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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 1, 'A9': -3, 'Lhash': '599745562807072199', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 207.81865630058442, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [7, [1, 1]], [11, [1, -1]], [13, [1]]], 'bad_primes': [2, 7, 11, 13], 'central_character': '26026.1', 'coefficient_field': '1.1.1.1', 'conductor': 26026, 'conductor_radical': 2002, 'degree': 2, 'euler_factors': [[1, -1], [1, 0, 3], [1, 0, 5], [1, 1], [1, -1], [1], [1, 2, 17], [1, -3, 19], [1, -3, 23], [1, 3, 29], [1, -4, 31], [1, 2, 37], [1, -6, 41], [1, -1, 43], [1, -3, 47], [1, 4, 53], [1, -10, 59], [1, 10, 61], [1, 2, 67], [1, 13, 71], [1, 12, 73], [1, 4, 79], [1, -5, 83], [1, -17, 89], [1, -1, 97]], 'gamma_factors': [[], [0]], 'index': 14, 'label': '2-26026-1.1-c1-0-14', 'leading_term': '7.5844656874', '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/26026/n', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.790474198375536, 2.9253689438314, 2.778195188794002, 1.158650127850815, -1.237094489081014, -2.992845622263962, -2.928926072927991, -1.160772809954178, 0.8177400374002932, 1.385831340038135, 0.3490649614650582, -0.8462945806776764, -0.6856240960878714, 0.645175693922662, 1.404208923113951, 0.4100212849005608, -1.33603529308417, -1.715948301111247, -0.1729109209123478, 1.420446045472989, 1.092535334717885, -0.6061439486848866, -1.359622256076923, -0.4220367422258193, 0.1751492081393734, -1.377159446579866, -3.592523429786053, -3.434337180633069, -0.9385986221103595, 0.1820821757137961, -2.309558217594289, -5.391020607488408, -4.544909517648195, -0.3530062370895103, 1.892045977067773, -0.2865022515302058, -2.791209101325337, -0.9979584306274883, 3.122122121072587, 3.744874102332877, -0.07228283942988999, -2.97207957471771, -1.350704344159734, 1.658979742616589, 1.700820534875559, -0.1467629784875279, -0.1466800570108362, 1.328360285725157, 0.7669971928038049, -1.849239279586838, -2.690072206995828, -0.6864548970438301, 0.6655252822142632, -0.4941731896166758, -1.375701230454508, -0.05054598426711931, 0.8631044507263632, -0.6777160389035105, -1.891708914914157, -0.261115538795622, 1.3393059089875, -0.3133118864932718, -2.482077790055666, -1.236873017942359, 0.9354616118218616, -0.6059117945029489, -3.654376947663486, -2.658122857896997, 0.8381323061751088, 0.6745023139750421, -1.945610304800486, 0.4285925972054543, 7.626034664905101, 10.32977973353698, 5.109199760047715, -0.08145056840307989, 0.5007528537132623, 2.101133452982577, 0.01237770889590512, -2.057530038642959, -0.5194045620899918, 0.8372179163649783, -1.063927200264217, -2.105209407007433, 0.7184940395747401, 2.99487898982692, 1.242976158612029, -0.7729817131392911, 0.1429095035045082, 0.9682163191809404, -0.2948892075079248, -0.5647951944174824, 0.8596248744353981, 0.1468768558713697, -2.444585894844986, -1.868416524979095, 1.523406622623272, 1.999273459669046, -0.2830149463373285, 0.1193440888968011, 2.308038568821887, 0.9303034551628971, -1.904524694991382, -0.4867223094191223, 1.858835736453956, -1.077127266163655, -4.41738818482729, -0.5101775934675148, 4.968111137026242, 2.33471187964893, -3.857477660147353, -3.328100314184227, 1.307381969642067, 1.486775738756922, -0.8371874344176585, 0.2647214107320152, 1.776513104349292, -0.3624991832251038, -1.561890292709132, 1.382501941009443], 'positive_zeros': ['1.122766604981150', '2.134621400232531', '2.810757887952815', '3.388099632975368', '4.057152065453532', '4.771573372147429', '5.412635916139514', '6.096586664062398', '6.311067698130772', '7.366675254843577', '7.541939600361533', '8.521838702282211', '8.978742267885733', '9.560005477250310', '10.24593208253038', '10.84961118961589', '11.47499035952529', '11.77691999006290', '12.32954513224216', '13.07902976876355', '13.42577433730644', '14.00714229784389', '14.41852914970733', '15.02681847638622', '15.47164140540995', '16.11408338097482', '16.45111466821658', '17.17922116568247', '17.55985581773410', '17.98121162006302', '18.99156583601836', '19.19396436172267', '19.75097986520202'], 'prelabel': '2-26026-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.415916769341603, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 599745562807072199, 'z1': {'__RealLiteral__': 0, 'data': '1.122766604981150', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.134621400232531', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.810757887952815', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 207.81865630058442, 'bad_primes': [2, 7, 11, 13], 'central_character': '1.1', 'conductor': 26026, 'conductor_radical': 2002, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, -1, 1, -3, 0, 1, 0, 0, -1, 0, 1, -2, -3, 3, 0, 0, 1, 3, 0, -5, 0, 0, -1, -3, 0, 4, 1, 0, -2, 0, -3, -2, 3, 0, 0, 6, 0, 1, 1, 0, 3, 3, 0, 1, -5, 0, 0, -4, 0, 0, -1, 0, -3, 10, 0, -10, 4, 3, 1, 0, 0, -2, -2, 0, 0, -13, -3, -12, -2, 0, 3, -1, 0, -4, 0, 9, 6, 5, 0, 0, 1, 0, 1, 17, 0, 0, 3, 0, 3, 0, 0, 1, 1, -3, -5], 'euler11': [1, -1, 0], 'euler13': [1, 0, 0], 'euler17': [1, 2, 17], 'euler19': [1, -3, 19], 'euler2': [1, -1, 0], 'euler23': [1, -3, 23], 'euler29': [1, 3, 29], 'euler3': [1, 0, 3], 'euler31': [1, -4, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, -1, 43], 'euler47': [1, -3, 47], 'euler5': [1, 0, 5], 'euler53': [1, 4, 53], 'euler59': [1, -10, 59], 'euler61': [1, 10, 61], 'euler67': [1, 2, 67], 'euler7': [1, 1, 0], 'euler71': [1, 13, 71], 'euler73': [1, 12, 73], 'euler79': [1, 4, 79], 'euler83': [1, -5, 83], 'euler89': [1, -17, 89], 'euler97': [1, -1, 97], 'euler_factors': [[1, -1, 0], [1, 0, 3], [1, 0, 5], [1, 1, 0], [1, -1, 0], [1, 0, 0], [1, 2, 17], [1, -3, 19], [1, -3, 23], [1, 3, 29], [1, -4, 31], [1, 2, 37], [1, -6, 41], [1, -1, 43], [1, -3, 47], [1, 4, 53], [1, -10, 59], [1, 10, 61], [1, 2, 67], [1, 13, 71], [1, 12, 73], [1, 4, 79], [1, -5, 83], [1, -17, 89], [1, -1, 97]], 'index': 14, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/26026/n'], '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': '2-26026-1.1-c1-0-14', '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': '2-26026-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.415916769341603, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 599745562807072199, 'z1': {'__RealLiteral__': 0, 'data': '1.122766604981150', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '599745562807072199', 'Lhash_array': ['599745562807072199'], 'label': '2-26026-1.1-c1-0-14', 'type': 'ECQ', 'url': 'EllipticCurve/Q/26026/n'}