-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': -3, 'A8': 0, 'A9': 1, 'Lhash': '2060341850640905820', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [-1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1218.4532545231223, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [11, [1, 1]], [17, [1]]], 'bad_primes': [2, 3, 11, 17], 'central_character': '152592.1', 'coefficient_field': '1.1.1.1', 'conductor': 152592, 'conductor_radical': 1122, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -2, 5], [1, 3, 7], [1, 1], [1, -1, 13], [1], [1, 5, 19], [1, 6, 23], [1, -8, 29], [1, -7, 31], [1, -1, 37], [1, 0, 41], [1, -5, 43], [1, -4, 47], [1, -12, 53], [1, 0, 59], [1, -1, 61], [1, 1, 67], [1, -10, 71], [1, 2, 73], [1, 8, 79], [1, -6, 83], [1, 2, 89], [1, -19, 97]], 'gamma_factors': [[], [0]], 'index': 14, 'label': '2-152592-1.1-c1-0-14', 'leading_term': '1.68468386758', '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/152592/z', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.684683867584902, 1.056504865319933, -0.3462311372793555, -1.235707643962782, -0.3998021104607317, 1.860183955694469, 3.4774702631386, 2.666291098341382, 0.3087418118030338, -0.7229719857545888, 0.7183606948418392, 2.089211377459144, 0.4245565402988136, -3.058703442453492, -4.042373129130358, -1.259265222377596, 1.268718651285285, 0.04247214341503782, -2.51502324534212, -1.839796150819458, 1.456378267469477, 2.631698674852249, 0.5269070061748296, -1.075014715500475, -0.3426670204159367, 0.1626375926631844, -0.447896755403164, 0.716467972979416, 3.544231173088152, 2.99716930219703, -1.817606812503927, -4.003660686371622, 0.107544355835989, 3.967927321146481, 1.763451918414302, -1.627528774884942, 0.08776778795759538, 3.420036132708774, 2.503944677997069, -0.1975469536503009, -0.1449613366332937, 0.4911009785221052, -0.5715372203017415, 0.4899040691664265, 4.66831144168213, 5.488244431801564, 1.009350431169244, -1.504340038012739, 0.7671044375297427, 1.532720468769845, -1.076878576689665, -1.483302316685743, 0.4766667957529206, -0.3288817407678339, -2.143928348017344, -0.5139499480715842, 0.3783341095267361, -3.202939452649179, -3.849190620606201, 2.81073873633703, 7.206555021487225, 3.26984289886135, -0.7284076726654488, 0.3240898091303792, 0.3584603278030643, -1.977332383685085, -0.9667109617483222, 1.700639036554367, 0.6057015857345835, -0.9263741076329354, 0.6557885784508479, 0.6373629016374444, -1.733095795837675, -0.6039492052100462, 1.823574114956075, -0.5934155299404358, -2.855266356947177, 0.4244313940791512, 2.224155280167015, -0.3253115367382707, 1.670878055989654, 7.539521922356451, 5.988333206815916, -0.834706022709124, -1.908374852076772, 0.45707928196991, -0.3700913942670229, -0.3323102781803076, 2.232967525995887, 1.353743571516573, -1.220720887894735, -0.130402010836814, 0.2438226857776201, -2.41329469979153, -1.70414135124664, 0.5255691272480914, -2.748590358129444, -5.26556391974387, -0.5214792461545878, 2.495629894755068, -0.6617467871519448, -1.190610225802148, 1.283933766454769, 0.2236953090478023, -0.4286189075091704, 1.530769572636641, -1.375341528437749, -5.916124205272078, -2.330577509202267, 2.165092138450931, -1.499491151570216, -4.320178788018354, -0.8725662446956731, 0.2912588419921946, -1.391033224511098, -0.05392387442584924, 0.8032047683590675, -0.662750330462566, -0.04819273416212459, -0.4130516650844083, -3.637802828699487], 'positive_zeros': ['0.4401688554225551', '1.051747413642080', '2.037758555646160', '2.408530616456116', '3.031877775409345', '3.843342338133745', '4.253835143190338', '4.891264099547732', '5.553415364457013', '6.084105148330069', '6.324384504296812', '6.667245722203187', '7.412717461836165', '7.995195464492958', '8.602610333513193', '8.994246248926836', '9.722050451774622', '10.03108504364267', '10.38041893480176', '10.70792784902242', '11.55556025534406', '11.93351285017199', '12.40338258791840', '12.92593219025158', '13.21307685086605', '13.80286329832687', '14.04321014910082', '14.66055106124251', '15.41643019482036', '15.70647568648580', '16.04065472407812', '16.57553369901667', '17.06122752610063', '17.41810170311795', '17.81672296645124', '18.29647526779100', '18.71276154186278', '19.22530830570881', '19.71205207038029', '19.90633872592062'], 'prelabel': '2-152592-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 34.90634977368906, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2060341850640905820, 'z1': {'__RealLiteral__': 0, 'data': '0.4401688554225551', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.051747413642080', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.037758555646160', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1218.4532545231223, 'bad_primes': [2, 3, 11, 17], 'central_character': '1.1', 'conductor': 152592, 'conductor_radical': 1122, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 2, 0, -3, 0, 1, 0, -1, 0, 1, 0, -2, 0, 0, 0, -5, 0, 3, 0, -6, 0, -1, 0, -1, 0, 8, 0, 7, 0, 1, 0, -6, 0, 1, 0, -1, 0, 0, 0, 5, 0, 2, 0, 4, 0, 2, 0, 0, 0, 12, 0, -2, 0, 5, 0, 0, 0, 1, 0, -3, 0, 2, 0, -1, 0, 6, 0, 10, 0, -2, 0, 1, 0, 3, 0, -8, 0, 1, 0, 6, 0, 0, 0, -8, 0, -2, 0, -3, 0, -7, 0, -10, 0, 19, 0, -1, 0], 'euler11': [1, 1, 0], 'euler13': [1, -1, 13], 'euler17': [1, 0, 0], 'euler19': [1, 5, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -8, 29], 'euler3': [1, 1, 0], 'euler31': [1, -7, 31], 'euler37': [1, -1, 37], 'euler41': [1, 0, 41], 'euler43': [1, -5, 43], 'euler47': [1, -4, 47], 'euler5': [1, -2, 5], 'euler53': [1, -12, 53], 'euler59': [1, 0, 59], 'euler61': [1, -1, 61], 'euler67': [1, 1, 67], 'euler7': [1, 3, 7], 'euler71': [1, -10, 71], 'euler73': [1, 2, 73], 'euler79': [1, 8, 79], 'euler83': [1, -6, 83], 'euler89': [1, 2, 89], 'euler97': [1, -19, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -2, 5], [1, 3, 7], [1, 1, 0], [1, -1, 13], [1, 0, 0], [1, 5, 19], [1, 6, 23], [1, -8, 29], [1, -7, 31], [1, -1, 37], [1, 0, 41], [1, -5, 43], [1, -4, 47], [1, -12, 53], [1, 0, 59], [1, -1, 61], [1, 1, 67], [1, -10, 71], [1, 2, 73], [1, 8, 79], [1, -6, 83], [1, 2, 89], [1, -19, 97]], 'index': 14, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/152592/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': '2-152592-1.1-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': 0, 'prelabel': '2-152592-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 34.90634977368906, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2060341850640905820, 'z1': {'__RealLiteral__': 0, 'data': '0.4401688554225551', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2060341850640905820', 'Lhash_array': ['2060341850640905820'], 'factors': ['2-152592-1.1-c1-0-14'], 'label': '2-152592-1.1-c1-0-14', 'type': 'ECQ', 'url': 'EllipticCurve/Q/152592/z'}