-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1527353777699493769406837172221', 'a10': [0.0, 0.0], 'a2': [0.9555728057861407, 0.2947551744109042], 'a3': [0.26694812817017366, -0.6801727377709194], 'a4': [0.8262387743159949, 0.5633200580636221], 'a5': [0.0, 0.0], 'a6': [0.45557280578614073, -0.5712702293735344], 'a7': [0.6234898018587335, 0.7818314824680298], 'a8': [0.6234898018587335, 0.7818314824680298], 'a9': [0.3416782217565979, 0.3170310594102608], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9555728057861407, -0.2947551744109042]]], [7, [[1.0, 0], [-0.6234898018587335, -0.7818314824680298]]], [17, [[1.0, 0], [-0.07473009358642425, -0.9972037971811801]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.2991', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '2284287042106211734021775281510', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9555728057861407, -0.2947551744109042]], [[1.0, 0], [-0.26694812817017366, 0.6801727377709194], [-0.7330518718298263, -0.6801727377709194]], [[1.0, 0], [0, 0], [-0.9555728057861407, 0.2947551744109042]], [[1.0, 0], [-0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [1.400968867902419, -1.2999091429019967], [0.07473009358642425, -0.9972037971811801]], [[1.0, 0], [0.42526990641357576, 1.8632292009656188], [-0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [-0.07473009358642425, -0.9972037971811801]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [0.03325802043898781, -0.44379744058707865], [-0.9888308262251285, -0.14904226617617444]], [[1.0, 0], [0, 0], [-0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0.6234898018587335, 1.0799160148203788], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.36534102436639504, 0.9308737486442042]], [[1.0, 0], [0, 0], [0.2225209339563144, -0.9749279121818236]], [[1.0, 0], [0, 0], [0.2225209339563144, 0.9749279121818236]], [[1.0, 0], [0, 0], [-0.8262387743159949, -0.5633200580636221]], [[1.0, 0], [1.6340207397322455, 1.1140564768884775], [0.36534102436639504, 0.9308737486442042]], [[1.0, 0], [0, 0], [-0.9555728057861407, -0.2947551744109042]], [[1.0, 0], [0, 0], [-0.36534102436639504, 0.9308737486442042]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-1.7818115801021357, 0.8580752324745262], [0.6234898018587335, -0.7818314824680298]], [[1.0, 0], [0, 0], [-0.8262387743159949, 0.5633200580636221]], [[1.0, 0], [-0.7330518718298263, 1.2696830865927278], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]], [[1.0, 0], [0.5356278435360241, 0.4969900095266461], [0.07473009358642425, 0.9972037971811801]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.16259205190913367, -0.41427779188744757], [-0.7330518718298263, -0.6801727377709194]], [[1.0, 0], [0, 0], [-0.9555728057861407, 0.2947551744109042]], [[1.0, 0], [1.211351760181443, 1.123970178357998], [0.07473009358642425, 0.9972037971811801]], [[1.0, 0], [0, 0], [-0.07473009358642425, 0.9972037971811801]], [[1.0, 0], [0, 0], [0.9009688679024191, 0.4338837391175581]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 1, 'label': '2-3332-3332.2991-c0-0-1', 'leading_term': '2.62036454077961360924207947466', '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/3332/1/cc/b/2991/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.6203645407796134, 2.5862373740013958, 2.5687456966445286, 2.5649186126196657, 2.5709056903550134, 2.5823155544305347, 2.594541744991514, 2.6030316717696773, 2.603483078085833, 2.5919737439152715, 2.565040298166089, 2.519723402132244, 2.4535933871258373, 2.364765933404954, 2.251913295744418, 2.1142735127230083, 1.9516579908316407, 1.7644566239143207, 1.5536389595165354, 1.3207496658280469, 1.067896550777266, 0.797729549339422, 0.5134093697575828, 0.21856483852628703, -0.08276161559993754, -0.38618046316389393, -0.6870332291513784, -0.9804815039185437, -1.2616055491257774, -1.5255107903819456, -1.7674400693915748, -1.9828891516842206, -2.1677226651828825, -2.3182873932986716, -2.431519676443541, -2.505043598964368, -2.5372566637040284, -2.527399790380608, -2.475608720443844, -2.3829442702911954, -2.251399343208344, -2.083881180646087, -1.8841679938680829, -1.6568398519691552, -1.4071844923069923, -1.1410795415912012, -0.8648534643999806, -0.5851283627024375, -0.308648505645999, -0.042099143624243794, 0.20807927464995088, 0.43587593598573227, 0.6358877357249234, 0.8034846944264461, 0.934956935930571, 1.0276377635527962, 1.0799978979864604, 1.091706669512192, 1.0636568748406712, 0.997951093924331, 0.8978484852294678, 0.7676724029875991, 0.6126805643161343, 0.43890089023612294, 0.25293750138444954, 0.061752613672079286, -0.12756880153646558, -0.308063804556729, -0.4731372520551431, -0.6167996696225649, -0.7338882757947385, -0.8202624482714398, -0.8729655135029389, -0.8903456706663961, -0.8721301129294465, -0.8194479515528197, -0.7347993371288564, -0.621970149904863, -0.48589372955737076, -0.3324632569567066, -0.16830050311403844, -0.0004886371219702718, 0.16372145089975926, 0.3172203867367156, 0.45335308507791516, 0.5662223708527473, 0.65097058212851, 0.7040266264401959, 0.7233068319586395, 0.708359327126874, 0.6604435668121886, 0.5825389468130158, 0.47927913751161877, 0.35681172787494236, 0.22258589255199707, 0.0850739543016036, -0.046564220118663006, -0.1628622148522105, -0.2544591977733541, -0.3125269457243334, -0.32919411822102185, -0.29794942164970933, -0.2140053417491489, -0.07460494427812628, 0.12074414337057948, 0.3701220828755415, 0.6691459504605103, 1.0110224098895564, 1.386706566335602, 1.7851651817494392, 2.1937378444506033, 2.598585155768044, 2.985208725164376, 3.3390239516566638, 3.6459634026450765, 3.8930862515533686, 4.06916784541065, 4.1652431496868, 4.175078625352011, 4.095549050234157, 3.926898871042086, 3.672871780366973, 3.340697220948061, 2.94092824734463, 2.4871314020629267, 1.9954357356323025, 1.483954541805334, 0.9720995023035728, 0.47981245381992405, 0.02674463101044954, -0.36858324208356913, -0.689604448707377, -0.9224770918052243, -1.0567668173437559, -1.0860085146164515, -1.0081180893493369, -0.8256308768812897, -0.5457499882828992, -0.18019560959732103, 0.2551453049735002, 0.7407607437151886, 1.2542298297871435, 1.7710882904796366, 2.265810543862385, 2.7128694851556046, 3.0878303208036657, 3.3684318574483867, 3.5356077029964066, 3.5744009904386025, 3.474729511668743, 3.2319634704626106, 2.847285255769453, 2.3278094304807873, 1.6864511752532878, 0.941542300148207, 0.11620516460527797, -0.7624940776086919, -1.6645810826811245, -2.55835670261362, -3.4116794715107277, -4.193292924553994, -4.874140237238743, -5.428607983448937, -5.8356427767293955, -6.079689155852394, -6.151404154109844, -6.048113280258762, -5.773983753713582, -5.339903296186431, -4.7630660286300746, -4.066280446436476, -3.277027414340628, -2.4263080091408815, -1.5473312545584956, -0.6740998171553924, 0.16004286117776564, 0.9238380382970766, 1.5894444164248722, 2.133616558228417, 2.5386741094204566, 2.79321641052828, 2.892548824312848, 2.838800605608524, 2.6407287600929963, 2.3132173734176082, 1.8764966047938707, 1.3551191955454813, 0.7767442500390428, 0.17078758736201294, -0.4329953695370465, -1.0059247736289134, -1.5217402328944398, -1.957807530362299, -2.2961291833585658, -2.52410972631111, -2.6350390402833854, -2.6282714285447737, -2.5090937264667206, -2.2882917385228927, -1.9814398856220214, -1.6079533038704505, -1.1899539970781439, -0.7510123417073135, -0.31483173931834346, 0.09605286365089308, 0.46149270115841207, 0.764793845958262, 0.9935795935086835, 1.1404005890627653, 1.203060480627275, 1.1846404592596507, 1.0932226074921239, 0.9413286199231942, 0.7451062754261315, 0.5233101509283095, 0.29613467880706107, 0.08396609875705417, -0.09387535699192436, -0.22033087902836318, -0.2816671471971102, -0.2683472171006287, -0.17565705382839256, -0.004050172704299332, 0.24081128567909846, 0.5483234912655313, 0.9035026909763525, 1.2878115993666732, 1.6802047551277444, 2.0583342050668683, 2.3998471369965992, 2.6837011748107664, 2.8914213530612356, 3.0082254477055987, 3.0239512487970397, 2.9337301679186067, 2.738365696811283, 2.44439189340993, 2.0638053300784143, 1.6134827543144, 1.114314997217492, 0.5901043495628212, 0.06628671951823648, -0.4314494607179019, -0.8785690592182047, -1.2530402536675038, -1.5365508467751088, -1.7155202593788055, -1.7818480260322955, -1.7333546392568404, -1.573888324721162, -1.3130907554420874, -0.9658346910367075, -0.5513658742080549, -0.09219907111604417, 0.3871671608702692, 0.8616414619041782, 1.3069544206766923], 'positive_zeros': ['1.20486968366875468888792793000021', '2.49656614761230653677973037554444', '3.31719893358087850546903761491420', '4.11342964533333174740743259444139', '4.85654544998407510798183896169574', '5.25161548501208230034663628552966', '6.55397446265531249749594981384961', '7.02970575319381856498580830921559', '7.87795270680791736355432575844201', '8.876694023626695280628366363633085'], 'prelabel': '2-3332-3332.2991-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.20408163265306123, 'root_number': '0.80141362186795665978698328953346 - 0.59811053049121596205926635490525*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.10204081632653061', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20486968366875468888792793000', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49656614761230653677973037554', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.31719893358087850546903761491', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '3332.2991', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/cc/b/2991/1'], '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': '2-3332-3332.2991-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': '2-3332-3332.2991-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.10204081632653061, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20486968366875468888792793000', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1527353777699493769406837172221', 'Lhash_array': ['1527353777699493769406837172221'], 'label': '2-3332-3332.2991-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/cc/b/2991/1'}