Database - lfunc_lfunctions

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Query: /api/lfunc_lfunctions/?_offset=0

Table lfunc_lfunctions

L-functions

Column	Type	Example
A10	numeric	0
A2	numeric	0
A3	numeric	1
A4	numeric	0
A5	numeric	-1
A6	numeric	0
A7	numeric	-3
A8	numeric	0
A9	numeric	1
Lhash	text	'1275462304916959603'
a10	jsonb	[0.0, 0]
a2	jsonb	[0.0, 0]
a3	jsonb	[0.5773502691896258, 0]
a4	jsonb	[0.0, 0]
a5	jsonb	[-0.4472135954999579, 0]
a6	jsonb	[0.0, 0]
a7	jsonb	[-1.1338934190276817, 0]
a8	jsonb	[0.0, 0]
a9	jsonb	[0.3333333333333333, 0]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	2197.738584912105
analytic_normalization	numeric	0.5
bad_lfactors	jsonb	[[2, [1]], [3, [1, -1]], [47, [1, -1]], [61, [1, -1]]]
bad_primes	bigint[]	[2, 3, 47, 61]
central_character	text	'275232.1'
coeff_info	jsonb
coefficient_field	text	'1.1.1.1'
conductor	numeric	275232
conductor_radical	integer	17202
conjugate	text
credit	text
degree	smallint	2
dirichlet_coefficients	jsonb
euler_factors	jsonb	[[1], [1, -1], [1, 1, 5], [1, 3, 7], [1, 3, 11], [1, 2, 13], [1, 2, 17], [1, 0, 19], [1, 9, 23], [1,...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[], [0]]
group	text
index	smallint	15
label	text	'2-275232-1.1-c1-0-15'
leading_term	text	'13.8277044908'
load_key	text	'Cremona'
motivic_weight	smallint	1
mu_imag	numeric[]	[]
mu_real	smallint[]	[]
nu_imag	numeric[]	[0.0]
nu_real_doubled	smallint[]	[1]
order_of_vanishing	smallint	2
origin	text	'EllipticCurve/Q/275232/p'
plot_delta	numeric	0.25
plot_values	jsonb	[0.0, -0.7984181189251114, -2.431832304987653, -2.999856452396133, -1.025577550625997, 2.53326425248...
positive_zeros	jsonb	['1.075210326959126', '1.998202388950464', '2.567357993791214', '2.767704038960937', '3.617219009779...
precision	smallint
prelabel	text	'2-275232-1.1-c1-0'
primitive	boolean	True
rational	boolean	True
root_analytic_conductor	double precision	46.88004463428022
root_angle	double precision	0.0
root_number	text	'1'
self_dual	boolean	True
sign_arg	numeric
spectral_label	text	'c1-0'
st_group	text	'SU(2)'
symmetry_type	text
trace_hash	bigint	1275462304916959603
types	jsonb
values	jsonb
z1	numeric	1.075210326959126
z2	numeric	1.998202388950464
z3	numeric	2.567357993791214

{'Lhash': '404570994277493008265808189308', 'a10': [10.0, -70.0], 'a2': [-2.0, -2.0], 'a3': [0.0, 0.0], 'a4': [0.0, 8.0], 'a5': [15.0, 20.0], 'a6': [0.0, 0.0], 'a7': [-19.0, -19.0], 'a8': [16.0, -16.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 9.303296677545992, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [2.0, 2.0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-15.0, -20.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '90.37', 'coefficient_field': 'CDF', 'conductor': 90, 'conductor_radical': 30, 'conjugate': '2621306452340631698591703567125', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, 2.0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-15.0, -20.0]], [[1.0, 0], [19.0, 19.0], [0, 2401.0]], [[1.0, 0], [202.0, 0], [14641.0, 0]], [[1.0, 0], [99.0, -99.0], [0, -28561.0]], [[1.0, 0], [-239.0, -239.0], [0, 83521.0]], [[1.0, 0], [0, -40.0], [-130321.0, 0]], [[1.0, 0], [541.0, -541.0], [0, -279841.0]], [[1.0, 0], [0, -200.0], [-707281.0, 0]], [[1.0, 0], [758.0, 0], [923521.0, 0]], [[1.0, 0], [-141.0, -141.0], [0, 1874161.0]], [[1.0, 0], [1042.0, 0], [2825761.0, 0]], [[1.0, 0], [759.0, -759.0], [0, -3418801.0]], [[1.0, 0], [-459.0, -459.0], [0, 4879681.0]], [[1.0, 0], [-1819.0, 1819.0], [0, -7890481.0]], [[1.0, 0], [0, 4600.0], [-12117361.0, 0]], [[1.0, 0], [-2082.0, 0], [13845841.0, 0]], [[1.0, 0], [-5081.0, -5081.0], [0, 20151121.0]], [[1.0, 0], [-3478.0, 0], [25411681.0, 0]], [[1.0, 0], [3479.0, -3479.0], [0, -28398241.0]], [[1.0, 0], [0, 7680.0], [-38950081.0, 0]], [[1.0, 0], [6081.0, -6081.0], [0, -47458321.0]], [[1.0, 0], [0, -5680.0], [-62742241.0, 0]], [[1.0, 0], [-561.0, -561.0], [0, 88529281.0]], [[1.0, 0], [1682.0, 0], [104060401.0, 0]], [[1.0, 0], [-7021.0, 7021.0], [0, -112550881.0]], [[1.0, 0], [-2159.0, -2159.0], [0, 131079601.0]], [[1.0, 0], [0, 280.0], [-141158161.0, 0]], [[1.0, 0], [-8479.0, 8479.0], [0, -163047361.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 11318323, 'index': 2, 'label': '2-90-5.2-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/90/5/g/a/37/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [0.609788987729194, 0.3806407496328772, 0.1382333500939443, -0.11311557854606659, -0.36868496569988435, -0.623265791379874, -0.8710968215550163, -1.1058350664272534, -1.3205741066680003, -1.507921274010637, -1.6601417275522319, -1.769373775428544, -1.827915401329003, -1.8285769428967675, -1.7650893631734987, -1.632551760506313, -1.4278959699197253, -1.1503407057575081, -0.8018031494152238, -0.3872327224732944, 0.08516945127986439, 0.6038806882244775, 1.1541677175132963, 1.7184025055009342, 2.2765965531682397, 2.8071538987116416, 3.287827194106908, 3.6968437254825064, 4.01415026569437, 4.222708607801389, 4.309759146236601, 4.267959641451116, 4.096301947890539, 3.8007123911330485, 3.3942526189414397, 2.896857506806237, 2.334574722951354, 1.7383056716947145, 1.1420876955840047, 0.5809997713503385, 0.08881495837037146, -0.3044414047944259, -0.5748423730766127, -0.7066202948816159, -0.6937422306068718, -0.5408252315231666, -0.2632563993143688, 0.1135606258923898, 0.5558405195474609, 1.023860954836674, 1.4750643487278228, 1.8675885288598932, 2.163936929401514, 2.3344596572678853, 2.360306027333072, 2.235531289470521, 1.9680966366168382, 1.5795900570916546, 1.1036103133905988, 0.5828878802362628, 0.0653527026527545, -0.4005151234545952, -0.7706139742001236, -1.009927422128635, -1.0964935292561961, -1.0241623832890148, -0.8037650601491553, -0.4624653470207843, -0.04125221299751841, 0.40926173694528234, 0.8343649118701096, 1.1815436967631745, 1.4068704268832684, 1.4807399178348541, 1.392233842892025, 1.1515016918384628, 0.7897387054118951, 0.35659894525061697, -0.08482027066735298, -0.4649811746082904, -0.7161791010565562, -0.7811619904681183, -0.6210611725334515, -0.22160922069799008, 0.4032400260063209, 1.2109133102095504, 2.1333068267780964, 3.0832085834181577, 3.9634713787102824, 4.677968103029139, 5.143072778462147, 5.298264252265295, 5.114474142920995, 4.599005433782714, 3.796218593602335, 2.7836805862719673, 1.664040954130003, 0.5534670287205535, -0.4320389259240862, -1.1907750905662218, -1.6481231053009382, -1.7662689691736821, -1.5494823225008034, -1.0441080048978248, -0.3330980089303693, 0.4743588401663162, 1.2568666419334373, 1.8967251889860466, 2.295601207339008, 2.387826794568166, 2.149446842771466, 1.60167609382293, 0.8081757597538533, -0.13358012082414397, -1.1057279446713757, -1.9863911727395986, -2.6667042801609613, -3.0660332672092045, -3.143156225905991, -2.9017216709989824, -2.389124835466397, -1.6889169786952685, -0.9078456227860323, -0.1594629315970853, 0.45320018790470373, 0.8532122299095706, 1.0011222737331982, 0.9003216509737599, 0.5954965039463609, 0.16438056667867473, -0.295890415987623, -0.685614427005666, -0.9197744007328259, -0.9428090037884806, -0.7383660512206414, -0.332297071964166, 0.2117355347737327, 0.803414287430672, 1.3418762088222043, 1.7340561065359499, 1.912073211644128, 1.8465394674345423, 1.5532843185805902, 1.092069597757945, 0.557238919719457, 0.0616800868851567, -0.2832737468714909, -0.38854650611023894, -0.20491647325964668, 0.2658005348792421, 0.9682827535674242, 1.8007854800259264, 2.6309337766459637, 3.3177813317913705, 3.736457587237126, 3.8010967905232063, 3.4818606128500877, 2.8127428696997154, 1.8883566833743322, 0.8498065546285067, -0.1382862307195152, -0.9158595481706457, -1.3557708593309377, -1.387379180371045, -1.0109445485538413, -0.29992257177263365, 0.6096999845713249, 1.541580708841943, 2.309135291906173, 2.7484630359494715, 2.748280356504392, 2.271412889976078, 1.3637538173952812, 0.14874037903386178, -1.1920362163140208, -2.448948904753484, -3.4200252437604477, -3.9459308826276263, -3.937968584869965, -3.39397152457705, -2.3990929587891943, -1.1112110169720204, 0.26651828641850644, 1.521040909546678, 2.466298744721071, 2.9749039278399416, 2.998808447467662, 2.5752343382916054, 1.8169042240140276, 0.8885860273353646, -0.02543332240989426, -0.7566118138558716, -1.1833290318901277, -1.2519942683107177, -0.9841285050494885, -0.4682744647562189, 0.16136702677455494, 0.755010286604669, 1.1797587880778966, 1.3477109086165333, 1.2338590631011195, 0.8800875647748821, 0.3845000775296067, -0.12158558126986353, -0.5039977171841683, -0.656837902190263, -0.5275612493254, -0.13042588496861113, 0.45482421369403897, 1.099013807604593, 1.6510827353362525, 1.9713021752405715, 1.962973682378141, 1.5955928939837987, 0.9141633210004052, 0.03225129826726303, -0.8901214229678934, -1.6792953616312356, -2.184581558515295, -2.3107265123575162, -2.0390032854845335, -1.4320145528868193, -0.620760468111194, 0.22358761239984798, 0.9273029890095962, 1.3529450080334573, 1.430745435364195, 1.175257296153357, 0.6830497777640787, 0.11134272062796009, -0.3582491103879945, -0.5631928082817965, -0.40114959831351826, 0.1407147474721046, 0.9754048771343812, 1.9280047061121282, 2.7682642359496623, 3.2576670042192517, 3.2013337370235306, 2.493666583884066, 1.1475694424847585, -0.6997343913616033, -2.806455280997191, -4.868300364034416, -6.574711633089583, -7.667905561677676, -7.992487548997033, -7.525187052932361, -6.378324415630668, -4.776131031444422, -3.008817139980821, -1.3740530343174933, -0.11823781244188922, 0.610044485141233, 0.7846685606890865, 0.49982280208492175, -0.05791251765404603], 'positive_zeros': ['0.31915024077190792149422476443453', '2.47843457632540443297977885334077', '5.02540478444843293350695594715264', '5.84004202866023806945442058512411', '7.51646940517610594856224128443318', '8.511558204659068927563556469106634', '9.725235533062304588575160156151325', '10.42437123745390542117313791807953', '12.19234498042640476904480803585356', '13.05231796696209738124488520595579'], 'prelabel': '2-90-5.2-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.050130600080264, 'root_angle': -0.3155204779369584, 'root_number': '-0.4001470572427492 - 0.9164509439026008*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.315520477937', 'prec': 40}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.31915024077190792149422476443', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '2.47843457632540443297977885334', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.02540478444843293350695594715', 'prec': 100}}