-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 0, 'Lhash': '1676610229569355582', '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': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2365.232788191943, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [11, [1]], [17, [1, 1]]], 'bad_primes': [2, 3, 11, 17], 'central_character': '296208.1', 'coefficient_field': '1.1.1.1', 'conductor': 296208, 'conductor_radical': 1122, 'degree': 2, 'euler_factors': [[1], [1], [1, 0, 5], [1, -2, 7], [1], [1, 2, 13], [1, 1], [1, -4, 19], [1, -2, 23], [1, 0, 29], [1, 6, 31], [1, 0, 37], [1, 10, 41], [1, -4, 43], [1, 4, 47], [1, -2, 53], [1, 4, 59], [1, 0, 61], [1, 4, 67], [1, 2, 71], [1, -14, 73], [1, -6, 79], [1, -12, 83], [1, -2, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 104, 'label': '2-296208-1.1-c1-0-104', 'leading_term': '8.1595206458', '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/296208/dl', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.745216031211681, 1.939359294688968, 0.187991663575665, -1.992001823901196, -2.351353754747437, -0.6290742497343244, 0.7173898000786073, -0.2878001698255467, -1.948745287861619, -1.006540639691246, 2.160131909704888, 3.430426867528946, 1.208621195270179, -0.6422509012638574, 1.122553757584315, 3.522736673832747, 2.212265611215483, -0.9938488391720264, -1.346947620011259, 0.3616337391072898, -0.1849684722842719, -1.959310801101671, -0.3681099477889715, 2.978102461453468, 2.118288362529735, -1.895415545380418, -2.291270090987125, 0.8904342252355708, 1.309581546905094, -1.142483206237734, -1.077498843023592, 0.4815471627985931, -1.431708792384059, -4.073794633279465, -1.986624797966151, 1.121549671381267, -0.289043941210485, -1.974133269294443, 0.5800268892838388, 1.921912347363048, -1.381179372626282, -2.627808585945075, 0.7622842800641929, 1.823548897597221, -0.5896148512679966, -0.1613753818394723, 1.882852265296613, 0.2857005780226134, -0.79388797039871, 2.774568061580442, 4.073786351270188, -0.04006275027532014, -1.270926464342061, 2.022988113818256, 1.909891974492912, -0.6766793209300661, 0.7413136827945715, 2.218356184394986, -0.6454207298202247, -1.729604356383373, 0.3777815591575071, -1.200944073507602, -3.767455106738952, -0.3712312343655494, 2.794052160988581, -0.1224281124485188, -1.401577976521264, 1.53074882143228, 0.7711734888989471, -2.118717401795112, -0.4691653186671982, 1.118501337647852, -0.2085025219641658, 2.224032800009507, 5.908147453713633, 2.839675078093185, -0.7559727764997428, 1.489800974287175, 1.669675526912915, -1.888524460410305, -0.9551914442456082, 1.339525786285738, -0.8626113439921987, -0.8256006022835146, 2.723331577724918, 1.627647729628008, -0.7310385578368872, 1.552786476521704, 1.528879456657097, -1.383976672133348, 1.396719233124198, 4.599270943004253, 0.7209627324315319, -1.619319384359045, 0.7979712790530027, -0.3204522106949795, -2.179574777203084, 0.2599311050421071, 0.2052317906325469, -1.574570675136319, 1.948551309155062, 3.723711666795551, -0.08410108860852279, 0.8769067312316055, 4.661047099781617, 1.533774150742531, -1.678951451684537, 0.3892544143089583, 0.3686788750387773, -0.03579791513131387, 2.678819658530374, 0.3562946371168375, -4.636721525428529, -2.118943226859061, 1.018710123273114, -0.9757687643741644, 0.2009994179477653, 1.957563238392679, -1.851471154623442, -1.8546537822489], 'positive_zeros': ['0.7697513077710186', '1.581374403056555', '1.960904154120774', '2.585307076123598', '3.364583509906286', '3.645458309576007', '4.412030425056754', '4.935474867060247', '5.225234468325810', '5.775744709896233', '6.378682699349237', '6.928273134920524', '7.382326897560924', '7.888606358879243', '8.127687984164392', '8.878218332744144', '9.224926622680326', '9.707589251911823', '10.16213122101403', '10.69867782392244', '11.18416937183549', '11.51654857419279', '12.02648281875856', '12.33016225938049', '12.99763039045799', '13.35474586173119', '13.90973805940963', '14.18320262479447', '14.70353218403105', '15.19158574243862', '15.40390374496585', '16.01781791664298', '16.49205308053098', '16.87360387423780', '17.30464713009849', '17.78904617629179', '18.19314116820362', '18.33938528178593', '19.14898933209376', '19.38068649816900', '19.86240351885338'], 'prelabel': '2-296208-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 48.63365900476688, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1676610229569355582, 'z1': {'__RealLiteral__': 0, 'data': '0.7697513077710186', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.581374403056555', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.960904154120774', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2365.232788191943, 'bad_primes': [2, 3, 11, 17], 'central_character': '1.1', 'conductor': 296208, 'conductor_radical': 1122, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -1, 0, 4, 0, 0, 0, 2, 0, -5, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 4, 0, 0, 0, -4, 0, -3, 0, 0, 0, 2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 14, 0, 0, 0, 0, 0, 6, 0, 0, 0, 12, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 2, 13], 'euler17': [1, 1, 0], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, 6, 31], 'euler37': [1, 0, 37], 'euler41': [1, 10, 41], 'euler43': [1, -4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 0, 5], 'euler53': [1, -2, 53], 'euler59': [1, 4, 59], 'euler61': [1, 0, 61], 'euler67': [1, 4, 67], 'euler7': [1, -2, 7], 'euler71': [1, 2, 71], 'euler73': [1, -14, 73], 'euler79': [1, -6, 79], 'euler83': [1, -12, 83], 'euler89': [1, -2, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 5], [1, -2, 7], [1, 0, 0], [1, 2, 13], [1, 1, 0], [1, -4, 19], [1, -2, 23], [1, 0, 29], [1, 6, 31], [1, 0, 37], [1, 10, 41], [1, -4, 43], [1, 4, 47], [1, -2, 53], [1, 4, 59], [1, 0, 61], [1, 4, 67], [1, 2, 71], [1, -14, 73], [1, -6, 79], [1, -12, 83], [1, -2, 89], [1, 2, 97]], 'index': 104, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/296208/dl'], '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': '2-296208-1.1-c1-0-104', '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': '2-296208-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 48.63365900476688, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1676610229569355582, 'z1': {'__RealLiteral__': 0, 'data': '0.7697513077710186', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1676610229569355582', 'Lhash_array': ['1676610229569355582'], 'factors': ['2-296208-1.1-c1-0-104'], 'label': '2-296208-1.1-c1-0-104', 'type': 'ECQ', 'url': 'EllipticCurve/Q/296208/dl'}