Formats: - HTML - YAML - JSON - 2026-05-02T07:33:18.146140
Query: /api/lfunc_lfunctions/?_offset=0
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1674913732452192988', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 356.83547655269797, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [7, [1]], [19, [1, -1]]], 'bad_primes': [2, 3, 7, 19], 'central_character': '44688.1', 'coefficient_field': '1.1.1.1', 'conductor': 44688, 'conductor_radical': 798, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -2, 5], [1], [1, -4, 11], [1, 2, 13], [1, -6, 17], [1, -1], [1, 0, 23], [1, 10, 29], [1, -8, 31], [1, 2, 37], [1, 6, 41], [1, 4, 43], [1, 8, 47], [1, -6, 53], [1, 4, 59], [1, -10, 61], [1, 8, 67], [1, 12, 71], [1, -14, 73], [1, -4, 79], [1, 4, 83], [1, 6, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'id': 7846167, 'index': 83, 'label': '2-44688-1.1-c1-0-83', 'leading_term': '6.46067916386', '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/44688/bm', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.504467572220269, 2.35754714745759, 2.091887836343986, 0.8654131508245558, -0.3389193766279512, -0.3685771268694622, 0.893181304906031, 2.039486876859855, 1.317563477177078, -1.352601287021684, -3.782550787511512, -3.55875810060094, -0.8651136434258434, 1.333823664851626, 0.5362324828681233, -2.213912596043807, -3.43189115370855, -1.495829268866467, 1.299560580112057, 1.816538136973736, 0.2110188956305501, -0.647387466816385, 0.4005713043653019, 1.19201505321661, -0.02563166252084891, -1.435413233677368, -0.4895905082107728, 1.482991138795265, 0.8146094729708588, -2.387969804211286, 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0.4198918772983534, 1.579715545231249, -0.7487833344738742, -0.04452207545933617, 2.39600344583049, 1.512618354702382, -0.310153647421737, 0.8265152164188551, 1.632715870566288, -0.1483046174233683, 0.2984859848305803, 3.866388492464735, 3.815895040914201, -0.4702182217572384, -1.318199711460976, 1.938157382288735, 2.188986003589889, -0.4429537027414456, -0.2357819798255912, 0.6572618091659026, -2.320038491388435, -4.288944031015007, -0.9087435028095596, 0.946171467015962, -3.015115596817966, -4.923019978033341, -0.846085659547903, 1.388969156868915, -1.171865785841703, -1.784364767942432, 0.315129778864754, -0.5024524718061669, -2.223160404463956, 0.1998413204844402, 2.690218484214105, 0.7868579298054444, -0.9376553115020634, 0.1158011720484237, -0.007421192691588254], 'positive_zeros': ['1.162084855780186', '1.593784312272460', '2.386637622302613', '3.324325471108684', '3.803966824451326', '4.622313188641969', '5.281956984737790', '5.679538425723471', '6.246566277134628', '6.806279733588987', '7.321298842379672', '8.004159166560160', '8.607101624401666', '9.439124078587726', '9.688355327293514', '10.07688391778665', '10.68840103448215', '11.44080483370212', '11.92248945009487', '12.08301223187036', '12.91474954550532', '13.34576461425909', '13.90958649170243', '14.36675793973701', '14.88200467330003', '15.27421289787631', '16.07457526174926', '16.68439695126662', '16.93153030181855', '17.20556050102500', '17.88554966223138', '18.24706493053580', '18.86826337038522', '19.32313937686557', '19.70699201096956'], 'prelabel': '2-44688-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 18.890089373867397, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1674913732452192988, 'z1': {'__RealLiteral__': 0, 'data': '1.162084855780186', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.593784312272460', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.386637622302613', 'prec': 57}}