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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': -4, 'A8': -1, 'A9': 1, 'Lhash': '133235012071059853', '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': [-1.5118578920369088, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2463.7841543666073, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1]], [11, [1]], [17, [1, 1]]], 'bad_primes': [2, 3, 5, 11, 17], 'central_character': '308550.1', 'coefficient_field': '1.1.1.1', 'conductor': 308550, 'conductor_radical': 5610, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1], [1, 4, 7], [1], [1, -2, 13], [1, 1], [1, -4, 19], [1, 0, 23], [1, -6, 29], [1, -8, 31], [1, -10, 37], [1, 6, 41], [1, 4, 43], [1, 12, 47], [1, 6, 53], [1, -12, 59], [1, 2, 61], [1, 8, 67], [1, 12, 71], [1, -2, 73], [1, 8, 79], [1, 12, 83], [1, 6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 4, 'label': '2-308550-1.1-c1-0-4', 'leading_term': '0.28859476971', '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/308550/h', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.288594769709654, -0.2201922845079059, -1.22348774021562, -1.55098211092524, -0.6801099848435986, 0.1030968290486844, -1.181915061441667, -4.227724507536858, -5.749619953019244, -3.420597426995018, 0.3565286965711115, 1.261519530265738, -0.48464359032553, -0.2476449626678865, 3.160859159898138, 4.493675816393121, 0.5092289347957708, -3.371844769631897, -0.917903173661018, 4.2511611929521, 3.937526590415625, -1.22732635051168, -3.215724341355488, -0.2353704556575324, 1.638545811370494, 0.2730334832483756, -0.2668116439602999, 0.478698856130415, -1.070625711915015, -3.18424253947537, -1.070639749770996, 2.545501481481045, 1.587739906613578, -1.335561004584061, -0.08149862973443103, 2.585545290211759, 0.9951669957914193, -1.81165124612724, -1.039894119967951, 0.3891790267133525, -0.2088548026342041, 0.3725545813218357, 1.809755822830625, -0.4409633507591049, -3.754882046132277, -2.402297510042565, 0.06432444367921968, -1.013852610487539, -0.6469401621968699, 3.275062186420786, 3.268916516259261, -0.7548940570333067, -0.2152323783819182, 2.426678081694677, -0.3016374623557057, -0.8597955879805916, 7.595009384126702, 11.59699498980643, 2.460892568830582, -4.476836672560397, 0.4696829594360887, 4.771306686211742, 1.618432157292016, -0.4919069612385982, 0.3566401681760264, -0.5081376366567543, -0.7024355986539093, 0.7285280478989686, -0.9795317682999065, -3.303237853438704, -1.265936725327245, 0.3920455995394249, -1.020488456566701, -0.05991514084582531, 2.040771657670869, 0.4665144777680913, -0.3219650527178303, 1.776393664280017, 0.9322847361338169, -0.6679094907755504, 1.513686985182419, 0.5884084297616609, -4.101885294159942, -1.797844388835816, 3.55778025729527, 0.5572464308713246, -2.694585668830998, 1.868187202822719, 3.386595877490738, -0.6754241905254137, -0.2181078494814233, 1.107282615080414, -2.389798695581737, -2.429212140807047, 0.159875503005223, -3.516840581602568, -5.252643027348166, 1.365040256257962, 3.430363133715073, -1.348891013138141, -1.185159603197242, 0.9979101141041727, -1.047585947803254, -0.5995597958561889, 1.783828697644818, -0.5730972158052691, -2.086845836238964, 0.06287632979182847, -0.3315254790294269, 0.2507902114006825, 5.001967888864585, 5.003710562122494, 0.3621234524650394, -0.4221987312092837, 0.1261179856671106, -0.6282522044964238, 0.2851610604170183, -0.6417503610828936, -2.711778020461849, 0.110280806102663, 0.8053629270930872], 'positive_zeros': ['0.1844792744605169', '1.169926536596563', '1.321575125069958', '2.470729236992899', '2.932063530617283', '3.275074670661814', '4.023691386322010', '4.541656004584977', '5.190839731265652', '5.767067524078785', '6.295286966343102', '6.577272974873611', '6.886129811367520', '7.563229071063593', '8.115556545566336', '8.506298545161316', '9.071647629942965', '9.637404849134472', '9.934057778549646', '10.18995308632263', '10.72184729395197', '11.48035136752343', '11.58896797850063', '12.04849430639541', '12.69400343725032', '13.01590119424420', '13.48152286773847', '13.78941242322609', '14.55572752720278', '14.98420055343656', '15.62099060044343', '15.88930752954788', '16.15932004867232', '16.60754095854144', '16.91756712786861', '17.61803501066845', '17.84004566222619', '18.25556442700316', '18.80168205311420', '19.04697751887629', '19.59112071187877', '19.85642912054175'], 'prelabel': '2-308550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 49.63652036924634, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 133235012071059853, 'z1': {'__RealLiteral__': 0, 'data': '0.1844792744605169', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.169926536596563', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.321575125069958', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2463.7841543666073, 'bad_primes': [2, 3, 5, 11, 17], 'central_character': '1.1', 'conductor': 308550, 'conductor_radical': 5610, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, -4, -1, 1, 0, 0, -1, 2, 4, 0, 1, -1, -1, 4, 0, 4, 0, 0, 1, 0, -2, -1, -4, 6, 0, 8, -1, 0, 1, 0, 1, 10, -4, -2, 0, -6, -4, -4, 0, 0, 0, -12, -1, 9, 0, 1, 2, -6, 1, 0, 4, -4, -6, 12, 0, -2, -8, -4, 1, 0, 0, -8, -1, 0, 0, -12, -1, 2, -10, 0, 4, 0, 2, -8, 0, 1, 6, -12, 4, 0, 4, -6, 0, -6, 0, -8, 0, -8, 12, 0, 1, -2, -9, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, -2, 13], 'euler17': [1, 1, 0], 'euler19': [1, -4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -10, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 12, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -12, 59], 'euler61': [1, 2, 61], 'euler67': [1, 8, 67], 'euler7': [1, 4, 7], 'euler71': [1, 12, 71], 'euler73': [1, -2, 73], 'euler79': [1, 8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 0], [1, 4, 7], [1, 0, 0], [1, -2, 13], [1, 1, 0], [1, -4, 19], [1, 0, 23], [1, -6, 29], [1, -8, 31], [1, -10, 37], [1, 6, 41], [1, 4, 43], [1, 12, 47], [1, 6, 53], [1, -12, 59], [1, 2, 61], [1, 8, 67], [1, 12, 71], [1, -2, 73], [1, 8, 79], [1, 12, 83], [1, 6, 89], [1, 2, 97]], 'index': 4, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/308550/h'], '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': '2-308550-1.1-c1-0-4', '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': '2-308550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 49.63652036924634, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 133235012071059853, 'z1': {'__RealLiteral__': 0, 'data': '0.1844792744605169', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '133235012071059853', 'Lhash_array': ['133235012071059853'], 'label': '2-308550-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/308550/h'}