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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': -2, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '1371131238478994409', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [-1.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 851.0056595417961, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [5, [1]], [7, [1]], [29, [1, 1]]], 'bad_primes': [3, 5, 7, 29], 'central_character': '106575.1', 'coefficient_field': '1.1.1.1', 'conductor': 106575, 'conductor_radical': 3045, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, 1], [1], [1], [1, -4, 11], [1, -2, 13], [1, 3, 17], [1, -7, 19], [1, -5, 23], [1, 1], [1, 0, 31], [1, 8, 37], [1, -5, 41], [1, 4, 43], [1, -7, 47], [1, 1, 53], [1, 2, 59], [1, -1, 61], [1, 4, 67], [1, 0, 71], [1, -1, 73], [1, 8, 79], [1, 6, 83], [1, -11, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 14, 'label': '2-106575-1.1-c1-0-14', 'leading_term': '1.71026795352', '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/106575/bo', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.710267953517636, 1.192947409465034, -0.01175914102900834, -0.9570611906284096, -0.7340923956737001, 0.3855278489978338, 0.6430352734482117, -1.563708028100285, -5.342167310248592, -7.306073584371245, -4.943155914338602, 0.09717722113564155, 3.295616086417572, 2.365112960465986, -0.1495905644552576, -0.5105150937192876, 1.157990886872397, 1.622904256972699, -0.1098978714328565, -1.267609666331908, -0.1018803251596314, 1.001315091576059, -0.3285165294007411, -1.966147892095377, -0.760178281541287, 1.505983651554282, 0.5929097215552184, -2.64357128986125, -3.122683413368541, -0.43816625562995, -0.1959397648668186, -4.309978572629775, -6.952736527692217, -4.056527666451896, -0.06235670912540902, 0.006256277581616686, -1.36486837708568, -0.2947002162650292, 0.7610739547134051, -1.224081970355101, -2.594678001701498, 0.2697441017704927, 3.084574896632281, 1.166909248849206, -1.545190827451157, -0.01051241479872275, 2.32177138074381, 0.856515818134052, -0.8612790391881053, 1.132975665209843, 2.645927048367202, 0.00437842591146868, -2.053639213659053, -0.05402370647631003, 1.267207205398666, -0.5709548265424654, -0.6591225113331107, 1.736516230874258, 0.641309250553096, -3.125284893412846, -1.915473312118303, 2.89988875382387, 2.579001346869736, -1.569104876633658, -0.9666507737484848, 2.770200093101391, 1.863566482145018, -1.633607338625763, -1.390376161344791, 0.1462133330553561, -0.8971313383298664, -1.055337434903642, 0.9869803340964554, 0.6445095868948867, -1.172270327557124, 0.3958632886730965, 1.888253637099226, -1.280631486315458, -2.909302585075524, 1.001583587052343, 1.727202060437668, -3.942243720794185, -5.364124118938616, -0.01505823672369346, 0.9971395973442146, -3.85676423222419, -4.477100109134926, -0.5580323751762277, 0.3261773149181926, -0.6583371873107055, 0.3441999817297494, 0.3728477926361546, -0.7341867192178296, 0.9140005549029613, 1.81892173734594, -1.806968359695803, -3.242919847796633, 0.502177485487843, 1.479432217124236, -0.3177586147370911, 3.254273068054691, 7.182415708507019, 1.995150288996318, -4.207586071718507, -1.633390672785474, 1.652359163616726, -1.012522543241656, -2.265916636573142, 0.07809106755729497, 0.141449294829547, -0.06546566791212263, 2.591506583060413, 2.697571622883104, -0.1129713250104336, 0.01522886690567408, -0.1415945974432567, -4.109322991588903, -3.888268458894777, 1.793868657193202, 2.337684472627942, -1.146556470542538], 'positive_zeros': ['0.4976776405949813', '1.166586481976076', '1.609823480398435', '2.745029612406719', '3.480730947252364', '3.838766905422960', '4.486587132360428', '5.014480054472738', '5.461320943376679', '6.072465570336759', '6.548424422519609', '7.301398602280318', '7.477299291482188', '8.507023890426365', '8.750982664823389', '9.288855929868968', '9.632545081910866', '10.23339704943708', '10.83181856989420', '11.25084586632107', '11.83131513931223', '12.14944815329349', '12.75030818950192', '13.25490788274199', '13.68275974351283', '14.07117957748162', '14.54155547422789', '15.09525249002139', '15.64582697532864', '16.06106642091121', '16.61987842972733', '17.19214391535451', '17.34257597513736', '17.87963324229260', '18.32241656854668', '18.71477065649333', '19.17235571405029', '19.69435640046288'], 'prelabel': '2-106575-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 29.172001294765433, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1371131238478994409, 'z1': {'__RealLiteral__': 0, 'data': '0.4976776405949813', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.166586481976076', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.609823480398435', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 851.0056595417961, 'bad_primes': [3, 5, 7, 29], 'central_character': '1.1', 'conductor': 106575, 'conductor_radical': 3045, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, -2, 0, 0, 0, 0, 1, 0, 4, 2, 2, 0, 0, 4, -3, 0, 7, 0, 0, 0, 5, 0, 0, 0, -1, 0, -1, 0, 0, 0, -4, 0, 0, -2, -8, 0, -2, 0, 5, 0, -4, -8, 0, 0, 7, -4, 0, 0, 3, -4, -1, 0, 0, 0, -7, 0, -2, 0, 1, 0, 0, -8, 0, 0, -4, 6, -5, 0, 0, 0, 1, 0, 0, -14, 0, 0, -8, 0, 1, 0, -6, 0, 0, 0, 1, 0, 11, 0, 0, -10, 0, 0, 0, 0, 2, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, -2, 13], 'euler17': [1, 3, 17], 'euler19': [1, -7, 19], 'euler2': [1, 0, 2], 'euler23': [1, -5, 23], 'euler29': [1, 1, 0], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 8, 37], 'euler41': [1, -5, 41], 'euler43': [1, 4, 43], 'euler47': [1, -7, 47], 'euler5': [1, 0, 0], 'euler53': [1, 1, 53], 'euler59': [1, 2, 59], 'euler61': [1, -1, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, -1, 73], 'euler79': [1, 8, 79], 'euler83': [1, 6, 83], 'euler89': [1, -11, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 2], [1, 1, 0], [1, 0, 0], [1, 0, 0], [1, -4, 11], [1, -2, 13], [1, 3, 17], [1, -7, 19], [1, -5, 23], [1, 1, 0], [1, 0, 31], [1, 8, 37], [1, -5, 41], [1, 4, 43], [1, -7, 47], [1, 1, 53], [1, 2, 59], [1, -1, 61], [1, 4, 67], [1, 0, 71], [1, -1, 73], [1, 8, 79], [1, 6, 83], [1, -11, 89], [1, -2, 97]], 'index': 14, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/106575/bo'], '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': '2-106575-1.1-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': '2-106575-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 29.172001294765433, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1371131238478994409, 'z1': {'__RealLiteral__': 0, 'data': '0.4976776405949813', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1371131238478994409', 'Lhash_array': ['1371131238478994409'], 'factors': ['2-106575-1.1-c1-0-14'], 'label': '2-106575-1.1-c1-0-14', 'type': 'ECQ', 'url': 'EllipticCurve/Q/106575/bo'}