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lfunc_lfunctions • Show schema
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{'A10': 2, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -2, 'A6': 0, 'A7': 1, 'A8': -1, 'A9': 0, 'Lhash': '295044095559333971', 'a10': [0.6324555320336759, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2069.57868966795, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [7, [1, -1]], [11, [1]], [17, [1, 1]]], 'bad_primes': [2, 3, 7, 11, 17], 'central_character': '259182.1', 'coefficient_field': '1.1.1.1', 'conductor': 259182, 'conductor_radical': 7854, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 2, 5], [1, -1], [1], [1, -4, 13], [1, 1], [1, 4, 19], [1, -8, 23], [1, -8, 29], [1, 4, 31], [1, -6, 37], [1, 6, 41], [1, 2, 43], [1, 10, 47], [1, 4, 53], [1, -14, 59], [1, 10, 61], [1, -8, 67], [1, 8, 71], [1, -14, 73], [1, 4, 79], [1, -16, 83], [1, -14, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 102, 'label': '2-259182-1.1-c1-0-102', 'leading_term': '5.19731985037', '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/259182/z', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.101189485365169, 1.187718239016547, 0.132888607555973, -0.8468892615067207, -0.286569540126343, 1.43256185291021, 1.916773502698072, -0.1806178817062437, -2.590457562878177, -1.890773965638649, 1.396187948520624, 2.865855386092201, 0.6513086776210165, -1.35651726361378, 0.3782170911987381, 2.786278131636959, 0.9837029425969485, -2.924572740808924, -2.720541935365216, 0.8840958835909516, 0.5009232720573852, -5.192323906752963, -8.222276890696312, -4.346120888781623, 0.1849726435835325, -0.03286434273113767, -1.070754854441332, 1.190415381438002, 3.043753498143224, 1.096965314391756, -0.9011573921923146, 0.003331551205563488, 0.6485410721530607, -0.385650054608108, 0.09178173180452176, 1.495546582085052, -0.2250450668272403, -2.716761019750677, -0.509257158425865, 3.27043760612803, 2.184086354103693, -0.9902813984977888, -0.7308185513876604, 0.2135564365465871, -1.208100306265512, -1.195854323780652, 0.3538291209063276, -2.013311996608536, -5.381608635273391, -2.342367694314204, 1.960960698189338, -0.7157566450885329, -3.230112170093714, 1.814671953635402, 4.099177759381905, -3.589185372782094, -8.857042338114091, -4.007482307669772, 0.3788380554584559, -0.9053979653400139, -0.3542006724746755, 2.136873093897373, 0.7439210585766776, -0.8315027064160938, 1.134088934513238, 1.060523001098539, -1.377192476575424, 0.2482669420039654, 3.006936007870629, 1.084501193949089, -0.4808227576621362, 1.599273241430407, 1.313010966410927, -1.130544964425302, -0.08409680748325649, 1.36101401173428, -0.02697230721600509, 0.4590254332805368, 1.958395721425281, -0.3528268313136919, -1.498305865466452, 1.423426432046566, 0.9096949512121871, -1.775428448037087, 1.03412675108728, 2.851630847910925, -0.7590247551666244, 2.819201265308076, 13.34333322076371, 12.55223735087032, 2.162261820294566, -1.025696017622954, 0.578638436960113, -0.6923964643031806, 1.169783826355515, 4.694857242925984, 1.551368747045166, -0.9818387520139867, 3.305227661218262, 4.348664131984721, 0.424687086821112, 0.0213800616977725, -0.3678711840323481, -4.146322847204267, -3.231462291106223, 1.31920060070512, 1.191179868181076, -0.2694007564944976, 0.5094808447949067, -0.1125464337493353, 0.2291331599849926, 2.716835376035939, 1.316802683733909, -0.9219400516802718, 1.031578815445034, 0.2677527631159995, -2.383481643906967, 1.896097386184653, 5.095777425546777, -0.1523384099692353], 'positive_zeros': ['0.7754723439433850', '1.296414104640936', '1.984365459701136', '2.648101652693151', '3.304691992328280', '3.718642361007202', '4.309292752615603', '4.933026804576104', '5.279756483928833', '6.231193458244456', '6.495418811756514', '6.901147686396039', '7.599173975666767', '7.999449166160492', '8.408819027004096', '8.735691468326171', '9.232219383414268', '9.778741859932121', '10.40294216891527', '10.87056800448334', '11.06480256962807', '11.65963871344174', '11.85140546584353', '12.60408623320482', '12.96288815608321', '13.43027938271185', '13.90487231334379', '14.69364674525473', '14.88210032603321', '15.28145251147044', '15.81810214674571', '16.13055624783570', '16.59731477080245', '16.98274270348712', '17.59580165709430', '17.83042341593984', '18.36713200570108', '18.75858970582864', '19.24484930199624', '19.43594003278194', '19.97281532699135'], 'prelabel': '2-259182-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 45.49262236525775, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 295044095559333971, 'z1': {'__RealLiteral__': 0, 'data': '0.7754723439433850', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.296414104640936', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.984365459701136', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2069.57868966795, 'bad_primes': [2, 3, 7, 11, 17], 'central_character': '1.1', 'conductor': 259182, 'conductor_radical': 7854, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -2, 0, 1, -1, 0, 2, 0, 0, 4, -1, 0, 1, -1, 0, -4, -2, 0, 0, 8, 0, -1, -4, 0, 1, 8, 0, -4, -1, 0, 1, -2, 0, 6, 4, 0, 2, -6, 0, -2, 0, 0, -8, -10, 0, 1, 1, 0, 4, -4, 0, 0, -1, 0, -8, 14, 0, -10, 4, 0, 1, -8, 0, 8, -1, 0, 2, -8, 0, 14, -6, 0, -4, 0, 0, -4, -2, 0, 6, 16, 0, 2, 2, 0, 0, 14, 0, 4, 8, 0, 10, 8, 0, 12, -1, 0, -1], 'euler11': [1, 0, 0], 'euler13': [1, -4, 13], 'euler17': [1, 1, 0], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, -8, 23], 'euler29': [1, -8, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, 2, 43], 'euler47': [1, 10, 47], 'euler5': [1, 2, 5], 'euler53': [1, 4, 53], 'euler59': [1, -14, 59], 'euler61': [1, 10, 61], 'euler67': [1, -8, 67], 'euler7': [1, -1, 0], 'euler71': [1, 8, 71], 'euler73': [1, -14, 73], 'euler79': [1, 4, 79], 'euler83': [1, -16, 83], 'euler89': [1, -14, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 2, 5], [1, -1, 0], [1, 0, 0], [1, -4, 13], [1, 1, 0], [1, 4, 19], [1, -8, 23], [1, -8, 29], [1, 4, 31], [1, -6, 37], [1, 6, 41], [1, 2, 43], [1, 10, 47], [1, 4, 53], [1, -14, 59], [1, 10, 61], [1, -8, 67], [1, 8, 71], [1, -14, 73], [1, 4, 79], [1, -16, 83], [1, -14, 89], [1, -12, 97]], 'index': 102, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/259182/z'], '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': '2-259182-1.1-c1-0-102', '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': '2-259182-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 45.49262236525775, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 295044095559333971, 'z1': {'__RealLiteral__': 0, 'data': '0.7754723439433850', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '295044095559333971', 'Lhash_array': ['295044095559333971'], 'label': '2-259182-1.1-c1-0-102', 'type': 'ECQ', 'url': 'EllipticCurve/Q/259182/z'}