Database - lfunc_lfunctions

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Query: /api/lfunc_lfunctions/?_offset=0

Table lfunc_lfunctions

L-functions

Column	Type	Example
A10	numeric
A2	numeric
A3	numeric
A4	numeric
A5	numeric
A6	numeric
A7	numeric
A8	numeric
A9	numeric
Lhash	text	'1339108554973449305423634231645'
a10	jsonb	[1.4851428436397418, 0.0]
a2	jsonb	[-1.6683608417812013, 0.0]
a3	jsonb	[2.799089668498607, 0.0]
a4	jsonb	[0.7834278983888783, 0.0]
a5	jsonb	[-0.8901808328551697, 0.0]
a6	jsonb	[-4.6698915955574, 0.0]
a7	jsonb	[4.910076928497781, 0.0]
a8	jsonb	[2.029681255531456, 0.0]
a9	jsonb	[4.834902972295641, 0.0]
accuracy	smallint	100
algebraic	boolean	True
analytic_conductor	double precision	67.08232273807768
analytic_normalization	numeric	0.5
bad_lfactors	jsonb	[[31, [[1.0, 0], [1.0, 0]]], [271, [[1.0, 0], [-1.0, 0]]]]
bad_primes	bigint[]	[31, 271]
central_character	text	'8401.1'
coeff_info	jsonb
coefficient_field	text	'CDF'
conductor	numeric	8401
conductor_radical	integer	8401
conjugate	text
credit	text
degree	smallint	2
dirichlet_coefficients	jsonb
euler_factors	jsonb	[[[1.0, 0], [1.6683608417812013, 0], [2.0, 0]], [[1.0, 0], [-2.799089668498607, 0], [3.0, 0]], [[1.0...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[], [0]]
group	text	'GL2'
index	smallint	398
label	text	'2-8401-1.1-c1-0-398'
leading_term	text	'2.91125650916427197489978311287'
load_key	text	'CMFs-workshop'
motivic_weight	smallint	1
mu_imag	numeric[]	[]
mu_real	smallint[]	[]
nu_imag	numeric[]	[0.0]
nu_real_doubled	smallint[]	[1]
order_of_vanishing	smallint	0
origin	text	'ModularForm/GL2/Q/holomorphic/8401/2/a/d/1/39'
plot_delta	numeric	0.05078125
plot_values	jsonb	[2.911256509164272, 2.902760447325958, 2.8772449727689806, 2.8346376242916254, 2.774848187940182, 2....
positive_zeros	jsonb	['1.05637038686555626942508251052925', '1.67570086142444463399628457808920', '2.19306856755521927311...
precision	smallint
prelabel	text	'2-8401-1.1-c1-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	8.190379889729028
root_angle	double precision	0.0
root_number	text	'1'
self_dual	boolean	True
sign_arg	numeric	0
spectral_label	text	'c1-0'
st_group	text
symmetry_type	text
trace_hash	bigint
types	jsonb	['CMF']
values	jsonb
z1	numeric	1.05637038686555626942508251053
z2	numeric	1.67570086142444463399628457809
z3	numeric	2.19306856755521927311831373024

{'Lhash': '100595201649575992426292164033', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [190.5484840028542, 0], 'a6': [0, 0], 'a7': [0, 4097.7443115610295], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 117.32503969760468, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '288.127', 'coefficient_field': 'CDF', 'conductor': 288, 'conductor_radical': 6, 'conjugate': '2313068217588659866373525307073', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-190.5484840028542, 0], [390625.0, 0]], [[1.0, 0], [0, -4097.7443115610295], [-5764801.0, 0]], [[1.0, 0], [0, -8804.590813398949], [-214358881.0, 0]], [[1.0, 0], [2752.5922525766114, 0], [815730721.0, 0]], [[1.0, 0], [96418.55168436287, 0], [6975757441.0, 0]], [[1.0, 0], [0, 5160.348318936832], [-16983563041.0, 0]], [[1.0, 0], [0, -482342.82997560076], [-78310985281.0, 0]], [[1.0, 0], [1153436.4463917585, 0], [500246412961.0, 0]], [[1.0, 0], [0, 421771.36999763985], [-852891037441.0, 0]], [[1.0, 0], [-2094955.8538463998, 0], [3512479453921.0, 0]], [[1.0, 0], [-1119388.8909035882, 0], [7984925229121.0, 0]], [[1.0, 0], [0, 1000784.6202420453], [-11688200277601.0, 0]], [[1.0, 0], [0, 4110537.6114821145], [-23811286661761.0, 0]], [[1.0, 0], [-8869123.34767778, 0], [62259690411361.0, 0]], [[1.0, 0], [0, 17277551.250037894], [-146830437604321.0, 0]], [[1.0, 0], [-19968445.15034912, 0], [191707312997281.0, 0]], [[1.0, 0], [0, -6643098.948566904], [-406067677556641.0, 0]], [[1.0, 0], [0, -16136768.22653249], [-645753531245761.0, 0]], [[1.0, 0], [2881259.315523727, 0], [806460091894081.0, 0]], [[1.0, 0], [0, 4800143.916889434], [-1517108809906561.0, 0]], [[1.0, 0], [0, -21500897.233864147], [-2252292232139041.0, 0]], [[1.0, 0], [88990907.96124883, 0], [3936588805702081.0, 0]], [[1.0, 0], [-88970079.21122077, 0], [7837433594376961.0, 0]], [[1.0, 0], [44059339.61382462, 0], [10828567056280800, 0]], [[1.0, 0], [0, -27932579.26296568], [-12667700813876160, 0]], [[1.0, 0], [0, 124580759.46635996], [-17181861798319200, 0]], [[1.0, 0], [215414824.11201525, 0], [19925626416901920, 0]], [[1.0, 0], [-95121791.83041678, 0], [26584441929064320, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23241264, 'index': 1, 'label': '2-288-4.3-c8-0-1', 'leading_term': '0.369468793815812675773262621821720418085676302725267529', 'load_key': 'CMFs-workshop', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/288/9/g/e/127/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 24}, 'plot_values': [0.36946879381581266, 0.09343392715629174, -0.16336517916341092, -0.3964453993083462, -0.6017833934329047, -0.7758911427384533, -0.9158820515688014, -1.0195264386783747, -1.0852954002993953, -1.1123922046118386, -1.1007705689328453, -1.051139375429805, -0.964953596238766, -0.8443914221175495, -0.6923178175201118, -0.5122349563425049, -0.30822022342346433, -0.08485269382653765, 0.152870778566832, 0.3996285232752998, 0.6498745330008437, 0.8979447532286505, 1.1381673221328203, 1.3649747760447617, 1.573016140657386, 1.7572667665582953, 1.913133742603804, 2.036554734596692, 2.1240881516867742, 2.1729926401884323, 2.1812940446663824, 2.1478381589099884, 2.072327813623852, 1.9553431111770345, 1.7983439174508278, 1.6036540525749523, 1.3744269810184742, 1.1145931810211245, 0.8287897667377894, 0.5222733359514323, 0.20081741334230668, -0.1294037548821819, -0.46194293400011044, -0.7902167053114376, -1.107648590389376, -1.4078154960153992, -1.6845942904702809, -1.9323051961091726, -2.145848628493981, -2.3208321339956304, -2.4536841793542847, -2.541751730072622, -2.583378819652254, -2.57796365643144, -2.525992234851415, -2.4290469068870486, -2.289788918478604, -2.1119145143706732, -1.9000848501507377, -1.6598306081210663, -1.3974328781395255, -1.119782518839975, -0.834220841104571, -0.5483650364629954, -0.2699222906117122, -0.006496959578482057, 0.2346044724553214, 0.44656570291926734, 0.6232451270920355, 0.7593475196404517, 0.850577996294257, 0.8937736648368354, 0.8870088057751844, 0.8296699856239778, 0.722498190227763, 0.5675958585026778, 0.3683975811413231, 0.1296041834045088, -0.14291908777523593, -0.442278531003748, -0.7607193577795047, -1.0898207309747767, -1.4207138384817966, -1.744317556457974, -2.0515855723379364, -2.3337583044798813, -2.582612595328041, -2.7907019865107903, -2.9515804206441616, -3.060002463472834, -3.11209360293416, -3.1054848538673854, -3.0394067668335394, -2.9147389886393884, -2.734012726039488, -2.501364792138234, -2.222443331362346, -1.9042667832562, -1.555039114171026, -1.1839257734842965, -0.8007961708857847, -0.4159396778348675, -0.03976318612705443, 0.3175209300085181, 0.646207039075547, 0.9373989711626891, 1.183293550783385, 1.3774355870928228, 1.5149355984538084, 1.5926424835342095, 1.609264568768817, 1.5654339327696205, 1.4637105931614445, 1.3085249926581832, 1.1060591837705118, 0.864069124173347, 0.5916524921408712, 0.2989683461692966, -0.003083282322601094, -0.30321222431524986, -0.5901085223960398, -0.852820432176959, -1.0811276380931851, -1.2658970735311976, -1.3994089867322719, -1.4756415749437648, -1.4905036108925973, -1.442005983825315, -1.3303649332723717, -1.1580319144887248, -0.9296474346192628, -0.6519187615778246, -0.3334240483879289, 0.01565195655552276, 0.38384292183753155, 0.7587766553780616, 1.1275894921578713, 1.477365641724128, 1.7955865713514723, 2.0705747823745178, 2.2919161605197034, 2.4508454691504222, 2.5405805103621857, 2.556591985187099, 2.496798102239302, 2.361675455163029, 2.1542805356600345, 1.8801793765520851, 1.5472861205552035, 1.1656146674648982, 0.7469508416202978, 0.304455617749006, -0.14778727519649076, -0.5952636995450082, -1.0235439075169084, -1.4188010866139666, -1.7683144120215195, -2.060937548608457, -2.287514456073818, -2.4412259754482943, -2.5178529705202406, -2.515944693483441, -2.436884444367757, -2.284848380210395, -2.066657365399773, -1.7915258882729626, -1.47071614164718, -1.117109215024577, -0.7447088163272053, -0.36809588430130885, -0.0018547390040268951, 0.3400070606463388, 0.6446223065933576, 0.9007885497454712, 1.099431821788678, 1.2339901755126297, 1.3007003845588552, 1.2987747124700837, 1.2304588366022475, 1.1009666404999454, 0.9182924916597469, 0.6929066070319057, 0.4373439743384736, 0.16570184098516125, -0.10693519046771678, -0.3651200889557305, -0.5936934891015966, -0.7784325872510749, -0.9066720204791716, -0.9678705583089329, -0.9540991861742726, -0.8604289622841094, -0.6852007926490775, -0.43016385688361486, -0.100474655953517, 0.29544566371267955, 0.7461921574781439, 1.2377856813794061, 1.7541962356110845, 2.2779599825010526, 2.79086555754132, 3.2746819333475607, 3.71189785511322, 4.086441862746773, 4.3843522193567805, 4.59436769300162, 4.708413046475559, 4.721957179442775, 4.6342269856554825, 4.448265933936429, 4.170832912755253, 3.8121437209614877, 3.3854644479278333, 2.9065725638778384, 2.3931075400767714, 1.8638379623804955, 1.3378761456688055, 0.8338739997430907, 0.3692351917371625, -0.040621590102383254, -0.38291526043639673, -0.6480411354624611, -0.8299708751856458, -0.9264944210757539, -0.9392916216843076, -0.8738287467207523, -0.7390829375559823, -0.5471054791329785, -0.312442247864071, -0.051436444577069945, 0.21855556132357462, 0.48000005197795836, 0.7160353679890783, 0.9112956770700638, 1.0526705217312546, 1.1299639990893127, 1.1364215753330877, 1.0690982394933675, 0.9290487192857891, 0.7213285130195188, 0.45480317943591175, 0.141772277409804, -0.20257685502278158, -0.5608620637669836, -0.9143154022054368, -1.243671596071646, -1.5300950232056938, -1.756101837520037, -1.9064334346935918, -1.9688390942238145, -1.9347292975644153, -1.799666776650504, -1.56366955963629, -1.231308835741042, -0.8115939728382703, -0.31764705058601045, 0.2338206540449621], 'positive_zeros': ['0.079355621834174737384007667933794', '1.01734971627839334369439187868203', '2.37949538473380197196769319294963', '3.81009747481828526646276364597534', '4.54040319696513960167029464692667', '5.98290477669341655295888568087587', '6.91346625050162194541076711081941', '7.79042273437970457361873198404479', '8.887126225968194204382776688269253', '9.961242559563353531285496438055193'], 'prelabel': '2-288-4.3-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.831668370920736, 'root_angle': 0.375, 'root_number': '-0.70710678118654752440084436210484903928483593768847403659 + 0.70710678118654752440084436210484903928483593768847403659*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.375', 'prec': 10}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.079355621834174737384007667934', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.01734971627839334369439187868', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.37949538473380197196769319295', 'prec': 100}}