419715317, 0.02280964715193061, -0.6592451174414375, -1.097964471588908, 1.442676777051534, 1.37449688845318, -2.281442061490497, -2.126210640879254, 0.606773215993276, -0.1472001762936273, -0.01488884832709814, 2.620644047801977, -1.042092456794962, -7.005505448199124, -1.536497178083352, 7.821731619240293, 5.099091483829054, -1.921377991651585, -1.174221300651566, -0.3791737991159087, -3.681869085596915, -2.274508676025945, 1.320919677579293, -0.8579811167621988, -1.965650550480836, 2.401414287996872, 3.063075976799713, -0.5946835498504568, -0.6370145429262006, 0.436789878520605], 'positive_zeros': ['0.7079398798325962', '1.239702592185978', '1.742391026177852', '2.724706422864139', '3.333508130709373', '3.732703840541345', '4.430878430899003', '4.795845372175042', '5.467611854647063', '5.977068611880498', '6.368215795410473', '6.876442110483498', '7.396090499326210', '7.833535395008192', '8.732397098095685', '8.936444016830404', '9.749854911711931', '10.10191958134812', '10.52324365593308', '11.32246246875700', '11.63162029526996', '11.98221331448762', '12.24570042489373', '13.10266887949457', '13.24201079889612', '13.88882283919385', '14.42892147640372', '14.88289275855204', '14.98938780994012', '15.65604217154658', '16.40153666209381', '16.71608145500798', '16.89534396860846', '17.33472917340203', '17.93652575015995', '18.56403650810412', '19.06201186311533', '19.19216970777760', '19.94177054866905'], 'prelabel': '2-139650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.39327573370395, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 787133501758140480, 'z1': {'__RealLiteral__': 0, 'data': '0.7079398798325962', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.239702592185978', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.742391026177852', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1115.110864227181, 'bad_primes': [2, 3, 5, 7, 19], 'central_character': '1.1', 'conductor': 139650, 'conductor_radical': 3990, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 0, -1, 0, 1, 1, 0, 6, -1, 0, 0, 0, 1, 7, 1, -1, 0, 0, 6, 6, -1, 0, 0, -1, 0, -4, 0, 8, 1, -6, 7, 0, 1, 8, -1, 0, 0, -10, 0, -4, 6, 0, 6, 0, -1, 0, 0, -7, 0, 11, -1, 0, 0, 1, -4, 5, 0, -6, 8, 0, 1, 0, -6, -13, 7, -6, 0, -10, 1, 2, 8, 0, -1, 0, 0, -17, 0, 1, -10, 7, 0, 0, -4, 4, 6, 17, 0, 0, 6, -8, 0, 0, -1, -1, 0, 6, 0], 'euler11': [1, -6, 11], 'euler13': [1, 0, 13], 'euler17': [1, -7, 17], 'euler19': [1, 1, 0], 'euler2': [1, -1, 0], 'euler23': [1, -6, 23], 'euler29': [1, 4, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -8, 37], 'euler41': [1, 10, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -11, 53], 'euler59': [1, -5, 59], 'euler61': [1, 6, 61], 'euler67': [1, 13, 67], 'euler7': [1, 0, 0], 'euler71': [1, 10, 71], 'euler73': [1, -2, 73], 'euler79': [1, 17, 79], 'euler83': [1, -7, 83], 'euler89': [1, -17, 89], 'euler97': [1, 1, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 0, 0], [1, 0, 0], [1, -6, 11], [1, 0, 13], [1, -7, 17], [1, 1, 0], [1, -6, 23], [1, 4, 29], [1, -8, 31], [1, -8, 37], [1, 10, 41], [1, 4, 43], [1, 0, 47], [1, -11, 53], [1, -5, 59], [1, 6, 61], [1, 13, 67], [1, 10, 71], [1, -2, 73], [1, 17, 79], [1, -7, 83], [1, -17, 89], [1, 1, 97]], 'index': 105, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/139650/gu'], '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': '2-139650-1.1-c1-0-105', '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': '2-139650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.39327573370395, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 787133501758140480, 'z1': {'__RealLiteral__': 0, 'data': '0.7079398798325962', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '787133501758140480', 'Lhash_array': ['787133501758140480'], 'label': '2-139650-1.1-c1-0-105', 'type': 'ECQ', 'url': 'EllipticCurve/Q/139650/gu'}