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_4929.2009'
a10	jsonb	[0.9485364419471455, 0.3166679938014725]
a2	jsonb	[0.8229838658936564, -0.5680647467311558]
a3	jsonb	[1.0, -2.8163065144692913e-30]
a4	jsonb	[0.3546048870425356, -0.9350162426854148]
a5	jsonb	[0.6007422642379789, 0.7994427634035012]
a6	jsonb	[1.0, -2.8163065144692913e-30]
a7	jsonb	[0.99675730813421, -0.08046656871672588]
a8	jsonb	[-0.23931566428755777, -0.970941817426052]
a9	jsonb	[1.0, -2.8163065144692913e-30]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	22.89017976766968
analytic_normalization	numeric	0
bad_lfactors	jsonb	[[3, [1]], [31, [1]], [53, [1]]]
bad_primes	bigint[]	[3, 31, 53]
central_character	text	'4929.2009'
coeff_info	jsonb	['x^156 - 1', '0.999188998171570 + 0.0402659401094151*I', '\\\\zeta_{156}']
coefficient_field	text
conductor	numeric	4929
conductor_radical	integer	4929
conjugate	text	'dirichlet_L_4929.1028'
credit	text
degree	smallint	1
dirichlet_coefficients	jsonb	['a^0', 'a^141', 0, 'a^126', 'a^23', 0, 'a^154', 'a^111', 0, 'a^8', 'a^92', 0, 'a^56', 'a^139', 0, '...
euler_factors	jsonb	[[1, 'a^141'], [0], [1, 'a^23'], [1, 'a^154'], [1, 'a^92'], [1, 'a^56'], [1, 'a^136'], [1, 'a^43'], ...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[0], []]
group	text
index	smallint	0
label	text	'1-4929-4929.2009-r0-0-0'
leading_term	text	'3.12381887653947268498873965652+0.650400699657357532849795415210*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/4929/2009'
plot_delta	numeric	0.3125
plot_values	jsonb	[3.1908095279316053, 4.035911284621309, 3.8680928042745575, 2.046515255744947, -0.0804663566729825, ...
positive_zeros	jsonb	['1.234420978521579517868946787873', '1.78260476752435185501696020094', '2.7190908051976356631361049...
precision	smallint
prelabel	text	'1-4929-4929.2009-r0-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	22.89017976766968
root_angle	double precision	0.0653408164783902
root_number	text	'0.916902064392550856277872134670+0.399112270310846899115606487032*I'
self_dual	boolean	False
sign_arg	numeric	0.0
spectral_label	text	'r0-0'
st_group	text	'mu(156)'
symmetry_type	text	'unitary'
trace_hash	bigint
types	jsonb	['DIR']
values	jsonb	[[1, '1.84926901173825777071201760849-0.246970944214859309349512070874*I']]
z1	numeric	1.23442097852
z2	numeric	1.78260476752
z3	numeric	2.7190908052

{'Lhash': '351285829006203298773618199873', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, -3.414213562373095], 'a6': [0, 0], 'a7': [0.585786437626905, 0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.795065251406015, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '4608.2305', 'coefficient_field': 'CDF', 'conductor': 4608, 'conductor_radical': 6, 'conjugate': '1761141680208303669911838442965', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.414213562373095], [-5.0, 0]], [[1.0, 0], [-0.585786437626905, 0], [7.0, 0]], [[1.0, 0], [0, -2.0], [-11.0, 0]], [[1.0, 0], [0, -2.8284271247461903], [-13.0, 0]], [[1.0, 0], [-7.656854249492381, 0], [17.0, 0]], [[1.0, 0], [0, -5.656854249492381], [-19.0, 0]], [[1.0, 0], [6.82842712474619, 0], [23.0, 0]], [[1.0, 0], [0, -3.414213562373095], [-29.0, 0]], [[1.0, 0], [7.414213562373095, 0], [31.0, 0]], [[1.0, 0], [0, -1.6568542494923801], [-37.0, 0]], [[1.0, 0], [0.3431457505076198, 0], [41.0, 0]], [[1.0, 0], [0, -9.65685424949238], [-43.0, 0]], [[1.0, 0], [4.48528137423857, 0], [47.0, 0]], [[1.0, 0], [0, -7.899494936611665], [-53.0, 0]], [[1.0, 0], [0, 4.0], [-59.0, 0]], [[1.0, 0], [0, 1.6568542494923801], [-61.0, 0]], [[1.0, 0], [0, 8.0], [-67.0, 0]], [[1.0, 0], [14.82842712474619, 0], [71.0, 0]], [[1.0, 0], [9.65685424949238, 0], [73.0, 0]], [[1.0, 0], [14.242640687119286, 0], [79.0, 0]], [[1.0, 0], [0, -13.313708498984761], [-83.0, 0]], [[1.0, 0], [-2.0, 0], [89.0, 0]], [[1.0, 0], [9.313708498984761, 0], [97.0, 0]], [[1.0, 0], [0, 13.556349186104045], [-101.0, 0]], [[1.0, 0], [5.0710678118654755, 0], [103.0, 0]], [[1.0, 0], [0, -7.31370849898476], [-107.0, 0]], [[1.0, 0], [0, -18.82842712474619], [-109.0, 0]], [[1.0, 0], [6.0, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23331308, 'index': 10, 'label': '2-4608-8.5-c1-0-10', 'leading_term': '1.040261811511417215003269396098613004991546333294203151', '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/4608/2/d/o/2305/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 17}, 'plot_values': [1.0402618115114173, 0.8856044563281336, 0.7217423700507097, 0.5490443427485099, 0.36791528081478564, 0.17883483128230934, -0.017603751595059745, -0.2206567374889401, -0.42939710171458806, -0.6426875253996562, -0.8591606389060332, -1.0772075689427578, -1.2949754929926636, -1.5103745739991492, -1.7210943523626945, -1.9246294118984495, -2.118313907103591, -2.2993643341267154, -2.464929740379605, -2.6121483923809112, -2.738209755029281, -2.840420477436887, -2.9162729324359575, -2.96351472258574, -2.980217450092761, -2.9648429575613706, -2.9163051873494883, -2.834025785857982, -2.717981601152259, -2.5687422928290635, -2.3874963957150883, -2.176064356051735, -1.9368972908209348, -1.67306050648017, -1.3882011493138229, -1.086499740570756, -0.7726057682421396, -0.45155795451670744, -0.1286902826404489, 0.1904746634391588, 0.5003430324545406, 0.7953752607858625, 1.0702169991024604, 1.3198322163175635, 1.539635010858186, 1.7256164662111446, 1.8744627895144166, 1.9836609788056154, 2.051588384028619, 2.077582763614948, 2.0619897935512026, 2.0061854567345714, 1.9125713205798758, 1.7845413897189102, 1.6264199836854185, 1.4433709183653645, 1.2412791428998275, 1.0266068758493685, 0.8062271685773178, 0.5872386711645586, 0.376766157133826, 0.1817520484152786, 0.008744743092875503, -0.13631004046657497, -0.24826845120308827, -0.3229717256779863, -0.35740709945091304, -0.3498404368228847, -0.2999151873855856, -0.2087130645297878, -0.07877281938743655, 0.08593536772088473, 0.28008106582063697, 0.49709013199414115, 0.7293049370550129, 0.9681851208737929, 1.204544264041254, 1.428816485305588, 1.6313457265552727, 1.802689418269358, 1.9339273740993637, 2.0169661840767423, 2.0448290953147232, 2.011921411810208, 1.9142618258413862, 1.7496708161650547, 1.5179083045266406, 1.220754131441724, 0.8620265621473924, 0.4475359197547673, -0.015027490013016656, -0.5162698137505347, -1.0453308664341863, -1.5901763515980356, -2.1379372207068092, -2.6752864086047508, -3.188841549337681, -3.6655809795090692, -4.093259435438407, -4.4608093948109016, -4.758714038175256, -4.979338329368967, -5.117205737933156, -5.169209633546012, -5.1347503364872935, -5.015791154980877, -4.8168294088087205, -4.544781342671975, -4.208782873796236, -3.819911188441595, -3.3908351880227614, -2.9354055728655872, -2.4681978286440667, -2.0040234431506647, -1.5574262369806728, -1.1421816646091998, -0.7708172754249298, -0.4541721833709119, -0.20101236960222213, -0.01771695190750261, 0.09195175892586926, 0.1269844626313285, 0.08916070647502775, -0.017018599168867145, -0.18450105819455126, -0.40395018098064517, -0.6641015508725757, -0.9521954041893049, -1.2544700358085434, -1.5566977480909163, -1.8447430226577992, -2.1051213130385507, -2.3255364047837483, -2.495374710281757, -2.606136166001458, -2.6517835522746336, -2.6289949962639696, -2.537308049244124, -2.3791479200203174, -2.1597370402689964, -1.886887956264904, -1.570686391471197, -1.2230760052055396, -0.8573606844318432, -0.4876439584875681, -0.1282281478728544, 0.20700199855631915, 0.5051852723982156, 0.7550535907909335, 0.9474402229961032, 1.0757037837689534, 1.1360482432046823, 1.1277232450277397, 1.0530938364490068, 0.9175741063372423, 0.7294249876025942, 0.499422365401199, 0.24040739375837003, -0.033263693532828854, -0.306348230067212, -0.5633982574596322, -0.7894653156505516, -0.9707983502186194, -1.095503810182314, -1.1541379614954053, -1.1402037313716613, -1.0505279600379485, -0.8854996447550456, -0.6491554369893551, -0.3491050706947181, 0.0037037080350257926, 0.3953740662077308, 0.8095892755927042, 1.2282620785908662, 1.632278374037502, 2.002304623392489, 2.31962488580274, 2.566971337932285, 2.729311647112314, 2.7945577025740764, 2.754162955583044, 2.6035798881861, 2.342554763758391, 1.9752435864738784, 1.5101408298163563, 0.9598206590581061, 0.34049871008805693, -0.3285693782858643, -1.025828924012439, -1.728276275309783, -2.4123822515553637, -3.0550493626552058, -3.634561107390882, -4.13148140264737, -4.5294638553655, -4.81593411630193, -4.982613820126019, -5.025861407155261, -4.9468131495883805, -4.751316617161189, -4.449658212955995, -4.056095858304827, -3.5882169642529638, -3.066150063858016, -2.5116654935260887, -1.9472059521588632, -1.3948913521743251, -0.8755439080401612, -0.4077787821623383, -0.0072028228489730345, 0.3142409134627554, 0.5487518605255561, 0.6929511212661774, 0.7479478243727459, 0.7191895330637837, 0.6161040147889262, 0.4515498662826578, 0.24110292417703108, 0.0022136042723326526, -0.246723118186908, -0.4873387959815785, -0.7022550393875805, -0.8759909188353358, -0.9957681509524156, -1.0521727897436615, -1.0396390813040435, -0.9567298848661014, -0.8061982018244449, -0.5948253972431466, -0.3330431009674325, -0.034356966125375026, 0.2853991292501591, 0.6089407674434897, 0.9184976154849608, 1.196814969815125, 1.4281396312717174, 1.5991376216160453, 1.6996940641275493, 1.7235509723252742, 1.668746487045609, 1.5378289112015362, 1.3378302418664152, 1.079996231316409, 0.779282702060968, 0.4536402455166082, 0.12312090275070911, -0.19114965184696167, -0.4680830686047014, -0.6877657636913556, -0.8325637327955259, -0.8881362043119381, -0.8443032297176305, -0.6957188584061172, -0.442310723991309, -0.08945824814285014, 0.3521053068284184, 0.8666676830917628], 'positive_zeros': ['0.27711565706114710016875860091610', '1.80003910916172094604559066926886', '2.90882498536768087829469425631300', '3.30481885441278746030408684627421', '4.21729156958271808481788530140027', '5.58396203307732431183139088583525', '5.75968445501680270211203448854647', '6.81431002346493054622580990996765', '7.40059968273424425885742643519087', '7.968286522095441317591790827302247'], 'prelabel': '2-4608-8.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': -0.25, 'root_number': '0.e-55 - 1.0000000000000000000000000000000000000000000000000000000*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 7}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.27711565706114710016875860092', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.80003910916172094604559066927', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.90882498536768087829469425631', 'prec': 100}}