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_5185.1934'
a10	jsonb	[1.0, -2.8163065144692913e-30]
a2	jsonb	[-0.20791169081775934, -0.9781476007338057]
a3	jsonb	[0.9510565162951535, 0.30901699437494745]
a4	jsonb	[-0.9135454576426009, 0.4067366430758002]
a5	jsonb	[1.0, -2.8163065144692913e-30]
a6	jsonb	[0.10452846326765347, -0.9945218953682733]
a7	jsonb	[-0.6691306063588582, 0.7431448254773942]
a8	jsonb	[0.5877852522924731, 0.8090169943749475]
a9	jsonb	[0.8090169943749475, 0.5877852522924731]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	557.2056350601307
analytic_normalization	numeric	0
bad_lfactors	jsonb	[[5, [1]], [17, [1]], [61, [1]]]
bad_primes	bigint[]	[5, 17, 61]
central_character	text	'5185.1934'
coeff_info	jsonb	['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}']
coefficient_field	text
conductor	numeric	5185
conductor_radical	integer	5185
conjugate	text	'dirichlet_L_5185.1874'
credit	text
degree	smallint	1
dirichlet_coefficients	jsonb	['a^0', 'a^43', 'a^3', 'a^26', 0, 'a^46', 'a^22', 'a^9', 'a^6', 0, 'a^30', 'a^29', 'a^10', 'a^5', 0,...
euler_factors	jsonb	[[1, 'a^43'], [1, 'a^3'], [0], [1, 'a^22'], [1, 'a^30'], [1, 'a^10'], [0], [1, 'a^8'], [1, 'a^6'], [...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[1], []]
group	text
index	smallint	0
label	text	'1-5185-5185.1934-r1-0-0'
leading_term	text	'0.892838035045745600993112884793-0.930364879837064716566055519850*I'
load_key	text	'dirichlet'
motivic_weight	smallint	0
mu_imag	numeric[]	[0.0]
mu_real	smallint[]	[1]
nu_imag	numeric[]	[]
nu_real_doubled	smallint[]	[]
order_of_vanishing	smallint	0
origin	text	'Character/Dirichlet/5185/1934'
plot_delta	numeric	0.3125
plot_values	jsonb	[1.289472204608763, -0.6945978723259042, -2.7922634835232873, -3.369266724118483, -2.078141504473101...
positive_zeros	jsonb	['0.21817653287077892654698878182', '1.64858337507007779369348869464', '1.98850696145858363190527061...
precision	smallint
prelabel	text	'1-5185-5185.1934-r1-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	557.2056350601307
root_angle	double precision	-0.2565508228087693
root_number	text	'-0.0411484127391183749095451894853-0.999153045398477059878160709725*I'
self_dual	boolean	False
sign_arg	numeric	-0.25
spectral_label	text	'r1-0'
st_group	text	'mu(60)'
symmetry_type	text	'unitary'
trace_hash	bigint
types	jsonb	['DIR']
values	jsonb	[[1, '1.00682985492346525928905291790-0.162509050289085407751094527427*I']]
z1	numeric	0.218176532871
z2	numeric	1.64858337507
z3	numeric	1.98850696146

{'Lhash': '2606460035322369856229639030457', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.3590064527733454, 0.7846227413391295], 'a4': [0.0, 0.0], 'a5': [38.332708496453556, -22.131399569194915], 'a6': [0.0, 0.0], 'a7': [-42.396682685360176, -24.566670455657615], 'a8': [0.0, 0.0], 'a9': [-39.268734307546936, -68.01544296959436], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 11.577435865390568, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 7}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [42.396682685360176, 24.566670455657615]]]], 'bad_primes': [2, 7], 'central_character': '112.17', 'coefficient_field': 'CDF', 'conductor': 112, 'conductor_radical': 14, 'conjugate': '1049865701106578327271310430434', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.3590064527733454, -0.7846227413391295], [40.5, 70.14805770653953]], [[1.0, 0], [-38.332708496453556, 22.131399569194915], [312.5, -541.2658773652742]], [[1.0, 0], [42.396682685360176, 24.566670455657615]], [[1.0, 0], [-11.755689138133521, 20.361450865232843], [-7320.5, -12679.477936807967]], [[1.0, 0], [0, -136.26948705686573], [-28561.0, 0]], [[1.0, 0], [227.33270849645356, 131.25060044603418], [41760.5, 72331.3077494801]], [[1.0, 0], [-387.1618755891214, 223.52801309133966], [65160.5, -112861.29664659183]], [[1.0, 0], [374.58464861330845, 648.7996431335849], [-139920.5, 242349.41502044108]], [[1.0, 0], [-406.5241334699229, 0], [707281.0, 0]], [[1.0, 0], [-584.1987977567983, -337.28733314514324], [461760.5, 799792.6469284085]], [[1.0, 0], [372.6659634403241, 645.476382930247], [-937080.5, 1623071.0367820472]], [[1.0, 0], [0, -2476.1994369065465], [-2825761.0, 0]], [[1.0, 0], [-2636.683856479053, 0], [3418801.0, 0]], [[1.0, 0], [-579.0990158927415, 334.34297271312164], [2439840.5, -4225927.708364253]], [[1.0, 0], [-1014.6110289278928, 1757.3578520228464], [-3945240.5, -6833356.9940784415]], [[1.0, 0], [-1014.2220638089884, -585.5613815581772], [6058680.5, 10493942.45282681]], [[1.0, 0], [2022.049240528654, -1167.4306733338967], [6922920.5, -11990850.042760136]], [[1.0, 0], [3779.785970989699, -6546.781343490221], [-10075560.5, -17451382.700734083]], [[1.0, 0], [7575.3618996683035, 0], [25411681.0, 0]], [[1.0, 0], [-3284.179539412665, -1896.121941146963], [14199120.5, 24593598.1287928]], [[1.0, 0], [-3897.3306871288933, -6750.374764004567], [-19475040.5, 33731759.62546159]], [[1.0, 0], [0, 2181.4121343769225], [-47458321.0, 0]], [[1.0, 0], [-8050.379267857307, 4647.888637375999], [31371120.5, -54336374.59636556]], [[1.0, 0], [0, 9981.896376932204], [-88529281.0, 0]], [[1.0, 0], [675.551780792736, 390.0300024922172], [52030200.5, 90118950.7939956]], [[1.0, 0], [2383.9036793965824, -1376.3474310217562], [56275440.5, -97471922.1643193]], [[1.0, 0], [-7429.455634597135, -12868.194631701113], [-65539800.5, 113518264.3839281]], [[1.0, 0], [1378.3273655434277, -2387.333026583777], [-70579080.5, -122246553.3774938]], [[1.0, 0], [-6264.787676059151, 0], [163047361.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 12941154, 'index': 13, 'label': '2-112-7.3-c4-0-13', '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/112/5/s/c/17/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 27}, 'plot_values': [1.9176620956604242, 2.1855642632004852, 2.3776051494428683, 2.48487055305594, 2.5003369935002175, 2.419633809884728, 2.2421562827053436, 1.9723791067844791, 1.6211481677607573, 1.2066781946058835, 0.7549628474603233, 0.2993205892054683, -0.12113832328636416, -0.4642271652635378, -0.688525608909658, -0.7581013654459996, -0.6476537916818443, -0.3474322530563989, 0.13285188139903645, 0.7619377934903923, 1.4874765071604301, 2.239521011056614, 2.937135753275373, 3.4977154636476584, 3.84805738398539, 3.9357320732473062, 3.7389527961729443, 3.2730549039215244, 2.5919406015347612, 1.783447288606991, 0.9585176084685544, 0.2351693717893547, -0.2806013890802644, -0.51392910626429, -0.436666368546998, -0.07606770656344643, 0.4859522118684143, 1.123990045036215, 1.6897951261688908, 2.039359255578994, 2.061707468017361, 1.7036860723973637, 0.9851911183767726, 0.0006657528919722833, -1.094811440328419, -2.113333803659672, -2.871107412888635, -3.2272076478212712, -3.115668118839187, -2.5631024173346013, -1.68666463477196, -0.6712885632994944, 0.2700198128930242, 0.9446405327288208, 1.2264983504575395, 1.0884839361498144, 0.6121526819600716, -0.02930980142674189, -0.6123915854922223, -0.9199248733943939, -0.7995202798091996, -0.20862777840305785, 0.7665571677914605, 1.925138494780233, 2.9969844904908656, 3.709483625527082, 3.8589490102859174, 3.367603728057803, 2.309777999575655, 0.8984420708796511, -0.5662557161286574, -1.7739640467641682, -2.4861690731608888, -2.600278372072797, -2.1767097449916912, -1.4197890022997957, -0.6164439504230653, -0.04946809968725153, 0.08939668899096766, -0.23996150419660817, -0.911487366640919, -1.6708308382053267, -2.2158914414469084, -2.296314777337368, -1.8009474492543691, -0.8044565280180466, 0.4440972022446214, 1.5901187017199716, 2.280492277472282, 2.2760167172652155, 1.533033547813205, 0.22624731454933547, -1.2973391907016236, -2.6212390381089676, -3.3876060506268284, -3.4095043957243543, -2.7298211299246162, -1.6058408081152138, -0.42288923263803657, 0.4352908194707845, 0.7160531589918666, 0.3825860138028836, -0.37651055045482107, -1.217654252191705, -1.769313251746755, -1.7712423534329829, -1.1756624949609982, -0.17221096581447654, 0.8750430038650078, 1.5583850716834498, 1.579147176943108, 0.8664940165409671, -0.38316550840530494, -1.7639459652991445, -2.7977920152186635, -3.1033973578568124, -2.535296198398153, -1.2407654294187878, 0.38865245389167014, 1.855212127810279, 2.7325333367698774, 2.81634856074197, 2.1908555361379976, 1.1843884315129292, 0.23058970804103077, -0.31131208933645976, -0.3060573591506299, 0.09915713131959777, 0.5333848079869253, 0.5575204805313065, -0.1434632247682468, -1.6089831704265807, -3.5558626282138364, -5.459898309400585, -6.738926212230595, -6.968386599480022, -6.044946451047169, -4.232035738544623, -2.0668540847180172, -0.16365899903218042, 1.0094685340563165, 1.291527310386588, 0.8630433486678838, 0.141686901937913, -0.415553479318428, -0.5186779782676973, -0.17035089576531365, 0.3442240252278936, 0.599922747026019, 0.24506952533952786, -0.8092299664918879, -2.311011521959875, -3.7416338605650545, -4.5172589405911205, -4.235212902376303, -2.8594136727885155, -0.7612496974421342, 1.4080270066400145, 2.9650957164583542, 3.460804009533439, 2.8525490468943056, 1.5087635509549746, 0.042991196483819716, -0.9509672937085304, -1.1476577171701607, -0.6138576960166647, 0.24558901607702063, 0.8936164613735156, 0.9233673625050633, 0.25581880858206957, -0.8198372190446452, -1.7834721956074466, -2.136588307815809, -1.6523874870735116, -0.5039469791846213, 0.7945699009187588, 1.6124059641919946, 1.49238521301378, 0.3727492808968872, -1.3653670847773514, -3.052269984295632, -4.01973931039659, -3.895780050888915, -2.7682549520165787, -1.1404695236506421, 0.3019550606869485, 1.0048068516144126, 0.7925730839618134, -0.06724645159163423, -1.0127214016339485, -1.4767179821535568, -1.17582379201334, -0.2567315146171158, 0.774070283911901, 1.3057802885907694, 0.9401003037911008, -0.2877852800826749, -1.8977545532187587, -3.175750232054907, -3.5104154322736254, -2.693746936266441, -1.0374432815270493, 0.7566732025694777, 1.9148190362114015, 1.9475423609174787, 0.8730059283161451, -0.8005832283109284, -2.324014858914161, -3.0645919229288663, -2.795877499201509, -1.7779238074306842, -0.5920715818259219, 0.18118561693839785, 0.27285672083293955, -0.1378219888315644, -0.5330767667452805, -0.3563532940452885, 0.6557975816009193, 2.2885594838591854, 3.9167205341828932, 4.801372842677691, 4.469391011984424, 2.980337097178101, 0.9365134304270828, -0.7803720987798757, -1.4223188013824677, -0.7341556850157189, 0.9223020677235473, 2.74388298723228, 3.875126313939571, 3.8159297635214258, 2.643830819967741, 0.9429887428542837, -0.5162074726571138, -1.1744525652221058, -0.9478398413827441, -0.2230570659257038, 0.4063735257781142, 0.5118507588396787, 0.09916276762575335, -0.3793648154218621, -0.2836775553487755, 0.8224005681600701, 2.8641769432500204, 5.212654579654545, 6.9453788443021045, 7.287229592841439, 6.004227821330199, 3.5407669616163027, 0.8214722304785023, -1.1852105067776635, -1.917867053479343, -1.45530223304566, -0.4160841586950716, 0.4127785659419831, 0.5106778970868725, -0.11674855079278788], 'positive_zeros': ['2.05613442288679508967014770300273', '3.12104594664633140801520099635436', '5.51916616734500772110138704190146', '6.17938491817661141425647596802151', '7.55870314721141627525028584818199', '9.086389614799628272286931510870673', '10.01163245977653558842473032437347', '10.76557133943018932524791102047765', '12.23502338810913389658151238568835', '13.56064283095955711336842793683602'], 'prelabel': '2-112-7.3-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.4025631317273994, 'root_angle': 0.23007721055090913, 'root_number': '0.12485191601635352 + 0.9921753872511883*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.230077210551', 'prec': 40}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.05613442288679508967014770300', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.12104594664633140801520099635', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.51916616734500772110138704190', 'prec': 100}}