-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '531550234214326060850149879959', 'a10': [92336810.17889129, 65654918.829156555], 'a2': [-205.0930294094436, 205.0930294094436], 'a3': [-8389.668454011553, -8389.668454011553], 'a4': [0.0, -18590.301424685797], 'a5': [-65048.26474737848, -385170.8891886236], 'a6': [3441325.0379481455, -1.276297055397792e-58], 'a7': [-4201040.070220864, 4201040.070220864], 'a8': [-9628235.538553791, -9628235.538553791], 'a9': [0.0, 97726352.53647321], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.116227192831357, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '8.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [65048.26474737848, 385170.8891886236]]]], 'bad_primes': [5], 'central_character': '5.3', 'coefficient_field': 'CDF', 'conductor': 5, 'conductor_radical': 5, 'conjugate': '1262874317191579143999011169595', 'degree': 2, 'euler_factors': [[[1.0, 0], [205.0930294094436, -205.0930294094436], [0, -65536.0]], [[1.0, 0], [8389.668454011553, 8389.668454011553], [0, 43046721.0]], [[1.0, 0], [65048.26474737848, 385170.8891886236]], [[1.0, 0], [4201040.070220864, -4201040.070220864], [0, -33232930569601.0]], [[1.0, 0], [-164170857.11471644, 0], [45949729863572160, 0]], [[1.0, 0], [-205181507.01621562, -205181507.01621562], [0, 665416609183179900]], [[1.0, 0], [-2005521690.113018, 2005521690.113018], [0, -48661191875666870000]], [[1.0, 0], [0, 6447169027.623825], [-288441413567621170000, 0]], [[1.0, 0], [-20783202039.078484, -20783202039.078484], [0, 6132610415680999000000]], [[1.0, 0], [0, -706157193019.5623], [-250246473680347360000000, 0]], [[1.0, 0], [356624093961.3802, 0], [727423121747185300000000, 0]], [[1.0, 0], [-211875232106.151, 211875232106.151], [0, -12337511914217166000000000]], [[1.0, 0], [-8103371358759.525, 0], [63759030914653050000000000, 0]], [[1.0, 0], [6407719405036.81, 6407719405036.81], [0, 136614025729312090000000000]], [[1.0, 0], [2973462223279.8916, -2973462223279.8916], [0, -566977372488557300000000000]], [[1.0, 0], [-80938945770068.16, -80938945770068.16], [0, 3876269050118517000000000000]], [[1.0, 0], [0, -16426000104672.596], [-21559177407076400000000000000, 0]], [[1.0, 0], [-182779603312969.5, 0], [36751693856637463000000000000, 0]], [[1.0, 0], [464887479343234.75, -464887479343234.75], [0, -164890958756244160000000000000]], [[1.0, 0], [933424372421364.8, 0], [416997623116370000000000000000, 0]], [[1.0, 0], [-872119096836962.4, -872119096836962.4], [0, 650377879817809600000000000000]], [[1.0, 0], [0, 524105709706272.94], [-2301619141096101800000000000000, 0]], [[1.0, 0], [-1595236877033815.5, -1595236877033815.5], [0, 5072820298953864000000000000000]], [[1.0, 0], [0, 5357139568657464.0], [-15496731425178937000000000000000, 0]], [[1.0, 0], [6014910390309317.0, -6014910390309317.0], [0, -61425365346268570000000000000000]], [[1.0, 0], [-11515983047272250, 0], [117257864492369850000000000000000, 0]], [[1.0, 0], [2075508848744943.8, 2075508848744943.8], [0, 160470643909878750000000000000000]], [[1.0, 0], [-14325157311121042, 14325157311121042], [0, -295216374856540750000000000000000]], [[1.0, 0], [0, -5291403525787303.0], [-397030588105939700000000000000000, 0]], [[1.0, 0], [-20798482259736404, -20798482259736404], [0, 706732552679793200000000000000000]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-5-5.3-c16-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 16, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [16], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5/17/c/a/3/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [0.4003986435020978, 0.2652909171262592, 0.0817875091669825, -0.14109818871993993, -0.39305737585198713, -0.6627946347184306, -0.9383682965733611, -1.2075560254247149, -1.4582384269585895, -1.678792563983722, -1.858486279172937, -1.9878632369487512, -2.0591076634838967, -2.066376965955476, -2.0060898404989485, -1.877157232072036, -1.681143691105805, -1.4223473806925124, -1.107788312946182, -0.7470964041811631, -0.3522936783603896, 0.06253157669666626, 0.481656723685159, 0.8882560045209237, 1.2650190865886817, 1.5948394336888136, 1.8615495204294943, 2.050674743167015, 2.15017339418798, 2.151126640572779, 2.048340471320389, 1.8408214104897374, 1.5320897535911324, 1.1302983989921225, 0.6481321293971571, 0.10247141779776564, -0.486183716877793, -1.094520990519103, -1.6974309194449075, -2.2691913087764832, -2.784768257136422, -3.2211677534152217, -3.55876157214824, -3.782504561768647, -3.8829585706298464, -3.8570419764527397, -3.7084335866467937, -3.4475756838597222, -3.091242866249359, -2.6616702292994296, -2.1852649871430083, -1.6909579751039074, -1.2082833347601212, -0.765303492666809, -0.3865196228563523, -0.09092254712987075, 0.10965677291313274, 0.21174602881915092, 0.22084963195755475, 0.15139007520469155, 0.02592225806506362, -0.12637479260985657, -0.27186412688089906, -0.3751491854941069, -0.40212164838659165, -0.32312939809083735, -0.11600357319411388, 0.23132809765969187, 0.7189031578475144, 1.333686980420301, 2.049601523322046, 2.82870475798236, 3.623508559893901, 4.380318012623301, 5.043371260347018, 5.559466359375393, 5.882690164989296, 5.978823278551983, 5.828991535443499, 5.432172455502491, 4.806244702409805, 3.9873858242294538, 3.0277699584329145, 1.9916804467813545, 0.9503170607191417, -0.02427325778023217, -0.8655966302753172, -1.5188291109087646, -1.9460262138398587, -2.1298566750834076, -2.075412106401444, -1.8098208926476418, -1.3796129945682603, -0.8460211996406908, -0.2786385667171917, 0.2519455651473503, 0.6817631304468711, 0.9605032235486995, 1.0571554452928746, 0.9635696977155443, 0.6954494301198328, 0.2905729180959576, -0.19564425627204973, -0.6968086176583576, -1.1437036312462117, -1.4729962178908624, -1.6354382507697223, -1.6025189388420515, -1.3706690411409346, -0.9623856955777446, -0.4240110259489592, 0.1796822145878843, 0.7735200955305466, 1.2816206764061857, 1.6375300335115393, 1.7934577618508998, 1.7273192417463676, 1.446520510960798, 0.9878087436816153, 0.413014651357267, -0.19892899478837747, -0.7627696786761203, -1.1991517117306245, -1.4466205968920574, -1.4717026335871721, -1.2755183389936677, -0.8957878935892981, -0.40367297839295435, 0.1043996105810069, 0.5190644523609401, 0.7329841380760576, 0.6564828820951994, 0.23166747199144705, -0.5570481818459537, -1.6776963301012588, -3.0518001763663287, -4.561873519318962, -6.06462081478962, -7.408230124756816, -8.451493127465861, -9.082131082884874, -9.231721706199629, -8.885024787855174, -8.082251190034391, -6.913812438938458, -5.508185363296345, -4.014563632446274, -2.582782532528301, -1.3434591829188791, -0.39130250606991895, 0.22590253809033517, 0.5109883796240452, 0.5132673952539741, 0.3173026544732438, 0.026481238383342844, -0.2558460479757706, -0.44446542042762854, -0.48654587087285767, -0.36956076120679826, -0.12148254838046345, 0.19681309943838457, 0.5056081571207325, 0.7243434045694371, 0.7902449946589238, 0.6740367493679562, 0.38960333126779517, -0.004540717389907979, -0.4126973041784005, -0.7174463040856549, -0.8006866944972074, -0.5666549562219536, 0.037249346769216145, 1.0058358424914537, 2.270793142966638, 3.7062370258081283, 5.144831105198364, 6.4022447751371265, 7.30609137802007, 7.724486776113509, 7.589198431337778, 6.909088878926686, 5.771103233481737, 4.328161933269092, 2.775634924923429, 1.320175144673545, 0.146181584193282, -0.614254352289647, -0.9025339665521653, -0.7419548679983317, -0.23165751891682146, 0.47295019456007514, 1.1898489633087235, 1.7447764732213522, 2.0039747778802335, 1.8991905893653194, 1.4401758538328868, 0.712243550940607, -0.14074472708778593, -0.9447803815692546, -1.5300818131114247, -1.7648018549918265, -1.5814865354718872, -0.991056369019343, -0.08149064658621402, 0.9985980212053294, 2.0682983722196067, 2.9490320269626364, 3.4985607642518124, 3.6375317128922897, 3.363208344032699, 2.7476439643946686, 1.92076631073217, 1.0419971190433988, 0.2664638573301535, -0.2869585586893866, -0.5588894791860466, -0.5589239614433755, -0.3592829937675167, -0.07404752307815915, 0.171356883272606, 0.2734610082855588, 0.1790691609626722, -0.0982635967632663, -0.4779606971314533, -0.8291566431518043, -1.0013350482698686, -0.8624121744933485, -0.3357515409151777, 0.572634441285827, 1.7637109339036903, 3.055498991923302, 4.21285440502347, 4.991764124846248, 5.189469596920467, 4.689960357835927, 3.4948239229936306, 1.7320866633442193, -0.35995552790371005, -2.4717272568928097, -4.277082156673453, -5.493075882693813, -5.932777392086738, -5.540263355498844, -4.400466761285543, -2.721717553464724, -0.7945238195441954, 1.0648465556932971, 2.5742253602061798, 3.536430052514206, 3.870818767012013, 3.6194885584442287, 2.9277370836503036, 2.004096056382401, 1.0696791363089677, 0.3087475649418411, -0.16821740991850795, -0.3408919000631229], 'positive_zeros': ['0.41931919893275409725806967856592', '3.66519258132799312901559417840666', '6.18369301974784976561432232958190', '9.737361915736190198564016379712446', '10.57799134037337712394631246826736', '11.66879319787202060165138365463697', '14.93676856051539899374808162225018', '16.61281428389725496005597227231004', '17.86098035679897946402536602098509', '19.46011054161238149142265189171998'], 'prelabel': '2-5-5.3-c16-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.848899294961364, 'root_angle': -0.3770459892740636, 'root_number': '0.3767371800058768 - 0.9263201915111317*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.188522994637', 'prec': 50}, 'spectral_label': 'c16-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41931919893275409725806967857', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.66519258132799312901559417841', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.18369301974784976561432232958', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 8.116227192831357, 'bad_primes': [5], 'central_character': '5.3', 'conductor': 5, 'conductor_radical': 5, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5/17/c/a/3/2'], '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': '2-5-5.3-c16-0-1', 'motivic_weight': 16, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [16], 'order_of_vanishing': 0, 'prelabel': '2-5-5.3-c16-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.848899294961364, 'root_angle': -0.1885229946370318, 'self_dual': False, 'spectral_label': 'c16-0', 'z1': {'__RealLiteral__': 0, 'data': '0.41931919893275409725806967857', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '531550234214326060850149879959', 'Lhash_array': ['531550234214326060850149879959'], 'label': '2-5-5.3-c16-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5/17/c/a/3/2'}