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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': 2, 'A8': -3, 'A9': 1, 'Lhash': '1205915504719269020', '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': [0.7559289460184544, 0], 'a8': [-1.0606601717798212, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1024.2490917671662, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [11, [1, 1]], [13, [1]], [23, [1, -1]]], 'bad_primes': [3, 11, 13, 23], 'central_character': '128271.1', 'coefficient_field': '1.1.1.1', 'conductor': 128271, 'conductor_radical': 9867, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, 1], [1, 0, 5], [1, -2, 7], [1, 1], [1], [1, 0, 17], [1, 2, 19], [1, -1], [1, 10, 29], [1, 4, 31], [1, 2, 37], [1, -2, 41], [1, -2, 43], [1, -8, 47], [1, 4, 53], [1, -12, 59], [1, 6, 61], [1, 2, 67], [1, 0, 71], [1, -6, 73], [1, -2, 79], [1, 4, 83], [1, -8, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 0, 'label': '2-128271-1.1-c1-0-0', 'leading_term': '0.893389658268', '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/128271/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.893389658267751, 0.1414252578914181, -1.60105918834242, -2.904187335508789, -2.258050151957322, 0.3352018897843691, 2.733953754649177, 2.515000034107617, -0.1071569398818236, -1.940881616289483, -0.3311720657671092, 3.348580836627838, 5.054837339055569, 3.109659596505725, 0.2570405966604834, -0.2820628243775137, 0.8721467732778662, 0.900228490739879, -0.4807047502477241, -0.928216395942252, 0.1212151011201066, 0.5038094700816453, -0.4256057781639816, -0.4570047433163724, 0.7887538638709783, 0.0803051584099118, -3.460418062619552, -5.082859342546281, -1.705563938517851, 1.880421098217372, 0.3296373085189691, -2.836141203148785, -1.157066740971332, 2.906799049619584, 1.994474708882919, -2.633081666287797, -3.106931698983614, 0.5454299888084435, 0.6161822016129977, -3.324971958364378, -3.284556492870078, 1.898743575842179, 4.105670922986597, 0.9162138918144325, -0.8984288224293081, 0.9737348192349821, 1.156528299175749, -1.315615191665463, -1.376646297152114, 0.9195723656853163, 0.7631828856867494, -1.019527321298145, -0.3658053339073904, 0.7781238619073285, -0.7764943147065289, -1.686906217987257, 0.5439565052497225, 1.441706852222337, -0.7449781929704044, -1.071158917824391, 0.735217196722657, -0.4538441505231342, -2.438651275371268, 0.7051070278596684, 4.302823427322443, 1.006772782915734, -3.418000985957106, -1.075519669676129, 2.428985820962456, 0.6472148480458235, -1.089698972089905, 0.4790190176567859, -0.3728289200145638, -3.194807070866074, -1.594739134046154, 0.7475029309878617, -1.892788633411906, -1.524917823739306, 7.250644592768459, 11.82262252022127, 4.580138418629437, -1.784659086351876, 0.8191260769660669, 3.078697151256652, 0.4312121924861316, -0.5020673883840151, 0.5375751959647667, -1.031303139650378, -2.227426670584785, -0.414085385242033, 0.1962539823668635, -0.5507645221921686, 1.034965681748127, 2.234275635717726, 0.4923723496882602, -0.2538908268836917, 0.04286750942460562, -1.532112797590111, -0.4406260236164887, 4.278630459775833, 2.812014425908991, -3.822374533713045, -2.090326189325243, 4.750961102259023, 2.061327072981064, -4.521233306511633, -1.983309484676378, 2.340083082213305, -0.296177706214221, -2.020610968965761, 0.02339703176449955, -0.9008438567497495, -1.368272835217748, 2.70600599345432, 2.723293006388086, -1.999756160774329, -0.4464070978044952, 4.482075137705954, 2.474109654418497, -1.087828085668108, 0.2070693574438892], 'positive_zeros': ['0.2740697612663297', '1.221894239416051', '1.990730208916066', '2.524709355132623', '3.536209223097084', '3.821203865401426', '4.416651995583703', '4.973711484313525', '5.396778860569447', '5.845168544812811', '6.257783077424973', '7.091946393983775', '7.521996597555198', '8.064984120871747', '8.606779255485796', '9.209072916087548', '9.545580024667254', '10.16417188592095', '10.81745235586309', '11.14114383828775', '11.62041558236618', '12.14429295284617', '12.59510321947257', '13.05158085169672', '13.41026305720696', '13.94893931926366', '14.42198078364747', '14.88513673294842', '15.20766401379188', '15.71482462767193', '16.29278628548286', '16.80628330787931', '17.30257562535551', '17.67948228786459', '17.96629364255534', '18.61710952713758', '18.86220535650441', '19.30851084078828'], 'prelabel': '2-128271-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.003891822201346, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1205915504719269020, 'z1': {'__RealLiteral__': 0, 'data': '0.2740697612663297', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.221894239416051', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.990730208916066', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1024.2490917671662, 'bad_primes': [3, 11, 13, 23], 'central_character': '1.1', 'conductor': 128271, 'conductor_radical': 9867, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, -1, 0, -1, 2, -3, 1, 0, -1, 1, 0, 2, 0, -1, 0, 1, -2, 0, -2, -1, 1, 3, -5, 0, -1, -2, -10, 0, -4, 5, 1, 0, 0, -1, -2, -2, 0, 0, 2, -2, 2, 1, 0, 1, 8, 1, -3, -5, 0, 0, -4, -1, 0, -6, 2, -10, 12, 0, -6, -4, 2, 7, 0, 1, -2, 0, -1, 0, 0, -3, 6, -2, 5, 2, -2, 0, 2, 0, 1, 2, -4, 2, 0, 2, 10, 3, 8, 0, 0, -1, 4, 8, 0, -5, 2, -3, -1, 5], 'euler11': [1, 1, 0], 'euler13': [1, 0, 0], 'euler17': [1, 0, 17], 'euler19': [1, 2, 19], 'euler2': [1, -1, 2], 'euler23': [1, -1, 0], 'euler29': [1, 10, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, -2, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 5], 'euler53': [1, 4, 53], 'euler59': [1, -12, 59], 'euler61': [1, 6, 61], 'euler67': [1, 2, 67], 'euler7': [1, -2, 7], 'euler71': [1, 0, 71], 'euler73': [1, -6, 73], 'euler79': [1, -2, 79], 'euler83': [1, 4, 83], 'euler89': [1, -8, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, -1, 2], [1, 1, 0], [1, 0, 5], [1, -2, 7], [1, 1, 0], [1, 0, 0], [1, 0, 17], [1, 2, 19], [1, -1, 0], [1, 10, 29], [1, 4, 31], [1, 2, 37], [1, -2, 41], [1, -2, 43], [1, -8, 47], [1, 4, 53], [1, -12, 59], [1, 6, 61], [1, 2, 67], [1, 0, 71], [1, -6, 73], [1, -2, 79], [1, 4, 83], [1, -8, 89], [1, -2, 97]], 'index': 0, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/128271/m'], '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': '2-128271-1.1-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': '2-128271-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 32.003891822201346, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1205915504719269020, 'z1': {'__RealLiteral__': 0, 'data': '0.2740697612663297', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1205915504719269020', 'Lhash_array': ['1205915504719269020'], 'label': '2-128271-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/128271/m'}