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_4164.1367'
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	[0.9410651686110088, 0.3382252924119271]
a6	jsonb	[1.0, -2.8163065144692913e-30]
a7	jsonb	[-0.586315149923405, 0.8100830481933905]
a8	jsonb	[1.0, -2.8163065144692913e-30]
a9	jsonb	[1.0, -2.8163065144692913e-30]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	19.3375347033022
analytic_normalization	numeric	0
bad_lfactors	jsonb	[[2, [1]], [3, [1]], [347, [1]]]
bad_primes	bigint[]	[2, 3, 347]
central_character	text	'4164.1367'
coeff_info	jsonb	['x^346 - 1', '0.999835120899773 + 0.0181584970560800*I', '\\\\zeta_{346}']
coefficient_field	text
conductor	numeric	4164
conductor_radical	integer	2082
conjugate	text	'dirichlet_L_4164.3503'
credit	text
degree	smallint	1
dirichlet_coefficients	jsonb	['a^0', 0, 0, 0, 'a^19', 0, 'a^467', 0, 0, 0, 'a^236', 0, 'a^120', 0, 0, 0, 'a^85', 0, 'a^281', 0, 0...
euler_factors	jsonb	[[0], [0], [1, 'a^19'], [1, 'a^467'], [1, 'a^236'], [1, 'a^120'], [1, 'a^85'], [1, 'a^281'], [1, 'a^...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[0], []]
group	text
index	smallint	0
label	text	'1-4164-4164.1367-r0-0-0'
leading_term	text	'0.00101361683191600643096105015295+0.616630712420862458878046721417*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/4164/1367'
plot_delta	numeric	0.3125
plot_values	jsonb	[0.6166315455113709, 1.9797434321772296, 3.2217307076795056, 3.0847543571790794, 1.2357540171274124,...
positive_zeros	jsonb	['1.41913533059032057802556786920', '2.16840421400423802968268241697', '2.93936370286604965853403433...
precision	smallint
prelabel	text	'1-4164-4164.1367-r0-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	19.3375347033022
root_angle	double precision	0.4994767630588298
root_number	text	'-0.999994595865540150666078031041+0.00328758873873077496172390387677*I'
self_dual	boolean	False
sign_arg	numeric	0.0
spectral_label	text	'r0-0'
st_group	text	'mu(346)'
symmetry_type	text	'unitary'
trace_hash	bigint
types	jsonb	['DIR']
values	jsonb	[[1, '0.910163192799472960431443501245+0.239246072435481172720071722475*I']]
z1	numeric	1.41913533059
z2	numeric	2.168404214
z3	numeric	2.93936370287

{'Lhash': '2168947849612674055864375034184', 'a10': [7.2308194784377156, 6.907622577287045], 'a2': [1.9400777560868137, -0.485899475547313], 'a3': [-4.6490244208824345, 0.0], 'a4': [3.527803399325692, -1.8853655284071813], 'a5': [2.6679854602034285, 4.2286940754969615], 'a6': [-9.019468866458393, 2.2589585279134257], 'a7': [-9.906813024329509, 0.0], 'a8': [5.928114781411191, -5.371913545322016], 'a9': [12.613428065961257, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 10.354250045691284, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [-1.9400777560868137, 0.485899475547313]]], [5, [[1.0, 0], [-2.6679854602034285, -4.2286940754969615]]], [19, [[1.0, 0], [0, 4.358898943540674]]]], 'bad_primes': [2, 5, 19], 'central_character': '380.39', 'coefficient_field': 'CDF', 'conductor': 380, 'conductor_radical': 190, 'conjugate': '535642498855194663445316129241', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.9400777560868137, 0.485899475547313]], [[1.0, 0], [4.6490244208824345, 0], [9.0, 0]], [[1.0, 0], [-2.6679854602034285, -4.2286940754969615]], [[1.0, 0], [9.906813024329509, 0], [49.0, 0]], [[1.0, 0], [0, 2.3629800558061764], [-121.0, 0]], [[1.0, 0], [0, 16.53874885531429], [-169.0, 0]], [[1.0, 0], [0, 21.499622877999386], [-289.0, 0]], [[1.0, 0], [0, 4.358898943540674]], [[1.0, 0], [6.865948613316573, 0], [529.0, 0]], [[1.0, 0], [36.170495229916625, 0], [841.0, 0]], [[1.0, 0], [0, 46.41338863353044], [-961.0, 0]], [[1.0, 0], [0, 17.747883804154956], [-1369.0, 0]], [[1.0, 0], [54.6944136228203, 0], [1681.0, 0]], [[1.0, 0], [4.276208225530284, 0], [1849.0, 0]], [[1.0, 0], [-40.99082865591779, 0], [2209.0, 0]], [[1.0, 0], [0, -10.7606282018297], [-2809.0, 0]], [[1.0, 0], [0, 70.44428472481202], [-3481.0, 0]], [[1.0, 0], [-101.47415418859856, 0], [3721.0, 0]], [[1.0, 0], [7.297596240280049, 0], [4489.0, 0]], [[1.0, 0], [0, -31.853134017850394], [-5041.0, 0]], [[1.0, 0], [0, -83.75707693947886], [-5329.0, 0]], [[1.0, 0], [0, -137.90910273896685], [-6241.0, 0]], [[1.0, 0], [99.86905736189743, 0], [6889.0, 0]], [[1.0, 0], [-76.92674840969677, 0], [7921.0, 0]], [[1.0, 0], [0, 155.5739775829711], [-9409.0, 0]], [[1.0, 0], [140.01931208458248, 0], [10201.0, 0]], [[1.0, 0], [-159.91386981571657, 0], [10609.0, 0]], [[1.0, 0], [-90.99829537191829, 0], [11449.0, 0]], [[1.0, 0], [113.07971008845145, 0], [11881.0, 0]], [[1.0, 0], [0, -198.26606440318648], [-12769.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 15715395, 'index': 75, 'label': '2-380-20.19-c2-0-75', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/380/3/h/a/39/101', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.1285873058083957, 1.409050584669579, 1.6596913330822098, 1.8757367000655496, 2.050709979703392, 2.1764497574068105, 2.243472586148465, 2.241653401750527, 2.1611698876744665, 1.9936367674392834, 1.7333400374212926, 1.378467005544363, 0.9322156912827373, 0.4036589653311451, -0.19176168166845786, -0.8322269973919588, -1.4901047321853933, -2.1331373131826252, -2.726246776195005, -3.2338855411481133, -3.622790379956617, -3.86492790489434, -3.9403622166905214, -3.839738572062961, -3.566069860220566, -3.1355419408987144, -2.5771225507172613, -1.9308648518498868, -1.2449336378077245, -0.5715370539971928, 0.03789803290318103, 0.5378338379773087, 0.893446104479824, 1.0845662794047208, 1.108184928839903, 0.9790825389752211, 0.7283513639312418, 0.39982726586584694, 0.044735242781170116, -0.2848705006946003, -0.5430630821968848, -0.6964487640605753, -0.7290586275727435, -0.6448876323314848, -0.4675083852555864, -0.23657128281103054, -0.0014615560710458532, 0.18714482495551982, 0.2866730097290132, 0.2715570328495192, 0.14014756346562637, -0.08174766909942367, -0.3416712741247328, -0.5660596616338424, -0.6701838844440877, -0.5713897880333214, -0.20386820524144894, 0.46727579936947106, 1.435036455893226, 2.6447634297868463, 3.995218820576027, 5.34706829076061, 6.538308638194056, 7.404962853518683, 7.804353214764886, 7.637579685271394, 6.867633712442796, 5.529947865348066, 3.7331120184605395, 1.6488724327224291, -0.5078219781904998, -2.5063080785686327, -4.131434301343556, -5.213878931642684, -5.654785861616512, -5.440604741053909, -4.645417285468936, -3.419965634307441, -1.9687684106997978, -0.5187486231367624, 0.7156628057103225, 1.5652437672340018, 1.9310456824656812, 1.797542235862026, 1.2316067031073465, 0.3675363884632095, -0.6191574496243197, -1.5444160407730176, -2.248762150786716, -2.6247864320433174, -2.6339352455234915, -2.3095864785293174, -1.7460636818203168, -1.0760135564584576, -0.44090414313689613, 0.03919428196318361, 0.2902207946360447, 0.29795177105260756, 0.10812801880827233, -0.1871097398640555, -0.47347638696098526, -0.6440725420105783, -0.6274765050263768, -0.4078320481244066, -0.031979076196341404, 0.398544954713353, 0.7494261324117509, 0.8849634189533782, 0.7020902529196751, 0.15925262775494725, -0.7068502764974484, -1.7812481350405185, -2.8884217818207265, -3.8248111065695016, -4.399661049576269, -4.4755633522627525, -3.9997168192650716, -3.0186166472605374, -1.67229923617529, -0.168705529731824, 1.2567933006874543, 2.3881710439269277, 3.0716291943736294, 3.2450309708600007, 2.947199664907668, 2.3049057642048947, 1.500516195390276, 0.7278663527587164, 0.1468256209055134, -0.15250008218199815, -0.16715314413796106, 0.024099519983089165, 0.28779144727383693, 0.4776805458396054, 0.48085029114978617, 0.2557889226414943, -0.14820151839826243, -0.5965776414473725, -0.9002482219155968, -0.8649809174080904, -0.34782222838189164, 0.6938012459133541, 2.173788922837777, 3.879060150391502, 5.503521255108756, 6.708682404845855, 7.1982912843306766, 6.790031835700953, 5.46692626472224, 3.3948876529561884, 0.900179661882276, -1.5902702603877852, -3.6338449298939035, -4.86418724022784, -5.0694894863154465, -4.239003523032555, -2.5665616815269097, -0.409651398576374, 1.7871086894121566, 3.586876276880905, 4.6523013964094035, 4.813242428301178, 4.095434714831355, 2.7044424915731873, 0.969923366047012, -0.7353940944582419, -2.0819035374777872, -2.8537185448984155, -2.9874435170715716, -2.5713947293827366, -1.8077959998803124, -0.9497833457654649, -0.23101165588483633, 0.1932454076254569, 0.27857271785517523, 0.09039477814363993, -0.22807645251356107, -0.5079047161383982, -0.6102656856845895, -0.46936276494235535, -0.11009851195254565, 0.3639383498055113, 0.8075336824176148, 1.0837238693934963, 1.110394326610875, 0.8885575135058477, 0.5029568647957137, 0.09431165464883788, -0.1884247168454083, -0.24074522980980398, -0.04299553471626869, 0.3255366056392778, 0.705155929952516, 0.9031195151708327, 0.7565597270330763, 0.1918448388500538, -0.7390066105684729, -1.8584934221462983, -2.903663766466776, -3.597210853658878, -3.7305791508463693, -3.234821931149443, -2.2166800815820555, -0.9459442905421124, 0.206499813502519, 0.8661062865858344, 0.7623836592675312, -0.18309295482891258, -1.8147909541912084, -3.762527235925288, -5.520784068628173, -6.57006620186439, -6.509795146253153, -5.167678229299599, -2.655506212519298, 0.6451579138032835, 4.165473373805639, 7.279708189210605, 9.450110716081165, 10.348762528772658, 9.925102233808117, 8.40264574526257, 6.207769654746597, 3.851805219663722, 1.799890848633898, 0.3626009626581311, -0.3613459879863125, -0.47864744686910426, -0.2375015363244288, 0.07097515586129567, 0.21388243958805664, 0.0887334427733347, -0.2545547416635889, -0.6465767495702354, -0.8732326175440461, -0.7660134685203461, -0.2765753443558077, 0.4903747337570072, 1.2982248402274412, 1.8482452994778102, 1.8764164848227356, 1.246213570110262, 0.006631205278905061, -1.6050180866448618, -3.2189692947574473, -4.432469618812058, -4.9236530818442, -4.545433926185031, -3.370528754936383, -1.6733312161985665, 0.14640830361444324, 1.6753117998868152, 2.599910746392984, 2.7880347386852304, 2.3143346216074496, 1.4238176656349188, 0.4466217187561964], 'positive_zeros': ['1.71099816402262103526597487698326', '3.74161848929931119389929279374671', '4.76602547520388145386992454326753', '5.75083123216655556551669375017640', '6.33308902070013393687691667256695', '7.04457177820696002469793391142760', '8.720234626899797021074298004215603', '9.923851975178804831836702481003632', '10.67210764390334600501281853781529', '11.86227467822747942128801624513211'], 'prelabel': '2-380-20.19-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.217802051974497, 'root_angle': 0.3323049349526809, 'root_number': '-0.4943936758643739 + 0.8692381107989412*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.332304934953', 'prec': 40}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.71099816402262103526597487698', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.74161848929931119389929279375', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.76602547520388145386992454327', 'prec': 100}}