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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '826221017169230620', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 129.22989063124024, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, 1]], [17, [1]]], 'bad_primes': [2, 7, 17], 'central_character': '16184.1', 'coefficient_field': '1.1.1.1', 'conductor': 16184, 'conductor_radical': 238, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1, 2, 5], [1, 1], [1, -2, 11], [1, 2, 13], [1], [1, -4, 19], [1, -4, 23], [1, 2, 29], [1, -8, 31], [1, -2, 37], [1, 0, 41], [1, -4, 43], [1, 12, 47], [1, 14, 53], [1, -12, 59], [1, -10, 61], [1, -4, 67], [1, -12, 71], [1, -4, 73], [1, -4, 79], [1, 12, 83], [1, -6, 89], [1, 0, 97]], 'gamma_factors': [[], [0]], 'index': 0, 'label': '2-16184-1.1-c1-0-0', 'leading_term': '0.810778434761', '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/16184/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.8107784347614325, 0.5595520863597259, -0.09381614203227613, -0.7856737495775012, -0.8911730631910363, 0.1467708343460416, 2.259987533415771, 4.451473238724962, 5.227332441047569, 3.699048548784325, 0.5398947813781425, -2.214907257724424, -2.691515251211814, -0.8493966359653747, 1.354069975731229, 1.738327283758445, 0.03129421199273828, -1.879272898744711, -2.012503730107269, -0.5067222146508514, 0.5910516686937834, -0.1601030595449848, -1.761801162068793, -2.001977034370303, -0.3399535637808216, 1.288032417981088, 1.010526737806573, -0.3425132180244011, -0.2582396684166494, 1.844339808794056, 3.40377170865416, 2.08621612149201, -0.5690437206891318, -0.6405980676816748, 2.894702899992529, 6.223117803908666, 5.325089828304006, 1.299868534241182, -1.014838469609285, 0.5149123060022376, 2.688408160645528, 1.757546874054728, -1.341663065885435, -2.737730271078974, -1.330838031306098, 0.1986441152019703, 0.05606691966508196, -0.1814838168250064, 0.9444689538040458, 1.735547550251006, 0.4403219924814587, -0.7427430348399509, 1.451235238878589, 5.275447844812008, 5.214605109272234, 0.1874356005113373, -3.883686620543413, -2.236269146331005, 1.766330436864439, 1.801551968966545, -1.979598087448688, -3.846908004504203, -1.697331953454608, 0.417025812031297, -0.3274133921334712, -1.304145670334542, 0.03893616581044435, 1.496767625823269, 0.5564433246608357, -0.7141616609100032, 0.2959473685787076, 1.330519806833982, -0.8118713618765212, -3.67691525657185, -2.565976520749459, 1.221528660241368, 2.261004300191881, 0.290354553681716, 0.2536501150078087, 2.755023690740117, 2.562778347363765, -1.364911301881208, -2.667033295283655, 1.737826148583641, 5.535674551397925, 2.993157787806455, -1.810257057594282, -2.178039907547821, 0.6787043417513874, 1.466111396588572, 0.1800868045571973, 0.1043236173305947, 0.5748178220062773, -0.6848593953783155, -1.657610504687964, 0.1534118034485505, 1.796675044025015, 0.216842365508056, -0.8502024061085723, 2.458381717647325, 5.422843188111016, 2.258484229232268, -2.347750412787357, -0.1500928274415387, 6.133937929603625, 7.046744611639677, 2.146252895955854, -0.6927765979040115, 0.462690118601761, 0.3863891563953006, -1.739046645450604, -1.548513579810358, 0.7348355432870107, 0.8857829113075214, -0.389230382179712, 0.5672797777233071, 1.992763501839235, 0.3649305177536144, -1.407813116741481, 0.4359259673305736, 1.936408819797879], 'positive_zeros': ['0.4688997943609977', '1.227217092623877', '2.540853776649938', '3.336215833968429', '4.003513856706236', '4.830469806307065', '5.222962080048572', '6.041089734273581', '6.679047673019052', '7.043094233052944', '7.937281611542202', '8.313581118506352', '9.343218833800638', '9.699893848600391', '10.39283817582267', '11.19503957099078', '11.52253801843719', '11.81630121752600', '12.55843172617478', '12.88724651370797', '13.75807937839698', '14.37905913483692', '14.87852515604695', '15.66540840594199', '15.94598825674874', '16.49527100637317', '17.07934702646598', '17.45729505980171', '17.93712276258081', '18.66533344415639', '19.29777523820917', '19.45962817696207'], 'prelabel': '2-16184-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.367932557472367, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 826221017169230620, 'z1': {'__RealLiteral__': 0, 'data': '0.4688997943609977', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.227217092623877', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.540853776649938', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 129.22989063124024, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 16184, 'conductor_radical': 238, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, -2, 0, -1, 0, 1, 0, 2, 0, -2, 0, 4, 0, 0, 0, 4, 0, 2, 0, 4, 0, -1, 0, 4, 0, -2, 0, 8, 0, -4, 0, 2, 0, 2, 0, 4, 0, 0, 0, 4, 0, -2, 0, -12, 0, 1, 0, 0, 0, -14, 0, -4, 0, -8, 0, 12, 0, 10, 0, -1, 0, 4, 0, 4, 0, -8, 0, 12, 0, 4, 0, 2, 0, -2, 0, 4, 0, -11, 0, -12, 0, 0, 0, 4, 0, 6, 0, 2, 0, -16, 0, -8, 0, 0, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 0], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 2, 29], 'euler3': [1, 2, 3], 'euler31': [1, -8, 31], 'euler37': [1, -2, 37], 'euler41': [1, 0, 41], 'euler43': [1, -4, 43], 'euler47': [1, 12, 47], 'euler5': [1, 2, 5], 'euler53': [1, 14, 53], 'euler59': [1, -12, 59], 'euler61': [1, -10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 0], 'euler71': [1, -12, 71], 'euler73': [1, -4, 73], 'euler79': [1, -4, 79], 'euler83': [1, 12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 0, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 2, 5], [1, 1, 0], [1, -2, 11], [1, 2, 13], [1, 0, 0], [1, -4, 19], [1, -4, 23], [1, 2, 29], [1, -8, 31], [1, -2, 37], [1, 0, 41], [1, -4, 43], [1, 12, 47], [1, 14, 53], [1, -12, 59], [1, -10, 61], [1, -4, 67], [1, -12, 71], [1, -4, 73], [1, -4, 79], [1, 12, 83], [1, -6, 89], [1, 0, 97]], 'index': 0, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/16184/b'], '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': '2-16184-1.1-c1-0-0', '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': '2-16184-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.367932557472367, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 826221017169230620, 'z1': {'__RealLiteral__': 0, 'data': '0.4688997943609977', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '826221017169230620', 'Lhash_array': ['826221017169230620'], 'label': '2-16184-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/16184/b'}