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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': 0, 'Lhash': '635677390101853588', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 316.20759200427045, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '39600.1', 'coefficient_field': '1.1.1.1', 'conductor': 39600, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, -4, 7], [1, -1], [1, -6, 13], [1, -2, 17], [1, 4, 19], [1, 6, 23], [1, -2, 29], [1, 8, 31], [1, -8, 37], [1, 6, 41], [1, -12, 43], [1, 10, 47], [1, 0, 53], [1, 4, 59], [1, 10, 61], [1, -2, 67], [1, 8, 71], [1, 2, 73], [1, 4, 79], [1, -4, 83], [1, -14, 89], [1, -4, 97]], 'gamma_factors': [[], [0]], 'index': 51, 'label': '2-39600-1.1-c1-0-51', 'leading_term': '3.2625760838', '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/39600/fd', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.262576083797257, 2.724877713886267, 1.274341613248091, -0.5027188803379, -1.665818409086006, -1.549921896224627, -0.523817752752424, 0.06779071000557488, -0.8764750221896779, -2.843425673734879, -3.822663385319881, -2.277645526832551, 0.918625149989747, 3.008399729375262, 2.236675995898478, -0.08855666987198728, -1.108472532373042, 0.03026951324463293, 1.091453955458813, -0.1575143554560943, -2.648570996787931, -3.251783531693874, -1.184768816297953, 0.6747908987410641, -0.1112123333777387, -1.754741168958066, -0.690247594339022, 2.879404313056777, 4.704104305833961, 2.432795444507708, -0.9379442970362215, -1.510224477904582, -0.07191852734210254, -0.1154051989448031, -1.705202695180146, -1.540493131345035, 0.7441774460702899, 1.028255898867127, -2.561308968311466, -5.627630963954823, -3.743552000926731, 0.6326208251483424, 2.049921973328335, 0.4373116234191863, 0.0814314890383738, 1.624104453885225, 1.500691684388975, -0.5409158269277029, -0.2654374825114078, 3.009639467104737, 4.079508718809145, 0.6648125660686921, -2.062937737384984, -0.07380115025058562, 2.704026157345159, 1.559782766561782, -0.9282550358898931, -0.4101063412242436, 1.119067777412999, 0.03246659605224141, -1.102820472169095, 1.478864414529664, 4.448159028335788, 2.816375943283453, -0.5019660407169557, 0.1820436339945261, 2.660579167108405, 1.184972082784315, -2.331632593121856, -1.938426369397763, 1.082234033030774, 1.235854162173322, -0.5402294290778664, -6.053913438680095e-05, 0.8334996412337372, -1.733104265298773, -3.711519471901511, -0.1269081360663525, 4.307167595410243, 2.812201461374855, -1.222964247373982, -1.147118304878878, 0.8371864923793217, -0.1902658703051133, -1.614741579982218, -0.02310027101116933, 0.889416667940722, -0.9848808199343926, -0.1766092307279945, 4.835194038330427, 6.365545050121892, 1.555674423960873, -1.896385583490685, -0.2730518854318264, 0.6094406906227491, -1.311144430629256, -1.178676810087505, 0.5274192174147138, -1.346459149119651, -4.249204654733606, -2.159277485199194, 1.539464774912483, 0.8313792221255005, -0.576211385859804, 1.728198600769758, 2.241381308204072, -2.604209440895294, -5.410326936209541, -1.932311347803239, 1.134088121005346, 0.2583301910062208, -0.006381582235948742, 0.3968400181400259, -2.381310570983108, -4.275967392143596, -0.2947272715392689, 3.014540519819433, -0.640977383154988, -4.229687582356251, -1.400130221344045, 1.666780997969846], 'positive_zeros': ['0.6765698902685878', '1.660916410543522', '1.807583563809322', '2.929507350263144', '3.739568267734295', '4.245340113096026', '4.732878629877993', '5.624914889765915', '5.984721601612912', '6.555336449893260', '7.416846157807032', '8.016458785688037', '8.224960630068043', '8.920282923462631', '9.344747013605740', '10.20860300351674', '10.83661568639745', '10.97805171475588', '11.67907698085934', '12.02650593407746', '12.78993988801142', '13.25521933128744', '13.88559629405687', '14.30263459735231', '14.75399690047446', '15.14645562550211', '15.94542161448995', '16.23256290601995', '16.82694068361904', '17.40235244920200', '17.90753032587352', '18.25000947291972', '18.61770579069236', '19.25571398773709', '19.90865801036640'], 'prelabel': '2-39600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.782226857294066, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 635677390101853588, 'z1': {'__RealLiteral__': 0, 'data': '0.6765698902685878', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.660916410543522', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.807583563809322', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 316.20759200427045, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 39600, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, 6, 0, 0, 0, 2, 0, -4, 0, 0, 0, -6, 0, 0, 0, 0, 0, 2, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, -6, 0, 12, 0, 0, 0, -10, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, -10, 0, 0, 0, 0, 0, 2, 0, 0, 0, -8, 0, -2, 0, 0, 0, 4, 0, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 14, 0, 24, 0, 0, 0, 0, 0, 4, 0, 0, 0], 'euler11': [1, -1, 0], 'euler13': [1, -6, 13], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, -8, 37], 'euler41': [1, 6, 41], 'euler43': [1, -12, 43], 'euler47': [1, 10, 47], 'euler5': [1, 0, 0], 'euler53': [1, 0, 53], 'euler59': [1, 4, 59], 'euler61': [1, 10, 61], 'euler67': [1, -2, 67], 'euler7': [1, -4, 7], 'euler71': [1, 8, 71], 'euler73': [1, 2, 73], 'euler79': [1, 4, 79], 'euler83': [1, -4, 83], 'euler89': [1, -14, 89], 'euler97': [1, -4, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, -4, 7], [1, -1, 0], [1, -6, 13], [1, -2, 17], [1, 4, 19], [1, 6, 23], [1, -2, 29], [1, 8, 31], [1, -8, 37], [1, 6, 41], [1, -12, 43], [1, 10, 47], [1, 0, 53], [1, 4, 59], [1, 10, 61], [1, -2, 67], [1, 8, 71], [1, 2, 73], [1, 4, 79], [1, -4, 83], [1, -14, 89], [1, -4, 97]], 'index': 51, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/39600/fd'], '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': '2-39600-1.1-c1-0-51', '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': '2-39600-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 17.782226857294066, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 635677390101853588, 'z1': {'__RealLiteral__': 0, 'data': '0.6765698902685878', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '635677390101853588', 'Lhash_array': ['635677390101853588'], 'factors': ['2-39600-1.1-c1-0-51'], 'label': '2-39600-1.1-c1-0-51', 'type': 'ECQ', 'url': 'EllipticCurve/Q/39600/fd'}