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_1861.1246'
a10	jsonb	[0.9999771775537991, -0.00675606183643797]
a2	jsonb	[-0.2571872006322887, -0.966361600970841]
a3	jsonb	[0.796938210212915, -0.6040608322864807]
a4	jsonb	[-0.8677094876618537, 0.49707166990445484]
a5	jsonb	[-0.25065253225872053, 0.9680771188662043]
a6	jsonb	[-0.7887035003337082, -0.6147737702288187]
a7	jsonb	[-0.5850489985953077, 0.8109979465095012]
a8	jsonb	[0.703514748819948, 0.7106806583781533]
a9	jsonb	[0.2702210217947286, -0.9627983170842234]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	8.642447666389383
analytic_normalization	numeric	0
bad_lfactors	jsonb	[[1861, [1]]]
bad_primes	bigint[]	[1861]
central_character	text	'1861.1246'
coeff_info	jsonb	['x^930 - 1', '0.999977177553799 + 0.00675606183643797*I', '\\\\zeta_{930}']
coefficient_field	text
conductor	numeric	1861
conductor_radical	integer	1861
conjugate	text	'dirichlet_L_1861.1047'
credit	text
degree	smallint	1
dirichlet_coefficients	jsonb	['a^0', 'a^659', 'a^834', 'a^388', 'a^270', 'a^563', 'a^325', 'a^117', 'a^738', 'a^929', 'a^299', 'a...
euler_factors	jsonb	[[1, 'a^659'], [1, 'a^834'], [1, 'a^270'], [1, 'a^325'], [1, 'a^299'], [1, 'a^645'], [1, 'a^440'], [...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[0], []]
group	text
index	smallint	0
label	text	'1-1861-1861.1246-r0-0-0'
leading_term	text	'0.0146813925487481532266728746745-0.397983024473722029149872356536*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/1861/1246'
plot_delta	numeric	0.3125
plot_values	jsonb	[-0.3982537269837173, 0.5256342350503547, 1.656906324468766, 2.3559472491816997, 1.9696910217294803,...
positive_zeros	jsonb	['0.14579056334056726241526328179', '1.73777517296465714530366830934', '2.59371148479116990540079437...
precision	smallint
prelabel	text	'1-1861-1861.1246-r0-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	8.642447666389383
root_angle	double precision	0.4882630313337199
root_number	text	'-0.997282029116613332656598610118+0.0736787242088949107093317919893*I'
self_dual	boolean	False
sign_arg	numeric	0.488263031334
spectral_label	text	'r0-0'
st_group	text	'mu(930)'
symmetry_type	text	'unitary'
trace_hash	bigint
types	jsonb	['DIR']
values	jsonb	[[1, '0.713373794163761061701150459367-0.319729993212340324521528449790*I']]
z1	numeric	0.145790563341
z2	numeric	1.73777517296
z3	numeric	2.59371148479

{'Lhash': '632816878700101573604228257276', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.9583144779274676, -0.9583144779274676], 'a4': [0.0, 0.0], 'a5': [-1.0416855220725323, 24.978288397588503], 'a6': [0.0, 0.0], 'a7': [-26.061659441733568, -26.061659441733568], 'a8': [0.0, 0.0], 'a9': [0.0, 79.16326672278922], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.269597046707549, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0416855220725323, -24.978288397588503]]]], 'bad_primes': [2, 5], 'central_character': '80.17', 'coefficient_field': 'CDF', 'conductor': 80, 'conductor_radical': 10, 'conjugate': '2893927267312859801794739095106', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.9583144779274676, 0.9583144779274676], [0, -81.0]], [[1.0, 0], [1.0416855220725323, -24.978288397588503]], [[1.0, 0], [26.061659441733568, 26.061659441733568], [0, 2401.0]], [[1.0, 0], [75.95657679517701, 0], [14641.0, 0]], [[1.0, 0], [99.14284027338739, -99.14284027338739], [0, -28561.0]], [[1.0, 0], [-77.91708148559572, -77.91708148559572], [0, 83521.0]], [[1.0, 0], [0, -640.4454719040631], [-130321.0, 0]], [[1.0, 0], [117.1341518596351, -117.1341518596351], [0, -279841.0]], [[1.0, 0], [0, 752.5341284326722], [-707281.0, 0]], [[1.0, 0], [708.2050246810744, 0], [923521.0, 0]], [[1.0, 0], [-1170.5123443940481, -1170.5123443940481], [0, 1874161.0]], [[1.0, 0], [-1822.208408746424, 0], [2825761.0, 0]], [[1.0, 0], [-2372.1186119372305, 2372.1186119372305], [0, -3418801.0]], [[1.0, 0], [2458.7850096743623, 2458.7850096743623], [0, 4879681.0]], [[1.0, 0], [-2118.2579044089043, 2118.2579044089043], [0, -7890481.0]], [[1.0, 0], [0, -5251.962584738821], [-12117361.0, 0]], [[1.0, 0], [1312.8850430090313, 0], [13845841.0, 0]], [[1.0, 0], [-5569.34618781471, -5569.34618781471], [0, 20151121.0]], [[1.0, 0], [7554.661986554997, 0], [25411681.0, 0]], [[1.0, 0], [-1206.346879536569, 1206.346879536569], [0, -28398241.0]], [[1.0, 0], [0, -3397.974912254437], [-38950081.0, 0]], [[1.0, 0], [928.4208713965768, -928.4208713965768], [0, -47458321.0]], [[1.0, 0], [0, -11981.927305166384], [-62742241.0, 0]], [[1.0, 0], [-4683.76369496135, -4683.76369496135], [0, 88529281.0]], [[1.0, 0], [779.9749877101913, 0], [104060401.0, 0]], [[1.0, 0], [-3498.857484179799, 3498.857484179799], [0, -112550881.0]], [[1.0, 0], [-6289.205134845164, -6289.205134845164], [0, 131079601.0]], [[1.0, 0], [0, -14318.884008921521], [-141158161.0, 0]], [[1.0, 0], [-11593.474954016057, 11593.474954016057], [0, -163047361.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 10801723, 'index': 2, 'label': '2-80-5.2-c4-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/80/5/p/g/17/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.044844368378546, 0.8005257925705821, 0.5423645444480623, 0.27372503053252045, -0.0017667458697025213, -0.28012299394118373, -0.5569091091690519, -0.8271860821866365, -1.0854915869997146, -1.3258693654767202, -1.5419543244040568, -1.7271180053609305, -1.874675790351862, -1.978153395089971, -2.031605939571142, -2.0299782906466226, -1.96949063389526, -1.848028621102561, -1.6655132991505075, -1.4242227607900892, -1.1290355075050518, -0.7875653194760586, -0.41015938456724726, -0.00973585302802171, 0.39855597848516605, 0.7978600156852567, 1.1703174324752963, 1.4979318261089556, 1.7635619612994116, 1.951993691152192, 2.0510289194267983, 2.052518295335923, 1.9532571056715653, 1.7556618584579133, 1.4681494194566078, 1.1051519777395404, 0.6867197806803371, 0.23768907189405314, -0.2135761272559952, -0.6368246590473855, -1.0018610727244834, -1.2806755962595469, -1.4496163110408227, -1.4914371829471285, -1.397045783016896, -1.1667788658686544, -0.8110540514602889, -0.35028198499448937, 0.1860256675446978, 0.7609540106400497, 1.33261945444329, 1.8571993956480393, 2.2923477271673196, 2.6007311239368773, 2.7533841826703886, 2.7325693574499907, 2.533844327132891, 2.1670866094144374, 1.6563016129279244, 1.038141416516502, 0.35917978759631314, -0.3278859919453956, -0.9688162385022008, -1.512801369908575, -1.9173638488531506, -2.1526986452627366, -2.2049809270991756, -2.078240532349281, -1.7945220668772177, -1.3922087834204502, -0.9225739644716695, -0.44481725904833685, -0.020024500629618018, 0.2953634329174518, 0.4558937064950162, 0.4325528829876069, 0.2166756014815443, -0.1782098723796684, -0.7169201822678815, -1.3456096856821247, -1.9970110328243105, -2.5974451340256905, -3.074887749979861, -3.3672139951282216, -3.4296696651598966, -3.240655168310609, -2.805057396976301, -2.1546168179200196, -1.3451474645432062, -0.4508007373603838, 0.44406382443402215, 1.2545132974664388, 1.9050620219601306, 2.3388542415858726, 2.524830081731799, 2.4618946854752117, 2.1794459113387843, 1.7340533900152688, 1.2025697249828442, 0.6724317887573982, 0.23031235389695318, -0.04944847608761158, -0.11511033666653457, 0.054916134037220475, 0.4483444034748076, 1.019754521999945, 1.6958639385274472, 2.384771258226804, 2.9880485207561147, 3.414117901505997, 3.5911069673582894, 3.4773771820988735, 3.0681756365059933, 2.3973465050337124, 1.5336983641426896, 0.572369785085859, -0.37773529433715125, -1.208765961686201, -1.8289336496610997, -2.1755488878588136, -2.2241352851495484, -1.9921806426681925, -1.5368294722770222, -0.9466988338691738, -0.3288840363330994, 0.20702126412268834, 0.5655555829592802, 0.680161671482384, 0.5237946178363179, 0.11362648528377162, -0.4910358586664079, -1.1974778123994836, -1.893765983981712, -2.4663218746612956, -2.818203187248402, -2.8852169169061352, -2.647238895336269, -2.132792424890886, -1.4159525826734507, -0.6058429626176953, 0.1698084028726899, 0.7845819519593672, 1.1336369065125238, 1.1510723762381543, 0.8214855136515514, 0.18369241287163987, -0.6742003460234679, -1.6277897389946085, -2.535508328265545, -3.260900843323175, -3.6944521459284734, -3.771356605095305, -3.4822076427108817, -2.8747010832350366, -2.0459148499730357, -1.1263114210365104, -0.25804071105144305, 0.4288512666637431, 0.8382685493606552, 0.9241800053550352, 0.6981341074121739, 0.22674679890383106, -0.3805356501616953, -0.9913770177420032, -1.4747665363308762, -1.7252473964195116, -1.6828012121733893, -1.344713885005707, -0.7671094495482439, -0.05565334087314726, 0.6531194123287388, 1.2166525745637977, 1.5129868213975697, 1.4643037202822466, 1.0529893072196361, 0.3270692613845245, -0.6062602715255747, -1.5981233481555472, -2.4835387117892362, -3.1105736247146134, -3.3677992653069917, -3.204957057258484, -2.6428853610969587, -1.770662292215798, -0.7302564495272788, 0.3086848583412696, 1.1793818222906087, 1.748186413321882, 1.9388978626563815, 1.7464859577919556, 1.2375080013195117, 0.5369934204780973, -0.19584705958343143, -0.798548367603506, -1.1370643739753086, -1.1320607868911792, -0.7746499019625325, -0.128367003227084, 0.6831686930095843, 1.5006604690650234, 2.160941221830638, 2.529969263029834, 2.5304551827641384, 2.1585127322322624, 1.4858141892929273, 0.6465645672721304, -0.18836082182157574, -0.8451482273780966, -1.182001369885537, -1.11830260213155, -0.6519971472696396, 0.13851308945390023, 1.1086118523420798, 2.0752323778345265, 2.8527360694084076, 3.2897567551515685, 3.2995480739090612, 2.8775826519854806, 2.1026699858877653, 1.1211927121393035, 0.1175351327272824, -0.7233247867416193, -1.2533830499817045, -1.3915261864465656, -1.1394839247657138, -0.5803534771454513, 0.14014235442076686, 0.8458452718398648, 1.3690697341227023, 1.5879638805935814, 1.4542538271353578, 1.0052243854976375, 0.3570638189178973, -0.31934468151814827, -0.8352995647556639, -1.026109806754019, -0.7889313902570533, -0.10833809911561172, 0.9361789424247166, 2.1828192350618885, 3.4179410711319456, 4.418261013952907, 4.996025007819897, 5.0376063674286495, 4.527251854720143, 3.5507759309279874, 2.2782557660616427, 0.9292966938564563, -0.2717650360769807, -1.1411227272599738, -1.5714703089111046, -1.55092205840589, -1.1608434798888927, -0.5532112856346149, 0.08731765271921742, 0.5880015989357797, 0.8291040791896565], 'positive_zeros': ['0.49920449577049735180187990288085', '2.87798910150210049080076702484221', '4.69039238448878153584298311986831', '5.95810166984472806623665259097810', '7.56490303886254670391438860643100', '9.006660288490275853507381135416492', '9.574828850261999111891192215249064', '11.18722451514396397444311028040952', '12.59481689992552011854242439442208', '12.84887932471180872111723350584465'], 'prelabel': '2-80-5.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8756907077617977, 'root_angle': -0.33147059915895527, 'root_number': '-0.4898301082678814 - 0.8718179081862655*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.331470599159', 'prec': 40}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.49920449577049735180187990288', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.87798910150210049080076702484', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.69039238448878153584298311987', 'prec': 100}}