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_5076.4471'
a10	jsonb	[1.0, -2.8163065144692913e-30]
a2	jsonb	[1.0, -2.8163065144692913e-30]
a3	jsonb	[1.0, -2.8163065144692913e-30]
a4	jsonb	[1.0, -2.8163065144692913e-30]
a5	jsonb	[0.9231518828401457, -0.38443543178106493]
a6	jsonb	[1.0, -2.8163065144692913e-30]
a7	jsonb	[-0.9981578895764273, 0.060669823440758594]
a8	jsonb	[1.0, -2.8163065144692913e-30]
a9	jsonb	[1.0, -2.8163065144692913e-30]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	545.4919582575166
analytic_normalization	numeric	0
bad_lfactors	jsonb	[[2, [1]], [3, [1]], [47, [1]]]
bad_primes	bigint[]	[2, 3, 47]
central_character	text	'5076.4471'
coeff_info	jsonb	['x^414 - 1', '0.999884834944106 + 0.0151761934884025*I', '\\\\zeta_{414}']
coefficient_field	text
conductor	numeric	5076
conductor_radical	integer	282
conjugate	text	'dirichlet_L_5076.1183'
credit	text
degree	smallint	1
dirichlet_coefficients	jsonb	['a^0', 0, 0, 0, 'a^388', 0, 'a^617', 0, 0, 0, 'a^485', 0, 'a^358', 0, 0, 0, 'a^228', 0, 'a^555', 0,...
euler_factors	jsonb	[[0], [0], [1, 'a^388'], [1, 'a^617'], [1, 'a^485'], [1, 'a^358'], [1, 'a^228'], [1, 'a^555'], [1, '...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[1], []]
group	text
index	smallint	0
label	text	'1-5076-5076.4471-r1-0-0'
leading_term	text	'1.60572048753246889520325256836+1.43822706989094135445710497716*I'
load_key	text	'dirichlet'
motivic_weight	smallint	0
mu_imag	numeric[]	[0.0]
mu_real	smallint[]	[1]
nu_imag	numeric[]	[]
nu_real_doubled	smallint[]	[]
order_of_vanishing	smallint	0
origin	text	'Character/Dirichlet/5076/4471'
plot_delta	numeric	0.3125
plot_values	jsonb	[2.15565196371042, 2.7623166114186755, 1.517278103277429, -0.463090383054147, -1.2694293111677708, -...
positive_zeros	jsonb	['0.858375599521906670776111834616', '1.57757276739209277035303539391', '2.4826690374758983163095038...
precision	smallint
prelabel	text	'1-5076-5076.4471-r1-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	545.4919582575166
root_angle	double precision	0.23250262229336088
root_number	text	'0.109717934222477493409078954655+0.993962763341742144799558528280*I'
self_dual	boolean	False
sign_arg	numeric	-0.25
spectral_label	text	'r1-0'
st_group	text	'mu(414)'
symmetry_type	text	'unitary'
trace_hash	bigint
types	jsonb	['DIR']
values	jsonb	[[1, '1.15937585638349257529514509829+0.0891070469909695011795552728504*I']]
z1	numeric	0.858375599522
z2	numeric	1.57757276739
z3	numeric	2.48266903748

{'Lhash': '425315657506810677281052203903', 'a10': [0.0, 0.0], 'a2': [-2.038207169275101, 0.0], 'a3': [-1.8727461330844934, 0.0], 'a4': [2.15428846488442, 0.0], 'a5': [0.0, 0.0], 'a6': [3.817044594685037, 0.0], 'a7': [-1.9233750718902705, 0.0], 'a8': [-0.3144718552638747, 0.0], 'a9': [0.5071780789829234, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 41.72183505611902, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [1.0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 11, 19], 'central_character': '5225.1', 'coefficient_field': 'CDF', 'conductor': 5225, 'conductor_radical': 1045, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.038207169275101, 0], [2.0, 0]], [[1.0, 0], [1.8727461330844934, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.9233750718902705, 0], [7.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.8512233163734737, 0], [13.0, 0]], [[1.0, 0], [-2.330333881926601, 0], [17.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-2.746530874833948, 0], [23.0, 0]], [[1.0, 0], [0.9729654020310864, 0], [29.0, 0]], [[1.0, 0], [0.005511781257893803, 0], [31.0, 0]], [[1.0, 0], [9.671240908158643, 0], [37.0, 0]], [[1.0, 0], [-6.6513729689349015, 0], [41.0, 0]], [[1.0, 0], [7.994128620392178, 0], [43.0, 0]], [[1.0, 0], [3.469815770634827, 0], [47.0, 0]], [[1.0, 0], [10.54926468705429, 0], [53.0, 0]], [[1.0, 0], [13.781445130956062, 0], [59.0, 0]], [[1.0, 0], [-3.746080456623601, 0], [61.0, 0]], [[1.0, 0], [-3.971721897010676, 0], [67.0, 0]], [[1.0, 0], [-14.268760963919323, 0], [71.0, 0]], [[1.0, 0], [-13.226331599319602, 0], [73.0, 0]], [[1.0, 0], [1.87656399111163, 0], [79.0, 0]], [[1.0, 0], [-10.961884287138913, 0], [83.0, 0]], [[1.0, 0], [-15.019530875899463, 0], [89.0, 0]], [[1.0, 0], [-7.572481426996066, 0], [97.0, 0]], [[1.0, 0], [15.051324790942381, 0], [101.0, 0]], [[1.0, 0], [-0.5434508598228533, 0], [103.0, 0]], [[1.0, 0], [14.737082102403404, 0], [107.0, 0]], [[1.0, 0], [17.371103381246677, 0], [109.0, 0]], [[1.0, 0], [12.886548944962456, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 21040002, 'index': 11, 'label': '2-5225-1.1-c1-0-11', 'leading_term': '0.20169610622692047314983177290147', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5225/2/a/n/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [0.20169610622692047, 0.19694068359381475, 0.18270696579532822, 0.15909694097689311, 0.1262946706570091, 0.08458612602443176, 0.03438451739590365, -0.02374104576809744, -0.08903600170934621, -0.16053242443339324, -0.2370252279583901, -0.31705477811726984, -0.3988979293195089, -0.4805691686201636, -0.5598331747259898, -0.6342296984987084, -0.7011112509079704, -0.7576936471031106, -0.8011190028231082, -0.828530314050188, -0.8371562772010825, -0.8244045328663683, -0.7879610520498115, -0.7258929439653431, -0.6367515651531178, -0.5196724691478579, -0.3744684731828092, -0.20171195231755878, -0.0028024196672982557, 0.2199844703482515, 0.4634701382088169, 0.723571786102837, 0.9953293410255794, 1.2729627023980106, 1.5499605413054458, 1.8192009484095226, 2.073103169963419, 2.3038085338989553, 2.503387484364324, 2.664068452325103, 2.7784831350826225, 2.8399216849411375, 2.8425903643068136, 2.7818634584297106, 2.654520692768156, 2.458961120288563, 2.195384459381671, 1.8659312017326897, 1.474773487660444, 1.02814976878191, 0.5343376361767765, 0.0035608646776255732, -0.5521713253506577, -1.1192926080008854, -1.6829729674892266, -2.2274722263704674, -2.7365462784017787, -3.1938962566607874, -3.5836486843603246, -3.8908527465522678, -4.101979277897597, -4.205404969983857, -4.191864735147174, -4.054855181176627, -3.7909727928122905, -3.400171700135092, -2.885927835345063, -2.2552988070806697, -1.5188718983027267, -0.6905961371946416, 0.21250170616937908, 1.1707132094669297, 2.162148264634328, 3.163326562124027, 4.149844321218593, 5.097096485088334, 5.981031652311025, 6.778914778737554, 7.4700712812457395, 8.036585707803932, 8.463928673682268, 8.741487331754856, 8.862977235173135, 8.826717010289205, 8.635751690908398, 8.297815735071062, 7.825132478450119, 7.2340528678708145, 6.544542533205148, 5.779532348388223, 4.964153348400466, 4.124881958671954, 3.2886257214923598, 2.481782861680809, 1.7293109484020182, 1.0538404546892661, 0.4748681173968262, 0.008062643460240179, -0.3352884586251059, -0.5486672093665843, -0.6305311317116109, -0.5843264415293, -0.41830574673281107, -0.1451555748262022, 0.21855295080779105, 0.6530693418963167, 1.1362970373448331, 1.6447210535104257, 2.1543917666335073, 2.641923648993784, 3.085466572514905, 3.465607930129458, 3.766166324930723, 3.974841873737312, 4.083694114121767, 4.089425860495793, 3.9934598213266113, 3.8018040013035956, 3.5247114594291955, 3.1761494396177032, 2.7731017904378223, 2.334736515171724, 1.8814768476553192, 1.4340190941064295, 1.0123433506290078, 0.6347639233527568, 0.3170647663255379, 0.07176154116150658, -0.09247386975665031, -0.17119815526046397, -0.16437150197790631, -0.07631361634548195, 0.08455748677330158, 0.3061914900903667, 0.5735538471764434, 0.8694239102332487, 1.1753033021368642, 1.4723888330937234, 1.7425606126007263, 1.9693348218781845, 2.138731993110849, 2.2400155621047326, 2.2662617608090083, 2.21473030913631, 2.0870154502110307, 1.8889681514431895, 1.6303921947418099, 1.3245287874984821, 0.9873556137193417, 0.636736304316394, 0.29146458291135074, -0.029746631290300713, -0.30927746721924537, -0.5315604163920989, -0.6839347740749006, -0.7573494262790058, -0.7468749606504815, -0.6519960525724793, -0.4766667555245156, -0.22912409391993113, 0.07853146735169014, 0.43096723952066085, 0.8104279416266142, 1.1976803434470171, 1.573041673664691, 1.9174354680603254, 2.213416542075925, 2.4461080282887533, 2.6039978994795123, 2.6795498962477113, 2.6695939133404116, 2.5754731324958984, 2.402938853287467, 2.161798304598376, 1.8653349031227417, 1.5295336405758582, 1.1721557482712104, 0.8117158140591096, 0.4664205498118203, 0.15313103070936288, -0.11359075401879284, -0.3222947814129404, -0.46526701439044776, -0.5389271963501806, -0.5439763398057414, -0.48528470919627703, -0.3715267087048561, -0.2145844973291714, -0.028756430640034903, 0.17018131322800528, 0.3660021069000994, 0.5430813959015962, 0.6874083395269932, 0.7874924179144953, 0.8351067455706765, 0.8258194496298829, 0.7592772883227543, 0.6392209657334296, 0.47322843778910034, 0.27219987869168644, 0.04961480652193588, -0.17939292028849063, -0.39908392403673554, -0.5942185050768499, -0.751145774856779, -0.8588038322515247, -0.9095623268455837, -0.8998475245647058, -0.8305028547094728, -0.7068541573455955, -0.538467515924686, -0.33860752031659397, -0.12342381333681171, 0.08908745707950612, 0.2802843733604424, 0.4321665893463376, 0.5286655569350184, 0.5568509849172109, 0.5079695023879519, 0.3782396942202273, 0.1693410941102067, -0.1114473307355265, -0.45148219571434295, -0.833363474876752, -1.2358897554934845, -1.6353118956885215, -2.006814521461439, -2.3261370826507526, -2.571233517478922, -2.723862949687632, -2.771003907289219, -2.705991549719023, -2.5292911291363676, -2.248840763814111, -1.8799215273784649, -1.4445414576708406, -0.9703506802939333, -0.48913555504214656, -0.03496864448703554, 0.35788352486645963, 0.6571732173516945, 0.834870243606027, 0.8692073385200787, 0.7464364806369006, 0.4621728112676111, 0.022223335076755984, -0.557174695399613, -1.2497473622822748, -2.0202139896919884, -2.8259187761057376, -3.6189912882867286, -4.348927775808746, -4.96545545117249, -5.421519446769406, -5.6762187286986405, -5.69751393327764, -5.464537417493858], 'positive_zeros': ['0.33551489458549249587905041395991', '1.42254798676236773362530402399125', '2.59017524957832229234425730543668', '3.54305444108268131969991759067487', '4.92679134378644718885176299345006', '5.25213042877619843819216550934722', '6.46836030493467430321935955152170', '6.67908157232295934778724062230048', '7.66301898290816200274902384041155', '8.112814795902207918782458274759115'], 'prelabel': '2-5225-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.459244155171642, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.33551489458549249587905041396', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.42254798676236773362530402399', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.59017524957832229234425730544', 'prec': 100}}