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	'dirichlet_L_5495.3408'
a10	jsonb	[1.0, -2.8163065144692913e-30]
a2	jsonb	[-0.23931566428755777, -0.970941817426052]
a3	jsonb	[0.46472317204376856, -0.8854560256532099]
a4	jsonb	[-0.8854560256532099, 0.46472317204376856]
a5	jsonb	[1.0, -2.8163065144692913e-30]
a6	jsonb	[-0.970941817426052, -0.23931566428755777]
a7	jsonb	[1.0, -2.8163065144692913e-30]
a8	jsonb	[0.6631226582407952, 0.7485107481711011]
a9	jsonb	[-0.5680647467311558, -0.8229838658936564]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	25.518672717253985
analytic_normalization	numeric	0
bad_lfactors	jsonb	[[5, [1]], [7, [1]], [157, [1]]]
bad_primes	bigint[]	[5, 7, 157]
central_character	text	'5495.3408'
coeff_info	jsonb	['x^52 - 1', '0.992708874098054 + 0.120536680255323*I', '\\\\zeta_{52}']
coefficient_field	text
conductor	numeric	5495
conductor_radical	integer	5495
conjugate	text	'dirichlet_L_5495.4297'
credit	text
degree	smallint	1
dirichlet_coefficients	jsonb	['a^0', 'a^37', 'a^43', 'a^22', 0, 'a^28', 0, 'a^7', 'a^34', 0, 'a^28', 'a^13', 'a^39', 0, 0, 'a^44'...
euler_factors	jsonb	[[1, 'a^37'], [1, 'a^43'], [0], [0], [1, 'a^28'], [1, 'a^39'], [1, 'a^1'], [1, 'a^20'], [1, 'a^31'],...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[0], []]
group	text
index	smallint	0
label	text	'1-5495-5495.3408-r0-0-0'
leading_term	text	'0.978793552817720026834740505206-0.719134047526931986991350911813*I'
load_key	text	'dirichlet'
motivic_weight	smallint	0
mu_imag	numeric[]	[0.0]
mu_real	smallint[]	[0]
nu_imag	numeric[]	[]
nu_real_doubled	smallint[]	[]
order_of_vanishing	smallint	0
origin	text	'Character/Dirichlet/5495/3408'
plot_delta	numeric	0.3125
plot_values	jsonb	[1.2145742453016206, 1.1452458658716753, 0.41527191012237774, -0.47548446932219424, -0.4457821933265...
positive_zeros	jsonb	['0.75444708015832621239178909077', '1.40598515409634972579065206267', '2.41658866023181079853441888...
precision	smallint
prelabel	text	'1-5495-5495.3408-r0-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	25.518672717253985
root_angle	double precision	-0.20169596276191284
root_number	text	'0.298865137506339221504381812237-0.954295357624313788706347050355*I'
self_dual	boolean	False
sign_arg	numeric	0.0
spectral_label	text	'r0-0'
st_group	text	'mu(52)'
symmetry_type	text	'unitary'
trace_hash	bigint
types	jsonb	['DIR']
values	jsonb	[[1, '0.697404378450233335281756269960-0.577718989968342654314709732153*I']]
z1	numeric	0.754447080158
z2	numeric	1.4059851541
z3	numeric	2.41658866023

{'Lhash': '4312949087865403808077902174699', 'a10': [0.0, 1.0], 'a2': [0.8660254037844386, -0.5], 'a3': [0.0, -1.0], 'a4': [4.582907174201562e-80, -2.6459426906140066e-80], 'a5': [-0.5, 0.8660254037844386], 'a6': [-0.5, -0.8660254037844386], 'a7': [-0.5, -0.8660254037844386], 'a8': [1.3229713455367871e-80, 1.0], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.08534011716024341, 'analytic_normalization': 0, 'bad_lfactors': [[3, [[1.0, 0], [0, 1.0]]], [19, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [3, 19], 'central_character': '171.94', 'coefficient_field': 'CDF', 'conductor': 171, 'conductor_radical': 57, 'conjugate': '3222105615230117627525088419856', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, 0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.8660254037844386, 0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0.8660254037844386, -0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.8660254037844386, -0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0.8660254037844386, 0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.8660254037844386, -0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [-0.8660254037844386, -0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0.8660254037844386, -0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.8660254037844386, 0.5], [0.5, -0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.8660254037844386, 0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [0, -2.0], [-1.0, 0]], [[1.0, 0], [-0.8660254037844386, -0.5], [0.5, 0.8660254037844386]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 19437640, 'index': 1, 'label': '2-171-171.94-c0-0-1', 'leading_term': '0.84282129998327644664845169269210', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/171/1/o/a/94/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.08203125', 'prec': 24}, 'plot_values': [0.8428212999832765, 0.8685698754297833, 0.9181429068641365, 0.9904218592136106, 1.083381133137334, 1.1946773043751673, 1.3220241858067372, 1.463331144281571, 1.6166890248728492, 1.780289428443156, 1.9523301627685687, 2.130931455688448, 2.314071527778993, 2.4995429332615187, 2.6849285064093156, 2.8675951839563534, 3.044704111643246, 3.2132357200657715, 3.3700286569125253, 3.511831526853117, 3.635366314994193, 3.7374021754454865, 3.8148379806429, 3.8647916787499828, 3.884694124755983, 3.8723846645174245, 3.82620538829579, 3.7450906591775985, 3.628648289116435, 3.477228606718949, 3.291977659485955, 3.074870938834541, 2.8287243241886637, 2.5571794223788897, 2.26466113336622, 1.9563060978985451, 1.6378616634807122, 1.3155561191948921, 0.9959421653491056, 0.6857168595476837, 0.39152256722249346, 0.11973468565757267, -0.12375695530262128, -0.33376514949822583, -0.5060122332113968, -0.6373178399072316, -0.7257583825704, -0.7707894676518133, -0.7733231816345402, -0.7357533662103556, -0.6619236047111653, -0.5570346526352735, -0.42749040768369684, -0.28068415530939445, -0.12472964784475132, 0.031855537566232224, 0.18050409729135472, 0.3129776823299335, 0.4217550402249483, 0.5004127538475586, 0.5439806144809733, 0.5492533295882093, 0.5150407820426878, 0.4423404850013529, 0.33441823157174577, 0.19678619126011446, 0.037071776588690555, -0.13522463661546902, -0.3090797816194992, -0.47239645499631366, -0.6125368570662443, -0.7169204967486154, -0.7736620705623958, -0.7722208125604939, -0.7040300340909056, -0.5630741737842815, -0.34638085129749757, -0.05439728761769332, 0.30877593632196676, 0.7353155097836195, 1.2137852889185712, 1.7294321820202652, 2.2646656172537316, 2.7997085026414914, 3.313397829850279, 3.7841037669756656, 4.190727774881556, 4.513733498756811, 4.73615942009082, 4.8445599177725045, 4.829821788692489, 4.687806594429875, 4.419775454852865, 4.032561958790487, 3.5384703920456935, 2.954890013322902, 2.3036310076888755, 1.6100032584879413, 0.9016743561237535, 0.20735741387733325, -0.44460860086089393, -1.0277140170155397, -1.5186913562877653, -1.8988066240782655, -2.1549524903880353, -2.280474268437434, -2.275671410832475, -2.1479330143046407, -1.9114848466287082, -1.586746734460036, -1.1993216314976571, -0.7786600357276776, -0.35646428715145095, 0.03508469007853084, 0.36518168115801336, 0.6062271749601649, 0.7355248553250597, 0.7367419398864578, 0.6010377959207921, 0.32778256164440916, -0.07519069343386807, -0.5918305247080194, -1.1986094626127342, -1.8657347897477414, -2.5587685356085013, -3.240570160889483, -3.8734524608853707, -4.42142430870951, -4.852384326592948, -5.140128340190571, -5.266040956694064, -5.220357676828506, -5.002907893471737, -4.623279681322914, -4.1003826829197205, -3.4614234870084424, -2.740346245378738, -1.975827335994153, -1.2089441579880482, -0.48066236876251767, 0.17069883060375177, 0.7118587229667842, 1.1166656858499115, 1.3677444508966534, 1.4575849464480104, 1.3889930537247053, 1.1748653317177784, 0.8372950980879523, 0.40606312383231025, -0.08339060270531835, -0.5923801882290298, -1.0816095821361613, -1.5138502257334479, -1.8564746376307646, -2.0836677083869626, -2.1781581554056064, -2.1323450193188345, -1.948736176714688, -1.6396647348663325, -1.2263014067749298, -0.737032734944283, -0.20532246233417847, 0.3327872196703496, 0.8413495368487958, 1.2871623635272338, 1.6421932916667863, 1.8855964901951394, 2.005167178196586, 1.998121783389788, 1.8711434461178797, 1.639689607448038, 1.3266165994996633, 0.9602308429232376, 0.5719230113462825, 0.19357642193270944, -0.1450391206652839, -0.4186737143153354, -0.6086041007575134, -0.7040720403112061, -0.7030313245607831, -0.6121372727396711, -0.4459760565573214, -0.22559620883681467, 0.02353423390159959, 0.2739695912180171, 0.49891396171449587, 0.674800168622935, 0.783585333063247, 0.81454774171221, 0.765408604310487, 0.6426578513945813, 0.4610310427608938, 0.24215926823455647, 0.01248935984342947, -0.19935874914643611, -0.3655733669296484, -0.46220728090088037, -0.4720272280397833, -0.3868812881673029, -0.20933985348708478, 0.0465803169949998, 0.3557264775183285, 0.6831857273155658, 0.986664266024931, 1.2197162934843813, 1.335586359009641, 1.2913634415114936, 1.0521028053195949, 0.5945573601718972, -0.08982374467951705, -0.9929253767081802, -2.0892479946603, -3.336567197313672, -4.677987253127533, -6.045288054094052, -7.363352230763955, -8.555360117622149, -9.548363849445863, -10.278805449066887, -10.697532354953678, -10.77388960532598, -10.498529881250633, -9.884676694520461, -8.967695164964043, -7.80295966029072, -6.462147025650692, -5.028216442013513, -3.5894506381007254, -2.233018053317973, -1.0385636499321724, -0.0723424309230045, 0.6176271291810683, 1.0049903273249605, 1.0867775903382833, 0.8832722294391283, 0.43603015494609926, -0.19578819457598678, -0.9404707668403687, -1.7197706207678793, -2.455382570210115, -3.0753359173535526, -3.519766421709797, -3.74558440542309, -3.729652111131329, -3.470213918015853, -2.986476409776971, -2.3163979968704047, -1.5129052504608436, -0.6388910593855637, 0.23854443166747916, 1.0540851810513978, 1.7498819075496854, 2.2804184801818015, 2.6161344518221705, 2.7454953410380667, 2.6753496183942804, 2.429573081440954], 'positive_zeros': ['3.40231692162563963078878105279622', '4.49483680603590198979315620537216', '5.43205268266639321517703319444647', '6.32975189902255865903931757234585', '8.146453088111622490090656980143601', '9.261724102180448573909808369698303', '9.830151359881541042159863280870558', '11.46165193614767954918030784073075', '12.20908379768565418980757631089547', '13.23814494038459796268873593366470'], 'prelabel': '2-171-171.94-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.29213030852727934, 'root_angle': 0.1388888888888889, 'root_number': '0.64278760968653932632264340990740 + 0.76604444311897803520239265055524*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.1388888888888889', 'prec': 54}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.40231692162563963078878105280', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.49483680603590198979315620537', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.43205268266639321517703319445', 'prec': 100}}