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_4159.1692'
a10	jsonb	[0.020398537391405354, 0.9997919281892065]
a2	jsonb	[0.020398537391405354, 0.9997919281892065]
a3	jsonb	[0.5576886669868294, -0.8300502097550806]
a4	jsonb	[-0.9991677993445829, 0.04078858606158557]
a5	jsonb	[1.0, 0.0]
a6	jsonb	[0.8412535328311812, 0.5406408174555976]
a7	jsonb	[-0.14231483827328514, 0.9898214418809327]
a8	jsonb	[-0.061161660821842705, -0.9981278731933669]
a9	jsonb	[-0.37796670142890654, -0.9258191900208981]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	19.314314800920712
analytic_normalization	numeric	0
bad_lfactors	jsonb	[[4159, [1]]]
bad_primes	bigint[]	[4159]
central_character	text	'4159.1692'
coeff_info	jsonb	['x^77 - 1', '0.996672582494193 + 0.0815092835470632*I', '\\\\zeta_{77}']
coefficient_field	text
conductor	numeric	4159
conductor_radical	integer	4159
conjugate	text	'dirichlet_L_4159.2431'
credit	text
degree	smallint	1
dirichlet_coefficients	jsonb	['a^0', 'a^19', 'a^65', 'a^38', 'a^0', 'a^7', 'a^21', 'a^57', 'a^53', 'a^19', 'a^73', 'a^26', 'a^40'...
euler_factors	jsonb	[[1, 'a^19'], [1, 'a^65'], [1, 'a^0'], [1, 'a^21'], [1, 'a^73'], [1, 'a^40'], [1, 'a^42'], [1, 'a^52...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[0], []]
group	text
index	smallint	0
label	text	'1-4159-4159.1692-r0-0-0'
leading_term	text	'0.782658211066772811829988986826-0.800374459963015678616874068708*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/4159/1692'
plot_delta	numeric	0.3125
plot_values	jsonb	[1.1194432328221602, -0.2689153751464723, -2.062580673897423, -3.086137851674827, -2.047996763518082...
positive_zeros	jsonb	['0.26024372137283109472779921479', '1.507971085335474079923971999384', '2.3592626510779232542649060...
precision	smallint
prelabel	text	'1-4159-4159.1692-r0-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	19.314314800920712
root_angle	double precision	-0.24643783614878803
root_number	text	'0.0223798669596166448589015936264-0.999749539412181904523297989412*I'
self_dual	boolean	False
sign_arg	numeric	0.0
spectral_label	text	'r0-0'
st_group	text	'mu(77)'
symmetry_type	text	'unitary'
trace_hash	bigint
types	jsonb	['DIR']
values	jsonb	[[1, '1.10772999539322626482594776016+0.120306080138923265528420445534*I']]
z1	numeric	0.260243721373
z2	numeric	1.50797108534
z3	numeric	2.35926265108

{'Lhash': '1028240685304560608413576063256', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -1.3852081065276893], 'a6': [0, 0], 'a7': [-160.7040599250805, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 46.19054010613843, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '288.145', 'coefficient_field': 'CDF', 'conductor': 288, 'conductor_radical': 6, 'conjugate': '691426922337849756605936147534', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.3852081065276893], [-3125.0, 0]], [[1.0, 0], [160.7040599250805, 0], [16807.0, 0]], [[1.0, 0], [0, 129.12912563073223], [-161051.0, 0]], [[1.0, 0], [0, -759.6593733020517], [-371293.0, 0]], [[1.0, 0], [323.408119850161, 0], [1419857.0, 0]], [[1.0, 0], [0, 198.51143964657953], [-2476099.0, 0]], [[1.0, 0], [1193.1527790260466, 0], [6436343.0, 0]], [[1.0, 0], [0, 5987.236459492113], [-20511149.0, 0]], [[1.0, 0], [-4872.448719100966, 0], [28629151.0, 0]], [[1.0, 0], [0, 3698.5618828402644], [-69343957.0, 0]], [[1.0, 0], [-10437.876074905475, 0], [115856201.0, 0]], [[1.0, 0], [0, -9873.106208437273], [-147008443.0, 0]], [[1.0, 0], [6297.980764045653, 0], [229345007.0, 0]], [[1.0, 0], [0, 21728.14645853646], [-418195493.0, 0]], [[1.0, 0], [0, -33513.43866855141], [-714924299.0, 0]], [[1.0, 0], [0, 48506.81791188421], [-844596301.0, 0]], [[1.0, 0], [0, 33182.38465996914], [-1350125107.0, 0]], [[1.0, 0], [-59464.131415729586, 0], [1804229351.0, 0]], [[1.0, 0], [-51278.62609737431, 0], [2073071593.0, 0]], [[1.0, 0], [-73724.54915355692, 0], [3077056399.0, 0]], [[1.0, 0], [0, 61627.9718549943], [-3939040643.0, 0]], [[1.0, 0], [-106734.7415131004, 0], [5584059449.0, 0]], [[1.0, 0], [-12562.912419472057, 0], [8587340257.0, 0]], [[1.0, 0], [0, -64962.80607856495], [-10510100501.0, 0]], [[1.0, 0], [-69035.89003744222, 0], [11592740743.0, 0]], [[1.0, 0], [0, 187321.62858322592], [-14025517307.0, 0]], [[1.0, 0], [0, -49350.46588717091], [-15386239549.0, 0]], [[1.0, 0], [171100.02570785602, 0], [18424351793.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23217118, 'index': 12, 'label': '2-288-8.5-c5-0-12', 'leading_term': '1.423873356746913958501785940637177947610563331847121570', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/288/6/d/b/145/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0625', 'prec': 10}, 'plot_values': [1.423873356746914, 1.4731344882529467, 1.4938903005703212, 1.4857460310408284, 1.4486830534867985, 1.38306179090433, 1.2896213399654164, 1.1694756595412998, 1.0241061504353952, 0.8553504368251273, 0.6653871537670836, 0.45671655141655015, 0.23213674686929753, -0.00528451016884515, -0.2522426407463725, -0.5052336252890003, -0.7605959118457273, -1.0145566822874412, -1.2632822061914804, -1.502931893159455, -1.7297155276409577, -1.9399530391662698, -2.1301360288598143, -2.2969901442178786, -2.4375372726845255, -2.5491564150392305, -2.6296420065956796, -2.6772583822461318, -2.690789034847162, -2.6695792994028213, -2.613571111582852, -2.5233285413421362, -2.4000528930664395, -2.2455862941611113, -2.062402864717089, -1.853586771105552, -1.6227967141317041, -1.3742166845093362, -1.112493130386413, -0.8426590176445561, -0.5700456166452043, -0.3001832107712814, -0.038692283254154976, 0.2088329107302299, 0.4369461506023235, 0.6404739028342065, 0.8146400335984939, 0.955187597392312, 1.0584945836449606, 1.1216804434776655, 1.142700240686659, 1.1204233807100417, 1.0546940727422598, 0.9463709747770297, 0.7973438579980112, 0.6105256015127754, 0.3898183838404344, 0.1400535636656429, -0.13309457398079436, -0.42322030473063305, -0.7233215354146245, -1.0259560578286777, -1.32341585481623, -1.6079156406377983, -1.8717911978889294, -2.107702544511913, -2.3088365491987344, -2.4691033322376565, -2.583320659381029, -2.6473805728058255, -2.658392715584888, -2.614799199197365, -2.516456436880752, -2.3646801125587062, -2.162250363038743, -1.913375301383798, -1.623612177082796, -1.2997467235890376, -0.9496325507585052, -0.5819937594428272, -0.2061952457195899, 0.1680136210232077, 0.5307751630336527, 0.8724116811647542, 1.18371740637794, 1.4562451592820773, 1.6825785298044142, 1.8565804480656374, 1.9736093810067017, 2.0306950616931987, 2.0266666334082455, 1.9622273515918147, 1.8399715053171162, 1.6643409575261927, 1.4415206109159275, 1.1792741265901066, 0.8867232905277451, 0.5740764683827432, 0.25231353886325375, -0.06716352389120273, -0.37290370962112906, -0.6537917328188141, -0.8994316914353491, -1.1005163721351392, -1.2491689553630547, -1.3392443514270633, -1.366578354946045, -1.3291742266505615, -1.2273181679085574, -1.0636173958911428, -0.8429570904562917, -0.5723752867208852, -0.26085773596950446, 0.0809422520495875, 0.44105105093983465, 0.8065783699099446, 1.164164197594763, 1.500453872952383, 1.802584567755602, 2.0586654890551164, 2.258233770174701, 2.392668354660666, 2.4555452037304644, 2.4429188621626357, 2.3535177608827085, 2.1888435502610553, 1.953168154166176, 1.653425995726791, 1.2990028365624258, 0.9014267419455262, 0.47397067538585497, 0.031179974442097205, -0.41165869478395745, -0.8390875141461341, -1.2360653241581099, -1.588550262903995, -1.8840539976321329, -2.112144813008155, -2.264878261248866, -2.337136436344919, -2.326860142010679, -2.2351621773798893, -2.0663145268875316, -1.8276072413547875, -1.529082041133119, -1.1831489466923037, -0.8040993254203633, -0.4075334137375183, -0.009724418541303542, 0.37305547173946674, 0.7252195935215525, 1.0325331280978853, 1.282732597186528, 1.4660711934371184, 1.5757651177295997, 1.6083197513502323, 1.563719167498582, 1.4454680100566666, 1.2604809217084314, 1.018821236534654, 0.7332972869292901, 0.4189311200214331, 0.09232038242090923, -0.2290806663676831, -0.5277308674343415, -0.7867895095446281, -0.990886671719076, -1.1268418931294293, -1.18429803188541, -1.1562402392269775, -1.0393744800055484, -0.8343458092427709, -0.5457834392451173, -0.1821672180679716, 0.24448184013412544, 0.7190762375454259, 1.2240833555345336, 1.740267836347153, 2.2475232107575183, 2.725756217932197, 3.155784072608742, 3.5202035250613366, 3.8041910443058757, 3.9961958610360937, 4.0884918696675525, 4.07756035394028, 3.964282927292785, 3.7539326502460515, 3.4559606209416724, 3.0835850029353233, 2.6531989994693457, 2.183623242198135, 1.6952359869649283, 1.2090209901606603, 0.745577626296607, 0.32414042897969475, -0.03834438407487416, -0.32803977790089234, -0.5348947459808271, -0.6531420532938033, -0.681589983967616, -0.6236908843194536, -0.4873800240650115, -0.28468956875960905, -0.031153714921328502, 0.25496827780924197, 0.5536148645750549, 0.8439465821641234, 1.1054219220227999, 1.3188711737432877, 1.4675138876855263, 1.5378675266592934, 1.520499497243751, 1.4105818947982236, 1.208217652313086, 0.9185179205584582, 0.5514228920046299, 0.12127130305845724, -0.35386314982808836, -0.8530379372294704, -1.3534688625924682, -1.8316677443794969, -2.2646335272474123, -2.631036016854821, -2.9123308145546005, -3.0937466058096077, -3.1650916597075214, -3.121334989981249, -2.9629287159156403, -2.69585120888356, -2.3313649655147546, -1.8854980761854994, -1.3782728754732823, -0.8327190814171163, -0.2737207011362568, 0.2732444725014262, 0.7834073831611462, 1.2339836883092685, 1.6053550799923018, 1.882091960454702, 2.053761122833241, 2.1154728937248537, 2.0681356404845705, 1.9184009486119782, 1.6782993294769903, 1.3645831422973056, 0.9978095903577485, 0.6012112806705292, 0.19941408646945755, -0.18292879433291442, -0.5225121947234191, -0.7986878869522773, -0.9946338891954752, -1.0983178235843114, -1.1031985795397128, -1.0086244050280653, -0.8199019661228226], 'positive_zeros': ['0.811138877794429212437438204469684', '2.63450772598622689659552819522092', '3.59512446852714993596139320886703', '5.03430027716428851880899563510739', '6.17421100959674518707073979630485', '7.04807935144683120879317297866935', '8.191875417616264626066574729469997', '9.251547355972995621733537971655981', '10.14270081095083580207701261713407', '10.84020334647214684597804972587717'], 'prelabel': '2-288-8.5-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.7963622700779, 'root_angle': 0.09022228931364841, 'root_number': '0.8435787209979791948177829994385971110547348418123346435 + 0.5370055320752418240417159825621498790461852372065397617*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.09022228931364838', 'prec': 54}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.811138877794429212437438204470', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.63450772598622689659552819522', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.59512446852714993596139320887', 'prec': 100}}