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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': 3, 'A4': 1, 'A5': 0, 'A6': 3, 'A7': 1, 'A8': 1, 'A9': 6, 'Lhash': '1888186378513640367', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [1.7320508075688774, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [1.2247448713915892, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [2.0, 0], 'algebraic': True, 'analytic_conductor': 818.8658727282308, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [5, [1]], [7, [1, -1]], [293, [1, 1]]], 'bad_primes': [2, 5, 7, 293], 'central_character': '102550.1', 'coefficient_field': '1.1.1.1', 'conductor': 102550, 'conductor_radical': 20510, 'degree': 2, 'euler_factors': [[1, -1], [1, -3, 3], [1], [1, -1], [1, 0, 11], [1, 2, 13], [1, -7, 17], [1, -4, 19], [1, 4, 23], [1, -2, 29], [1, -1, 31], [1, 2, 37], [1, 3, 41], [1, 1, 43], [1, -5, 47], [1, -6, 53], [1, 1, 59], [1, -12, 61], [1, -5, 67], [1, 12, 71], [1, 10, 73], [1, 1, 79], [1, 0, 83], [1, -5, 89], [1, -9, 97]], 'gamma_factors': [[], [0]], 'index': 15, 'label': '2-102550-1.1-c1-0-15', 'leading_term': '11.4012832655', '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/102550/bd', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [11.40128326552565, 10.02034222127604, 6.281075738721853, 1.620037806291145, -1.722961849567619, -2.208606793899291, -0.499438965058741, 1.0382195690381, 0.7583574560160348, -0.5801050865057121, -1.051046007606292, -0.2267268980222785, 0.3826572839249756, -0.2037773345686119, -0.8220890800076494, -0.1559046060668381, 0.706457568782983, -0.2479168786526982, -2.226019577524552, -2.106698406210854, 0.5025563154379766, 1.724688465853628, -0.7421919029862284, -3.023786285385703, -0.2617914948363224, 5.346907598124261, 6.887352249652641, 2.846908081095145, -0.9183567282456209, -0.5325374558842879, 0.8209618251208464, -0.0962960417797632, -0.9113926534799003, 0.618083289811239, 1.308452886101583, -1.270028288063379, -3.01822571614499, -0.3682126575721261, 2.520526927722763, 1.1660364197577, -0.6781735722710907, 1.208464831990462, 1.662405984672658, -4.967101158363073, -12.11295733470142, -9.878329277135165, -1.581129693938275, 1.966941841558901, 0.1102815027354891, 0.3972487113482908, 3.293995884771845, 3.009535708093988, -0.03077425418116404, -0.6626998732055824, 0.7088641966832543, 0.4132214473724929, -0.621982196864537, -0.2415601073357054, 0.02674740688131309, -0.2520887020108574, 1.074988730404413, 2.343677220836493, 0.4191121411302239, -1.266827002074189, 0.6220907098692066, 0.01470720775511187, -6.441514498961787, -8.357844100109727, -0.1354671610509602, 4.460585150861628, -4.200569594762112, -12.24723664406756, -6.789459110928826, 1.720981744215668, 1.04243509988339, -2.21941334953451, -0.2295772288453588, 1.516431992114679, -0.6338145294828216, -1.266193798184684, 0.4820441913920412, 0.1406839185195019, -0.946224160509124, -0.08780046533105389, -0.2910170236198992, -1.770178639466474, -0.4603182819059819, 1.040262736825145, -1.39829028078399, -1.860278937798422, 3.298179249239966, 4.584077642994323, -1.931547351305218, -5.246009977274497, -1.406139082416471, 0.153292699830277, -2.216164521025201, -1.378698310272352, 1.140674131386589, 0.3604382301669901, -0.4173644175384773, 0.5172070135213027, -0.8388545706648889, -2.417900817302039, -0.5580523364119295, -0.2337473566851947, -2.750951122741953, -1.173039647292485, 1.660939401069768, -2.005354052885663, -4.111770018072568, 2.615088192476814, 4.59954070726087, -4.053913796084368, -4.858838816921294, 7.33035224264398, 12.13124460912788, 4.032470421688522, -0.7604285715650144, 1.118628941944959, 0.5042462282582406], 'positive_zeros': ['0.8500919470014782', '1.562658630364033', '2.141550618871290', '2.807891138351247', '3.193556417047603', '3.783410803116784', '4.216075993120054', '4.955291100491178', '5.445178020972677', '6.012271335312487', '6.910054200299558', '7.323411173110374', '7.734764809242261', '8.172045398595461', '8.650840338305495', '9.273287018453793', '9.860154041825514', '10.13561767579777', '10.59147812445121', '11.56087722913514', '12.01579463058352', '12.20315065655958', '12.99688945948559', '13.36680083337880', '13.83002348437367', '14.34831482516369', '14.51906342904903', '14.84048949467439', '15.53679498843885', '15.93501222282437', '16.25086592058735', '17.00353471308208', '17.40904437987267', '18.17779486186881', '18.55998859788832', '19.01721334504273', '19.43860802818458', '19.92273300749209'], 'prelabel': '2-102550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.615832553469954, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1888186378513640367, 'z1': {'__RealLiteral__': 0, 'data': '0.8500919470014782', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.562658630364033', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.141550618871290', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 818.8658727282308, 'bad_primes': [2, 5, 7, 293], 'central_character': '1.1', 'conductor': 102550, 'conductor_radical': 20510, 'degree': 2, 'dirichlet_coefficients': [1, 1, 3, 1, 0, 3, 1, 1, 6, 0, 0, 3, -2, 1, 0, 1, 7, 6, 4, 0, 3, 0, -4, 3, 0, -2, 9, 1, 2, 0, 1, 1, 0, 7, 0, 6, -2, 4, -6, 0, -3, 3, -1, 0, 0, -4, 5, 3, 1, 0, 21, -2, 6, 9, 0, 1, 12, 2, -1, 0, 12, 1, 6, 1, 0, 0, 5, 7, -12, 0, -12, 6, -10, -2, 0, 4, 0, -6, -1, 0, 9, -3, 0, 3, 0, -1, 6, 0, 5, 0, -2, -4, 3, 5, 0, 3, 9, 1, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 2, 13], 'euler17': [1, -7, 17], 'euler19': [1, -4, 19], 'euler2': [1, -1, 0], 'euler23': [1, 4, 23], 'euler29': [1, -2, 29], 'euler3': [1, -3, 3], 'euler31': [1, -1, 31], 'euler37': [1, 2, 37], 'euler41': [1, 3, 41], 'euler43': [1, 1, 43], 'euler47': [1, -5, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, 1, 59], 'euler61': [1, -12, 61], 'euler67': [1, -5, 67], 'euler7': [1, -1, 0], 'euler71': [1, 12, 71], 'euler73': [1, 10, 73], 'euler79': [1, 1, 79], 'euler83': [1, 0, 83], 'euler89': [1, -5, 89], 'euler97': [1, -9, 97], 'euler_factors': [[1, -1, 0], [1, -3, 3], [1, 0, 0], [1, -1, 0], [1, 0, 11], [1, 2, 13], [1, -7, 17], [1, -4, 19], [1, 4, 23], [1, -2, 29], [1, -1, 31], [1, 2, 37], [1, 3, 41], [1, 1, 43], [1, -5, 47], [1, -6, 53], [1, 1, 59], [1, -12, 61], [1, -5, 67], [1, 12, 71], [1, 10, 73], [1, 1, 79], [1, 0, 83], [1, -5, 89], [1, -9, 97]], 'index': 15, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/102550/bd'], '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': '2-102550-1.1-c1-0-15', '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': '2-102550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.615832553469954, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1888186378513640367, 'z1': {'__RealLiteral__': 0, 'data': '0.8500919470014782', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1888186378513640367', 'Lhash_array': ['1888186378513640367'], 'label': '2-102550-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/102550/bd'}