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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -1, 'A6': 0, 'A7': -2, 'A8': -1, 'A9': 0, 'Lhash': '855208738617728176', 'a10': [0.31622776601683794, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 539.1339443672812, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [11, [1]], [31, [1, 1]]], 'bad_primes': [2, 3, 11, 31], 'central_character': '67518.1', 'coefficient_field': '1.1.1.1', 'conductor': 67518, 'conductor_radical': 2046, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, 1, 5], [1, 2, 7], [1], [1, -5, 13], [1, -1, 17], [1, -6, 19], [1, 6, 23], [1, -5, 29], [1, 1], [1, -1, 37], [1, 9, 41], [1, -4, 43], [1, 4, 47], [1, -5, 53], [1, 6, 59], [1, -2, 61], [1, -12, 67], [1, -4, 71], [1, -2, 73], [1, 14, 79], [1, -6, 83], [1, 3, 89], [1, 9, 97]], 'gamma_factors': [[], [0]], 'index': 34, 'label': '2-67518-1.1-c1-0-34', 'leading_term': '4.06232603696', '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/67518/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.9001930175461961, 1.157658363102804, 0.4659482092821769, -0.708394462477775, -1.196436833129581, -0.1553804840598728, 1.738673134710166, 2.499434422762169, 0.8263730152751936, -2.085703658499312, -3.441638374897676, -2.042319339124901, 0.0309971464552882, -0.02991482985810163, -1.739976192289125, -1.496318923102652, 2.356828613020765, 6.2046623872232, 5.078019968021129, -0.576010966904306, -4.791061951436602, -3.624192392327473, -0.08737558191982427, 0.6411280178948154, -1.367622226698488, -1.808495414894206, 0.4788716363403801, 1.777551711485211, -0.03936810144225534, -1.914665621795661, -0.9174044529031691, 0.8853886381523546, 0.465525492445955, -0.6344161443637163, 0.6250887115000713, 2.780486444630427, 2.258750268206866, -0.04881297424660878, -0.4528189628367867, 0.5400905227364418, -0.6318046070178732, -3.143580636354458, -2.681878160803407, 0.2335901293238974, 0.6463007475850014, -1.616664328815609, -1.699735965483698, 0.3823798960237316, -0.6862195908713511, -4.400259732153109, -3.77423770793872, 1.515830674453852, 3.167793499119005, -0.94579698930712, -2.79865624158693, 0.3698377901780581, 0.437473778227697, -5.838565105920383, -9.523495022079738, -5.039131158230118, 0.5690287575678002, 0.9292703530761659, -0.2818645473872452, 0.5146428205691196, 0.4405201872791275, -0.9396117670223523, 0.6186245152234945, 3.963640894799956, 3.137624221243176, -0.8177392189045009, -1.578539409315457, 0.3092061527270116, -0.1002820726788673, -1.415439590223552, -0.1027533764331009, 0.8816785344941978, -1.16350997179714, -2.096447505062585, -0.007301385521279459, 0.610312038541662, -0.4118017595030071, 1.658610571805125, 4.138110980406205, 0.9404698465799322, -3.014918594566406, -0.1780677564163598, 3.292975542488204, -0.6553322032955105, -4.893657846161274, -1.490394016002147, 2.159715226728275, -0.5415651573424611, -2.272436279204018, 0.7930199347183235, 0.71489259564087, -3.418765221278263, -2.640076639261473, 2.067226428979296, 1.58999003150541, -2.060506643221919, -1.219428336135181, 1.180095960239535, 0.008765763295047644, -1.003308286187922, 0.03427746380183641, -1.355219460132189, -3.82909177570788, -2.199222435286798, 0.3739513140128421, -0.4440577154756718, -0.492107104457452, 2.009586825200648, 1.754608604226987, -0.6587744168446285, -0.1453359077598947, 0.4073715969836003, -1.801277398042822, -0.5800937769545919, 4.377171365062802, 3.812980517380976], 'positive_zeros': ['0.8494925215699103', '1.521908814047104', '2.321845895397971', '3.244163758102956', '3.494324363203803', '4.119330109511241', '4.976499407679032', '5.758214901970017', '6.093378427180805', '6.704388993103794', '7.246242643101099', '7.857112593026686', '8.329858121009015', '8.677426886209602', '9.493317038399973', '9.851526074042678', '10.17890749910858', '10.97672664074634', '11.32982586676471', '11.94239712538742', '12.19067472876771', '12.92933584584752', '13.44978679040062', '13.97285419308251', '14.27602676130798', '15.21079076487157', '15.64887250159034', '15.88482101162792', '16.32270835952209', '16.70076311533239', '17.44229220820673', '17.94914001006563', '18.23497823287042', '18.76247002802098', '19.13457154398582', '19.75085244791285'], 'prelabel': '2-67518-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.21925804945716, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 855208738617728176, 'z1': {'__RealLiteral__': 0, 'data': '0.8494925215699103', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.521908814047104', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.321845895397971', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 539.1339443672812, 'bad_primes': [2, 3, 11, 31], 'central_character': '1.1', 'conductor': 67518, 'conductor_radical': 2046, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, -1, 0, -2, -1, 0, 1, 0, 0, 5, 2, 0, 1, 1, 0, 6, -1, 0, 0, -6, 0, -4, -5, 0, -2, 5, 0, -1, -1, 0, -1, 2, 0, 1, -6, 0, 1, -9, 0, 4, 0, 0, 6, -4, 0, -3, 4, 0, 5, 5, 0, 0, 2, 0, -5, -6, 0, 2, 1, 0, 1, -5, 0, 12, 1, 0, -2, 4, 0, 2, -1, 0, 6, 0, 0, -14, -1, 0, 9, 6, 0, -1, -4, 0, 0, -3, 0, -10, -6, 0, 4, -6, 0, -9, 3, 0, -4], 'euler11': [1, 0, 0], 'euler13': [1, -5, 13], 'euler17': [1, -1, 17], 'euler19': [1, -6, 19], 'euler2': [1, 1, 0], 'euler23': [1, 6, 23], 'euler29': [1, -5, 29], 'euler3': [1, 0, 0], 'euler31': [1, 1, 0], 'euler37': [1, -1, 37], 'euler41': [1, 9, 41], 'euler43': [1, -4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 1, 5], 'euler53': [1, -5, 53], 'euler59': [1, 6, 59], 'euler61': [1, -2, 61], 'euler67': [1, -12, 67], 'euler7': [1, 2, 7], 'euler71': [1, -4, 71], 'euler73': [1, -2, 73], 'euler79': [1, 14, 79], 'euler83': [1, -6, 83], 'euler89': [1, 3, 89], 'euler97': [1, 9, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 1, 5], [1, 2, 7], [1, 0, 0], [1, -5, 13], [1, -1, 17], [1, -6, 19], [1, 6, 23], [1, -5, 29], [1, 1, 0], [1, -1, 37], [1, 9, 41], [1, -4, 43], [1, 4, 47], [1, -5, 53], [1, 6, 59], [1, -2, 61], [1, -12, 67], [1, -4, 71], [1, -2, 73], [1, 14, 79], [1, -6, 83], [1, 3, 89], [1, 9, 97]], 'index': 34, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/67518/i'], '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': '2-67518-1.1-c1-0-34', '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': '2-67518-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.21925804945716, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 855208738617728176, 'z1': {'__RealLiteral__': 0, 'data': '0.8494925215699103', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '855208738617728176', 'Lhash_array': ['855208738617728176'], 'factors': ['2-67518-1.1-c1-0-34'], 'label': '2-67518-1.1-c1-0-34', 'type': 'ECQ', 'url': 'EllipticCurve/Q/67518/i'}