-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2028775186523124092327177432155', 'a10': [-1.5847857707538031, 1.1863557679066044], 'a2': [-0.9096319953545183, -0.41541501300188644], 'a3': [0.0, 0.0], 'a4': [0.6548607339452851, 0.7557495743542583], 'a5': [0.9487418461104453, -1.7374909659241222], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.28173255684142967, -0.9594929736144974], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5990043004761398, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9096319953545183, 0.41541501300188644]]], [3, [[1.0, 0], [0, 0]]], [89, [[1.0, 0], [-0.8776789895672557, 0.47924898672005684]]]], 'bad_primes': [2, 3, 89], 'central_character': '3204.431', 'coefficient_field': 'CDF', 'conductor': 3204, 'conductor_radical': 534, 'conjugate': '825610288949223440196509008493', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9096319953545183, 0.41541501300188644]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.9487418461104453, 1.7374909659241222], [-0.5406408174555976, -0.8412535328311812]], [[1.0, 0], [0, 0], [-0.21256528955297668, 0.9771468659711595]], [[1.0, 0], [0, 0], [-0.8412535328311812, -0.5406408174555976]], [[1.0, 0], [0.9125927160304135, -0.45681129715465596], [0.599277666511347, -0.8005412409243604]], [[1.0, 0], [0.39832597918231244, 0.14856790904975156], [0.7557495743542583, 0.6548607339452851]], [[1.0, 0], [0, 0], [-0.8776789895672557, -0.47924898672005684]], [[1.0, 0], [0, 0], [-0.47924898672005684, 0.8776789895672557]], [[1.0, 0], [-1.1341097206653419, -0.12192941521299733], [0.9771468659711595, 0.21256528955297668]], [[1.0, 0], [0, 0], [0.47924898672005684, 0.8776789895672557]], [[1.0, 0], [-0.7648791926009848, 1.84658172035428], [-0.7071067811865476, -0.7071067811865476]], [[1.0, 0], [1.5992776665113468, 0.8005412409243604], [0.599277666511347, 0.8005412409243604]], [[1.0, 0], [0, 0], [0.9771468659711595, -0.21256528955297668]], [[1.0, 0], [0, 0], [-0.9898214418809327, -0.14231483827328514]], [[1.0, 0], [0.13368245616045674, 1.8691249689690157], [-0.9898214418809327, 0.14231483827328514]], [[1.0, 0], [0, 0], [0.8005412409243604, -0.599277666511347]], [[1.0, 0], [0.27650058763420143, -1.5325397235125406], [-0.9369497249997617, -0.3494641795990983]], [[1.0, 0], [0, 0], [0.14231483827328514, 0.9898214418809327]], [[1.0, 0], [0, 0], [-0.5406408174555976, 0.8412535328311812]], [[1.0, 0], [-1.2963903918098558, -0.1863927988858961], [0.9594929736144974, 0.28173255684142967]], [[1.0, 0], [0, 0], [0.28173255684142967, -0.9594929736144974]], [[1.0, 0], [0, 0], [-0.07133918319923234, -0.9974521146102535]], [[1.0, 0], [-0.8776789895672557, 0.47924898672005684]], [[1.0, 0], [1.9140965909709213, -0.562029469152075], [0.8412535328311812, -0.5406408174555976]], [[1.0, 0], [0.24170254025599525, 0.5835215507460527], [-0.7071067811865476, 0.7071067811865476]], [[1.0, 0], [0, 0], [0.8776789895672557, -0.47924898672005684]], [[1.0, 0], [0, 0], [0.5406408174555976, -0.8412535328311812]], [[1.0, 0], [-0.3212922542043036, -1.4769566560786025], [-0.9096319953545183, 0.41541501300188644]], [[1.0, 0], [0.07133918319923234, 0.002547885389746459], [0.9974521146102535, 0.07133918319923234]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-3204-1068.431-c0-0-1', 'leading_term': '0.82675097193696220612971361529239', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3204/1/cd/b/431/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [0.8267509719369622, 0.8973899458010132, 0.9769907085896298, 1.066234588681971, 1.1647900177369528, 1.2713897717613205, 1.3839798268623522, 1.4998877700553732, 1.615979463294192, 1.7287936923940082, 1.8346574767839827, 1.9297896254698057, 2.010400132075707, 2.072790927629041, 2.1134609780606857, 2.1292164129272972, 2.1172844946480858, 2.0754287774342313, 2.002061705200534, 1.896350106944949, 1.7583085349698402, 1.5888751422647462, 1.389964808147974, 1.164494498613628, 0.9163763921118157, 0.6504751105392612, 0.37252645925077954, 0.08901637930162168, -0.1929796809729355, -0.465995102329034, -0.7224044935347996, -0.9546846932888761, -1.155697135020305, -1.3189826696194211, -1.4390584783134117, -1.5117055338684153, -1.5342342663738566, -1.505715735483318, -1.4271657672477673, -1.3016702269550495, -1.134440895280399, -0.932793294898211, -0.7060402529336613, -0.4652979271438293, -0.2232043875092342, 0.00644548089618976, 0.20914113955997715, 0.3701621436358879, 0.4751332874201512, 0.5106105924015735, 0.46467673607107157, 0.3275223719814078, 0.09198850072718545, -0.24595525024475728, -0.6868207958113152, -1.22732264498827, -1.8602292006903332, -2.574359510016168, -3.3547355166346353, -4.182893889499737, -5.037354912854213, -5.894238981914798, -6.728014254387432, -7.5123522828118325, -8.2210623304916, -8.829069883445385, -9.313400919791217, -9.654131054919667, -9.835257959300124, -9.845456589498212, -9.678679843515317, -9.334572219402125, -8.818670795920983, -8.142376144563633, -7.32268531117956, -6.381689379596899, -5.345848889790729, -4.245071023921368, -3.1116224665119536, -1.9789206649034978, -0.8802533684768272, 0.1525186258838507, 1.090217999875869, 1.9075092912204923, 2.5839046161980943, 3.1045679314701675, 3.4608773441890994, 3.6507155909633044, 3.678471261070773, 3.5547470655265223, 3.2957857860554984, 2.9226387499349826, 2.4601150165011814, 1.9355611927309164, 1.3775312394459187, 0.8144122043405077, 0.2730750754072037, -0.2223803939926519, -0.651722072983692, -0.9994658594251377, -1.255493802834082, -1.4153772982502122, -1.4803884411462012, -1.4571996234487572, -1.3572887686999895, -1.1960842736947608, -0.9918987724596652, -0.7647133558998407, -0.534883074483436, -0.3218397990704946, -0.14286940654207272, -0.012036627929111981, 0.06067715242608522, 0.06996995887127713, 0.01551148759701497, -0.09808798583515184, -0.261631967536371, -0.4619952644932776, -0.6830453687374946, -0.9067712767180016, -1.114549339330943, -1.2884658777085474, -1.4126112781481273, -1.4742605386438934, -1.4648609017370602, -1.3807580575475995, -1.2236078840720936, -1.0004399435453442, -0.7233608403736348, -0.4089087303148415, -0.07709329014024406, 0.249823184005111, 0.5487296165662163, 0.7971671029246735, 0.9748306456075304, 1.0649729593172346, 1.055615664659969, 0.9404835676345882, 0.7195939277385511, 0.39945373778527266, -0.007157195815186316, -0.4818127231619599, -1.0014445045804208, -1.5396662198140207, -2.0683376689358894, -2.559270895511252, -2.9859689111987904, -3.325283149424125, -3.558878913437205, -3.6744087961214156, -3.6663118008932747, -3.536179650894212, -3.292660059196867, -2.9508977116349646, -2.531545311809616, -2.059407077378396, -1.5618034262089726, -1.0667663153539777, -0.6011881990727859, -0.18905272071728924, 0.1501285288983996, 0.4025615268394231, 0.5610068372118905, 0.6251451918761048, 0.6014416422424547, 0.5025141325010088, 0.3460485644418767, 0.1533364096240142, -0.05245985505788675, -0.2481860204909116, -0.4125793177911304, -0.5280114233132843, -0.5819545914412919, -0.5680519660131904, -0.48670027401691157, -0.3450879342259769, -0.15667177451451073, 0.05988177235442292, 0.28222303282744376, 0.4862067101581524, 0.6480028468757743, 0.7462709643542099, 0.7642262948053271, 0.6914286742160739, 0.5251392255211528, 0.2711168191027735, -0.056236095604491505, -0.4344227434799337, -0.8340896403777152, -1.2208930673019298, -1.5578843823775403, -1.8082597605653394, -1.9382852277941935, -1.9201857590267888, -1.7347798723716732, -1.3736496934672016, -0.8406608719847755, -0.1526858175454924, 0.6605648297936113, 1.5576370807288682, 2.4873239642485085, 3.3914547195180056, 4.208324802857821, 4.876556435562985, 5.339140358650658, 5.547386897921814, 5.464510566818219, 5.068588136423361, 4.354664867119427, 3.3358354997073167, 2.0431924091020406, 0.5246086844420815, -1.1575963521926274, -2.9299831702905936, -4.712112005412865, -6.421199873914705, -7.977015222990179, -9.306688578223412, -10.34911761609363, -11.058667899025155, -11.407914853214875, -11.38923562636128, -11.015136984758563, -10.317292004768014, -9.34434782656249, -8.158652694483429, -6.832126595854942, -5.44156035417545, -4.0636684344868135, -2.770237819624284, -1.6237076584348074, -0.673482350597028, 0.046773468017255626, 0.5206820340581348, 0.7494510479791604, 0.7509251159885304, 0.5574830740340553, 0.21295864186679425, -0.23116739888058482, -0.7200036495032696, -1.1995847136845088, -1.6209762274305988, -1.9438387623057884, -2.139187108910579, -2.1911477118137124, -2.0975983113367396, -1.8696637464279944, -1.5301332746405487, -1.1109504123000895, -0.6499993649881044, -0.18746676218748454, 0.23791075446411947, 0.5923960750694686, 0.8503007099314299, 0.9962795753604691, 1.026682121323929, 0.9498504183443727], 'positive_zeros': ['1.60042143013055874164851277193807', '2.63499441574324512421294511459718', '3.06472122965138197913847275991138', '4.73713025257024005612191861108876', '5.65645552515230702180700414360705', '6.51099409287956042887175366890673', '6.68975534992429781885489691063492', '7.63077590592619462002587445012812', '8.202179579989305445326825230706915', '9.347318277364137122277793746508886'], 'prelabel': '2-3204-1068.431-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2645174180200682, 'root_angle': 0.7204216839934441, 'root_number': '-0.63844417472653606745781934501029 + 0.76966813352103404108458610665983*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.36021084199672204', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60042143013055874164851277194', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.63499441574324512421294511460', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.06472122965138197913847275991', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.5990043004761398, 'bad_primes': [2, 3, 89], 'central_character': '1068.431', 'conductor': 3204, 'conductor_radical': 534, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3204/1/cd/b/431/1'], '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': '2-3204-1068.431-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3204-1068.431-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2645174180200682, 'root_angle': 0.36021084199672204, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60042143013055874164851277194', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2028775186523124092327177432155', 'Lhash_array': ['2028775186523124092327177432155'], 'label': '2-3204-1068.431-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3204/1/cd/b/431/1'}