-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '405499534417134706250107575917', 'a10': [-2.867444178333747, -2.4060713524612862], 'a2': [0.6862416378687336, 0.7273736415730487], 'a3': [-1.6879750556308708, 0.38825276762433875], 'a4': [-0.05814482891047583, 0.9983081582712682], 'a5': [-3.717872470961272, 0.4345569682599843], 'a6': [-1.4407635962954253, -0.9613533479371009], 'a7': [-3.250504751657633, -1.6324648428840887], 'a8': [-0.766044443118978, 0.6427876096865394], 'a9': [2.6985195768640824, -1.3107219740590654], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.293576512744743, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6862416378687336, -0.7273736415730487]]], [3, [[1.0, 0], [1.6879750556308708, -0.38825276762433875]]]], 'bad_primes': [2, 3], 'central_character': '162.103', 'coefficient_field': 'CDF', 'conductor': 162, 'conductor_radical': 6, 'conjugate': '4900422288340348910918460651778', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6862416378687336, -0.7273736415730487]], [[1.0, 0], [1.6879750556308708, -0.38825276762433875]], [[1.0, 0], [3.717872470961272, -0.4345569682599843], [4.865224352899119, -1.1530793537122008]], [[1.0, 0], [3.250504751657633, 1.6324648428840887], [4.180110141919503, 5.614862349285307]], [[1.0, 0], [-2.0851175544298868, -4.833845824447015], [-7.548658016556069, 8.001110057303535]], [[1.0, 0], [0.20274666934348617, 0.048051843347076136], [11.61722432420436, 5.834389342606008]], [[1.0, 0], [0.2902165546846699, -1.645899870335257], [-15.974774553360442, -5.814342436536369]], [[1.0, 0], [-0.2867653458197024, -1.6263270922436637], [-17.854159794932258, 6.498382723187706]], [[1.0, 0], [7.815995216935875, -3.925340332848687], [13.734647609164082, -18.44883343336601]], [[1.0, 0], [-0.21610724713312499, 0.7218484754579259], [-24.229146530975157, -15.935760364053374]], [[1.0, 0], [4.771838275102453, 3.138487406101381], [12.278472747213861, 28.464699313288495]], [[1.0, 0], [-5.154673558074939, 1.8761477424983344], [28.343644395402187, -23.783141558401955]], [[1.0, 0], [-3.4321418152007714, 3.6378577934602787], [-2.383937985329509, -40.930634489122]], [[1.0, 0], [0.625285121428653, -0.8399036787738413], [-12.33253900657688, -41.19354902956602]], [[1.0, 0], [-4.5443566208908655, 2.9888703684521225], [18.61574900384037, -43.15615702337288]], [[1.0, 0], [2.4338153610276363, -4.215491861541456], [-26.5, -45.89934640057525]], [[1.0, 0], [4.738609663480446, -10.985331971732455], [-40.48825663425528, -42.91504485280987]], [[1.0, 0], [-0.12372842484421213, -2.124335013904844], [-60.58753982225852, 7.081667761639044]], [[1.0, 0], [-1.7920149394159341, -5.985746749244217], [-55.97768336466674, 36.817101530744004]], [[1.0, 0], [1.9764410629019853, 1.6584309669246873], [12.329020614352055, 69.92135046386677]], [[1.0, 0], [4.286323561733409, -3.596652519756988], [12.676316969685915, -71.89096596989118]], [[1.0, 0], [-2.969882802209759, -3.147891864442209], [-4.593441483927591, 78.86634450343018]], [[1.0, 0], [9.811317596264994, 10.399389099718384], [-4.826020799569494, 82.85957713651526]], [[1.0, 0], [-0.39695218931961485, 0.33308243565310264], [15.4546878123568, -87.64789001808651]], [[1.0, 0], [-1.8481817584525306, -0.216021466045306], [94.38535244624292, 22.369739462016696]], [[1.0, 0], [-0.6687998880118563, -11.482850615677954], [-100.31707413193624, 11.725384326648253]], [[1.0, 0], [5.887425046138069, -13.648585383379265], [-70.68288870047957, -74.91948508202401]], [[1.0, 0], [-1.2793692853228493, -2.215932603822259], [-53.5, 92.66471820493493]], [[1.0, 0], [5.385930928886335, -9.32870601488777], [-54.5, -94.39676901250381]], [[1.0, 0], [7.369823115621236, 9.899390429409188], [-32.408765296353195, 108.25281489165025]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-162-81.22-c1-0-0', 'load_key': 'CMFs-workshop', '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': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/103/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.3546770188019283, 0.216477348646553, 0.0788744960422048, -0.06396959356491969, -0.2168902646171428, -0.383340250312556, -0.5651651081162631, -0.762489209554011, -0.9736673713442049, -1.195279811481647, -1.4221721027361638, -1.6475570931292174, -1.8632012899753585, -2.0597162469685606, -2.2269684598722064, -2.354610833573447, -2.432726037700758, -2.4525579358401517, -2.4072927513919318, -2.292837924711154, -2.1085351399015573, -1.8577363116587344, -1.5481689772107543, -1.1920219057073622, -0.8056937966413618, -0.40916806998651484, -0.02500454901053468, 0.3230270211058872, 0.6116084859237354, 0.8197276746832891, 0.9305876467444394, 0.93340445324912, 0.8249107831190468, 0.6103825642343276, 0.3040242222874549, -0.07141279262860893, -0.4858451289544043, -0.9038982618174716, -1.28767885208598, -1.6000956207499308, -1.8084627410804575, -1.8880534779177525, -1.8252322705869342, -1.61978930778441, -1.2861387289585797, -0.853121777569033, -0.36227653355566525, 0.13541200808531523, 0.5840971327496177, 0.9286349911428183, 1.12062053426229, 1.1242747062816665, 0.9215095643276328, 0.5155175638816777, -0.06766955814256885, -0.7800303013990278, -1.554947644725868, -2.312999613907591, -2.96970027861982, -3.4444706126651847, -3.6699037344551324, -3.600267420751969, -3.218183742117044, -2.538553868163621, -1.6090523918238542, -0.5068795724427222, 0.6681050515369292, 1.8032881333367887, 2.7852481333935692, 3.512417871538342, 3.90696272546441, 3.9243771454757503, 3.559502273188957, 2.8480520054798415, 1.8632654910548654, 0.7079188245816029, -0.4974512091176379, -1.6287188758497035, -2.5729659897113435, -3.2419792307149295, -3.582631911848765, -3.5827023300553504, -3.27127203560296, -2.7135873667349037, -2.0010553848688395, -1.2377661231082417, -0.5254749490467658, 0.05074956229116974, 0.43406072785649547, 0.6027873723686765, 0.5717174563448081, 0.38749525035597626, 0.11885402708280081, -0.1567369549056041, -0.3678006659849759, -0.4624534559938766, -0.4184905566010073, -0.2480882242872763, 0.0038835952605331607, 0.26786992124077047, 0.4627775231156852, 0.5121102652289443, 0.36030115304657634, -0.013738685460882744, -0.588507933244954, -1.2990805455125198, -2.044202384570409, -2.700598517660615, -3.142440770326098, -3.2628778297748933, -2.9939687954673024, -2.321415233175727, -1.2911844282580889, -0.006372138733520121, 1.3857242475650668, 2.7146304082572463, 3.8126096956613345, 4.541232327772563, 4.814037741318461, 4.611201498720075, 3.983347608388179, 3.0434504571456955, 1.9478497145551255, 0.8693915067809376, -0.03275842685081818, -0.641312301731274, -0.9019187031408958, -0.8330511784278791, -0.522603387899473, -0.11144280350868274, 0.23340344080634085, 0.3512404825951794, 0.11996964653264236, -0.5179345999266683, -1.5408125218678685, -2.8476758917892555, -4.273008570598267, -5.6141784600925515, -6.666673781687615, -7.260758632187524, -7.292701852816055, -6.744593832398939, -5.688802900658958, -4.275976452024518, -2.7086287645117526, -1.2051704866243862, 0.038839124503580895, 0.8848017062304717, 1.2739522746655512, 1.2345371530665792, 0.871908266995934, 0.34354406602224014, -0.17594299995776352, -0.532680678631429, -0.6265119150528858, -0.4322274066583972, -0.004577066348408962, 0.5340869270596601, 1.0210584693887714, 1.2897751067365093, 1.2078913476893927, 0.708808630948724, -0.19019004858555252, -1.3873076395137802, -2.713542138291859, -3.9645544470714142, -4.940553252667711, -5.4858537798416105, -5.51973858566073, -5.0520309359340345, -4.180027675416207, -3.0674445316799277, -1.9099335227768786, -0.8946740719966128, -0.16284760677964802, 0.21683761096189985, 0.2578841624767198, 0.04710187621061106, -0.28059383387621506, -0.5775931433800873, -0.7207523395672442, -0.641421198295801, -0.3411188873197379, 0.11095559302219736, 0.598012124282116, 0.9884515385715956, 1.1731754177009517, 1.097894628656138, 0.7818341144002096, 0.31730864149949, -0.15078759072228812, -0.4615195085640566, -0.48215389172677353, -0.1493342653324867, 0.5035324899086259, 1.3407327879332784, 2.1438275078626714, 2.6537903229631308, 2.6275514748482607, 1.896815835129072, 0.41567357003506267, -1.7147492539471763, -4.251798685785021, -6.847708562387562, -9.110741571311763, -10.679044501932804, -11.291868420002558, -10.842816532244932, -9.403254069314254, -7.210254540221567, -4.621110784423262, -2.0437882884296705, 0.14194735334499786, 1.6558989221247373, 2.366157065350496, 2.3051454375372713, 1.6503625892201343, 0.6751587543551398, -0.31843374517310113, -1.0689699604098915, -1.4110363611198031, -1.3046175645916633, -0.8326599520612158, -0.1688941647176748, 0.4748713942402985, 0.9080048424219652, 1.0116397220064537, 0.7679686914417482, 0.26133621834506054, -0.3483747468913597, -0.8723789161492841, -1.146827146661282, -1.0792589877057284, -0.6751393422766472, -0.037303086106603954, 0.6616098964567775, 1.2263823571924684, 1.4934112222237919, 1.3771608489790421, 0.8960903656037291, 0.17063938992957323, -0.6067000971632583, -1.2216431480931285, -1.495478301388148, -1.3341392180505767, -0.7555193237190018, 0.11281391701991605, 1.0654876040591814, 1.8727279646118888, 2.34122388480745, 2.3660227756514973, 1.959091520581546, 1.246198117129246, 0.43222510578229134, -0.2563180030799633, -0.6363079126798965, -0.6227430611503446], 'positive_zeros': ['0.31988272978699971607451532457013', '3.25847412625980890352784494744243', '4.35250024462410606124283185947647', '5.84036426994346679103653530144502', '6.73699818138902261929748084783305', '8.179189970638095400606179187636265', '9.448207212497677717045141971783472', '10.86222048954233765337992825301768', '11.55229263213760161594430072112387', '12.24820829997505181692179551790883'], 'prelabel': '2-162-81.22-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.9837524699928714, 'root_number': '-0.9986975827172765 + 0.051020959170410954*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.491876234996', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31988272978699971607451532457', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.25847412625980890352784494744', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.35250024462410606124283185948', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.293576512744743, 'bad_primes': [2, 3], 'central_character': '81.22', 'conductor': 162, 'conductor_radical': 6, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/162/2/g/a/103/1'], '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': '2-162-81.22-c1-0-0', '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': '2-162-81.22-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1373550513119213, 'root_angle': 0.4918762349964357, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.31988272978699971607451532457', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '405499534417134706250107575917', 'Lhash_array': ['405499534417134706250107575917'], 'label': '2-162-81.22-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/162/2/g/a/103/1'}