-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '4159949628378547776323788761374', 'a10': [-3634.7987836648263, -4194.781411107763], 'a2': [13.79060073927005, 8.8626809468376], 'a3': [-11.881106908142838, -82.63491364390663], 'a4': [58.46043352027597, 128.01049342936798], 'a5': [-324.87548302324626, -95.39204872177369], 'a6': [568.5192729846405, -1244.8835610093136], 'a7': [482.42512529674246, -556.7482736432862], 'a8': [-29.693350626776837, 206.52178991506852], 'a9': [-4588.95711827828, 1347.4393848846053], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.184855586134804, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[23, [[1.0, 0], [56626.86211442757, -14079.202181714965]]]], 'bad_primes': [23], 'central_character': '23.2', 'coefficient_field': 'CDF', 'conductor': 23, 'conductor_radical': 23, 'conjugate': '1244229962265684057810338616345', 'degree': 2, 'euler_factors': [[[1.0, 0], [-13.79060073927005, -8.8626809468376], [53.173121664241464, 116.43289540537835]], [[1.0, 0], [11.881106908142838, 82.63491364390663], [-2098.411133294906, 616.1491018122067]], [[1.0, 0], [324.87548302324626, 95.39204872177369], [65722.93225243603, 42237.56386371856]], [[1.0, 0], [-482.42512529674246, 556.7482736432862], [-117202.38885609606, -815160.519710949]], [[1.0, 0], [-2700.7926319380313, 1735.694031970324], [8095263.394334984, -17726154.240544707]], [[1.0, 0], [-5942.705085917116, -6858.247267532756], [-8930045.048743483, 62109827.57283022]], [[1.0, 0], [-8999.765020804482, 19706.736534240285], [-268714684.5669143, -310113277.4608412]], [[1.0, 0], [-17238.67333338126, -37747.429271260145], [-585361503.0544883, 675543186.2765507]], [[1.0, 0], [56626.86211442757, -14079.202181714965]], [[1.0, 0], [-77365.68285084469, 169407.21510047864], [-11296266660.177124, -13036586678.190353]], [[1.0, 0], [-3838.122479275489, 26694.72820013899], [-26398159925.271572, -7751199118.883628]], [[1.0, 0], [321726.958456225, -94467.55849522895], [79861777016.43187, -51324047655.77947]], [[1.0, 0], [-271136.31179630524, -79612.80434099262], [163837720936.36267, 105292109833.99518]], [[1.0, 0], [33504.536721672666, 233029.1714467278], [-260808047454.81808, 76580152304.26135]], [[1.0, 0], [-1132067.3625030264, 0], [506623120463.0, 0]], [[1.0, 0], [47175.76275975712, -54443.73250282982], [-167178825883.7291, -1162754274227.0532]], [[1.0, 0], [-1230857.2435576154, -1420484.9820591705], [-354172033580.5869, 2463320601042.667]], [[1.0, 0], [36.71994124671207, -255.39280114142852], [-3015439669039.448, -885412974687.2823]], [[1.0, 0], [2830387.5688962727, 1818979.6407919757], [2517710590325.938, 5513017190818.247]], [[1.0, 0], [-3203689.208592867, -2058886.0373379292], [3778249458851.717, 8273212297666.309]], [[1.0, 0], [707340.9155315536, 1548860.556919586], [-7234507502401.917, 8349066728529.421]], [[1.0, 0], [-979774.7486428546, -1130720.33619862], [-2733001201580.1055, 19008440882430.1]], [[1.0, 0], [8231190.256377856, -2416895.5276886853], [22828298762110.785, -14670856789548.719]], [[1.0, 0], [-249439.4531624231, -1734889.5040522865], [-42439655045849.805, 12461407072626.938]], [[1.0, 0], [-3360850.9958538217, -986834.8912009749], [67971842263911.35, 43682850569256.94]], [[1.0, 0], [-977704.3682078635, 287079.9047673965], [90193765263322.45, -57964013318617.88]], [[1.0, 0], [9018922.684355991, -5796109.665333848], [51090806779615.266, -111873261824079.89]], [[1.0, 0], [-1593201.2226142376, 11080957.8994583], [-154073604384136.7, -45240092109687.42]], [[1.0, 0], [5410735.542010744, -11847858.19811595], [-119711104033871.12, -138153978746014.6]], [[1.0, 0], [-10986539.249224808, -7060620.049605038], [97730763624868.58, 214000521746204.44]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 10, 'label': '2-23-23.2-c7-0-10', 'load_key': 'CMFs-workshop', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/23/8/c/a/2/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [2.3254496929779354, 2.628150947372489, 2.8795482615761268, 3.074865176532533, 3.210245364275227, 3.2828631743166516, 3.291082950157876, 3.234658311921835, 3.114955312792269, 2.9351764614654634, 2.700556566965621, 2.41849679776857, 2.0986009159447683, 1.7525780424000508, 1.393980191860018, 1.0377507233791277, 0.6995720869297245, 0.39501775631678243, 0.13853349783921473, -0.057703958769815024, -0.184978911801948, -0.23918488896601692, -0.22181623864628552, -0.1406791657851752, -0.010197473400999978, 0.14879949324730954, 0.3098920766665372, 0.44253151246064854, 0.5141330468428845, 0.4927189349866556, 0.3499555385651655, 0.06435652128705094, -0.37563769841457456, -0.9690359342530521, -1.7004719508389803, -2.5394998977722603, -3.4412636128163805, -4.348686314612463, -5.19618282278251, -5.914726182312087, -6.437920878224893, -6.70856664043917, -6.68506360200367, -6.346934476826575, -5.69874209113698, -4.771773625926166, -3.6230487233809967, -2.33147717858854, -0.9913200364959605, 0.2965399224583886, 1.4346807158344548, 2.339476796896243, 2.950441095176628, 3.237331892337658, 3.2039594043797175, 2.8879713933851527, 2.356380603720239, 1.6971652068119194, 1.0078522869427604, 0.3824977264915061, -0.10118173231111581, -0.39265784948450894, -0.4757192420531714, -0.3706186550527052, -0.13065871664672216, 0.16653237288548142, 0.43191999526754543, 0.5803058380845181, 0.5455118322091641, 0.2929675191422802, -0.17257530089950102, -0.8058028666264855, -1.526668802653773, -2.2326903690146027, -2.8159206126791663, -3.1818388702057803, -3.2668546308112894, -3.0511313985045754, -2.564058250401168, -1.8808683975408824, -1.1104570897831365, -0.37612651215714243, 0.2075261310261957, 0.5573635960336824, 0.6396257159980689, 0.47911130403505636, 0.1571266734040304, -0.2022827613281887, -0.456013600822179, -0.4715636494963915, -0.15720180211815007, 0.5133917915821641, 1.4874673047221856, 2.6342463540414767, 3.7617513690771176, 4.6474448534100805, 5.077782554204277, 4.889623886019651, 4.005541601201876, 2.4557130422169404, 0.3812412124898744, -1.9828909954715117, -4.343097035872344, -6.394823516013458, -7.8739333201487876, -8.602097978137328, -8.517287555120708, -7.683148076543743, -6.275153175425844, -4.5460965083051175, -2.7777718243823637, -1.2286239247468964, -0.08805474390453434, 0.5533326352684319, 0.7117313353103351, 0.49534942459798254, 0.07090964311166079, -0.38031803081928856, -0.7063962962815629, -0.81813552587281, -0.7043404236175835, -0.42576589363676526, -0.0900663233468039, 0.18507473986131132, 0.3103067250099518, 0.25362493238628897, 0.05153942350834936, -0.20138496475767548, -0.38246610843729695, -0.3825262916133617, -0.14758706966342292, 0.29182963208890594, 0.8137350898507173, 1.2245310384274835, 1.3030718679722633, 0.859350862209447, -0.20669769318252856, -1.8622025572597427, -3.9273445825447943, -6.0970316190192575, -7.996197012445041, -9.257771691386441, -9.605709163433676, -8.922897449846355, -7.286307620665977, -4.95895502381795, -2.3385645300898017, 0.1263003625109377, 2.033284231360314, 3.1131338998001077, 3.285022227530081, 2.666406189234364, 1.534877129408405, 0.2517612010030842, -0.8327751839965636, -1.4684101946996269, -1.5639973997126944, -1.2021986008367462, -0.6061215715136995, -0.06773579683068714, 0.14166042601719014, -0.14631668756210894, -0.9453704017837632, -2.10782769964748, -3.364811808854636, -4.4016830133983404, -4.946991144601751, -4.849249406105979, -4.119352285873821, -2.9264814983251703, -1.5489944655312753, -0.2950590681996577, 0.5832837888676743, 0.9571140563882259, 0.8490513700677804, 0.4153603265419846, -0.11168467152488985, -0.5022828170938893, -0.6031028732962633, -0.3830125724359787, 0.0640369176318239, 0.5595059227807462, 0.9102229550354741, 0.9837298349920964, 0.7625511929876655, 0.35735940367318364, -0.02752579330385695, -0.1665504194850095, 0.10033406486497863, 0.7967736106923972, 1.7818364307320815, 2.7787811072099045, 3.456597865261668, 3.5417770522132144, 2.9254941746383407, 1.7297124561958477, 0.30587135422720324, -0.840654665702408, -1.1839731930846322, -0.333001673059009, 1.836833385809604, 5.116986183365124, 8.9885517208841, 12.733140670680918, 15.604316825757383, 17.013129545556943, 16.675842630252927, 14.682060833178163, 11.464297873110564, 7.6787549597823785, 4.032856322763055, 1.1099136670579837, -0.7594241619959492, -1.545185843094318, -1.47768137496197, -0.9382502451999366, -0.3208424470656967, 0.08940320299229103, 0.18334756883974881, 0.024460013105041638, -0.21609880171953116, -0.3558443545913806, -0.28931089324407083, -0.03418493405732034, 0.28117174724138017, 0.4816321761287564, 0.43290741780738123, 0.11530623585529873, -0.34908207330630014, -0.7306750638635963, -0.7786783243608699, -0.32814613100130063, 0.6140178310836989, 1.840866704864794, 2.9921053806411906, 3.6652208096641634, 3.5551872968503493, 2.573313659192714, 0.8998411289202461, -1.0539297973391606, -2.7667872217482423, -3.774197672835085, -3.8239534444056913, -2.965441955288292, -1.538165700692383, -0.05959575174282673, 0.9516352332016466, 1.1567737208215034, 0.5181857330928146, -0.6839351669474105, -1.9480800435762249, -2.72953730952216, -2.638369578584833, -1.586800115166707, 0.16800591662515527, 2.1034751608520033, 3.6076819004825125], 'positive_zeros': ['3.28162162951651285920631373479134', '4.23072543707188580111065243183944', '5.47937000219620821221270094789720', '8.571429639244069445430158882837031', '10.50418551456200920416144370422390', '11.32838523894282485716709339865479', '12.24759484041071144873943072663698', '14.34424236311161800874624410133303', '15.19226210564532656448660248784678', '15.87088315560327814099619173986896'], 'prelabel': '2-23-23.2-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6804580925906683, 'root_angle': 0.4549991056867143, 'root_number': '0.14090401347586237 + 0.9900232618410508*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.227499552843', 'prec': 47}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.28162162951651285920631373479', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.23072543707188580111065243184', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.47937000219620821221270094790', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.184855586134804, 'bad_primes': [23], 'central_character': '23.2', 'conductor': 23, 'conductor_radical': 23, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/23/8/c/a/2/12'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '2-23-23.2-c7-0-10', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-23-23.2-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6804580925906683, 'root_angle': 0.22749955284335716, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '3.28162162951651285920631373479', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '4159949628378547776323788761374', 'Lhash_array': ['4159949628378547776323788761374'], 'label': '2-23-23.2-c7-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/23/8/c/a/2/12'}