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_2951.2865'
a10	jsonb	[-0.9938228915787078, -0.11097774630139133]
a2	jsonb	[0.8706217673675811, -0.49195298371465285]
a3	jsonb	[-0.09715248369288586, -0.9952695086820974]
a4	jsonb	[0.515964523628501, -0.8566099522868118]
a5	jsonb	[-0.8106480088977173, -0.5855337784194576]
a6	jsonb	[-0.5742088714532249, -0.8187088444278674]
a7	jsonb	[0.618820997561454, 0.7855320317956785]
a8	jsonb	[0.02779812355325404, -0.999613557494554]
a9	jsonb	[-0.9811227898246071, 0.19338580942452796]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	317.1289930689384
analytic_normalization	numeric	0
bad_lfactors	jsonb	[[13, [1]], [227, [1]]]
bad_primes	bigint[]	[13, 227]
central_character	text	'2951.2865'
coeff_info	jsonb	['x^452 - 1', '0.999903384706381 + 0.0139004047683151*I', '\\\\zeta_{452}']
coefficient_field	text
conductor	numeric	2951
conductor_radical	integer	2951
conjugate	text	'dirichlet_L_2951.1750'
credit	text
degree	smallint	1
dirichlet_coefficients	jsonb	['a^0', 'a^415', 'a^332', 'a^378', 'a^271', 'a^295', 'a^65', 'a^341', 'a^212', 'a^234', 'a^433', 'a^...
euler_factors	jsonb	[[1, 'a^415'], [1, 'a^332'], [1, 'a^271'], [1, 'a^65'], [1, 'a^433'], [0], [1, 'a^66'], [1, 'a^307']...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[1], []]
group	text
index	smallint	0
label	text	'1-2951-2951.2865-r1-0-0'
leading_term	text	'2.32751375010050831939437135932-3.12950420774577033065830433218*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/2951/2865'
plot_delta	numeric	0.3125
plot_values	jsonb	[3.9001431823979766, 2.454677913099633, 0.42197637018331824, -0.7058811959168776, -0.357373445236999...
positive_zeros	jsonb	['0.705183278355450138794345734772', '1.3619268066660468116850585283', '2.10486995682076323203950486...
precision	smallint
prelabel	text	'1-2951-2951.2865-r1-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	317.1289930689384
root_angle	double precision	-0.29644790132789023
root_number	text	'-0.287715647345543801893892852310-0.957715879722443922380236448646*I'
self_dual	boolean	False
sign_arg	numeric	-0.25
spectral_label	text	'r1-0'
st_group	text	'mu(452)'
symmetry_type	text	'unitary'
trace_hash	bigint
types	jsonb	['DIR']
values	jsonb	[[1, '1.33633716230783288154052438492-1.05305270658697953511463013467*I']]
z1	numeric	0.705183278355
z2	numeric	1.36192680667
z3	numeric	2.10486995682

{'Lhash': '1631813171547818497318350033482', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -4.242640687119285], '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': '4608.2303', 'coefficient_field': 'CDF', 'conductor': 4608, 'conductor_radical': 6, 'conjugate': '259268708829447834713772408441', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [5.0, 0]], [[1.0, 0], [0, 4.242640687119285], [-7.0, 0]], [[1.0, 0], [0, -4.0], [-11.0, 0]], [[1.0, 0], [0, -6.0], [-13.0, 0]], [[1.0, 0], [0, 4.242640687119285], [-17.0, 0]], [[1.0, 0], [2.8284271247461903, 0], [19.0, 0]], [[1.0, 0], [-6.0, 0], [23.0, 0]], [[1.0, 0], [8.48528137423857, 0], [29.0, 0]], [[1.0, 0], [0, 4.242640687119285], [-31.0, 0]], [[1.0, 0], [0, 6.0], [-37.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-41.0, 0]], [[1.0, 0], [-2.8284271247461903, 0], [43.0, 0]], [[1.0, 0], [-6.0, 0], [47.0, 0]], [[1.0, 0], [-8.48528137423857, 0], [53.0, 0]], [[1.0, 0], [0, 4.0], [-59.0, 0]], [[1.0, 0], [0, 6.0], [-61.0, 0]], [[1.0, 0], [11.313708498984761, 0], [67.0, 0]], [[1.0, 0], [6.0, 0], [71.0, 0]], [[1.0, 0], [6.0, 0], [73.0, 0]], [[1.0, 0], [0, 4.242640687119285], [-79.0, 0]], [[1.0, 0], [0, 16.0], [-83.0, 0]], [[1.0, 0], [0, 12.727922061357855], [-89.0, 0]], [[1.0, 0], [12.0, 0], [97.0, 0]], [[1.0, 0], [8.48528137423857, 0], [101.0, 0]], [[1.0, 0], [0, -12.727922061357855], [-103.0, 0]], [[1.0, 0], [0, -16.0], [-107.0, 0]], [[1.0, 0], [0, 6.0], [-109.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 23372550, 'index': 51, 'label': '2-4608-24.11-c1-0-51', 'leading_term': '0.748538031269881433248053967225850512409088062247751745', '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/f/k/2303/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [0.7485380312698814, 0.9241234934411178, 1.093719695624254, 1.2562722448360197, 1.4105972598549914, 1.5553540180210508, 1.6890315776426266, 1.8099505863766137, 1.9162805282511635, 2.0060717976306033, 2.077301272321122, 2.1279295107502816, 2.155967312148249, 2.1595491287431523, 2.137010673337749, 2.086967994450105, 2.008395271920399, 1.900698605173521, 1.7637831195987586, 1.59811080603988, 1.4047466408675933, 1.185390718205781, 0.9423943701890105, 0.678758562525382, 0.39811323515483554, 0.10467671185221418, -0.19680517537457912, -0.5011400190773446, -0.8027889679031012, -1.0959845354746298, -1.3748638889583626, -1.6336147521844875, -1.8666304237713696, -2.068669835007346, -2.235018081343851, -2.3616424807625767, -2.44533896585136, -2.4838635252615267, -2.4760434915860996, -2.421863738982432, -2.322523311645744, -2.1804586535063595, -1.999330443062729, -1.7839720403019879, -1.5402987027664874, -1.2751779951030588, -0.9962631640390176, -0.7117926357147047, -0.43036016676733063, -0.16066149311611294, 0.08877548210774312, 0.30986889057967065, 0.49526060909182956, 0.6385840506656931, 0.7347123676071653, 0.7799774915137552, 0.7723508844588975, 0.7115776879419716, 0.5992571259462738, 0.43886352547598034, 0.23570412750486977, -0.0031880756914549357, -0.26922598677161635, -0.5525016722390699, -0.8420759894524006, -1.1263169615138848, -1.3932770967912549, -1.6310979041236506, -1.8284282473084499, -1.9748419964301018, -2.0612397404332485, -2.0802191810752433, -2.0263992702522686, -1.8966841963641823, -1.6904549629626642, -1.4096785017526108, -1.0589269644772934, -0.6453029626233382, -0.17826996642355772, 0.3306092875713482, 0.8680198359385748, 1.4193168258890394, 1.9690096402093327, 2.5012913305745115, 3.0005944468063266, 3.452152578148755, 3.842545918360857, 4.160209007599615, 4.395879536838444, 4.542968735274263, 4.597836369936968, 4.5599567026077725, 4.431965767081941, 4.219584909135018, 3.9314205004496845, 3.578644899248034, 3.1745688697796592, 2.7341205664644077, 2.2732506132598176, 1.8082865521924847, 1.3552628051170916, 0.9292541281512995, 0.5437412165044073, 0.2100365627407012, -0.06320313974295483, -0.2703547920138157, -0.40907779903288166, -0.4804201712932508, -0.48877385533287776, -0.4416778442834022, -0.34947441469715207, -0.22483061211834585, -0.08214355457583397, 0.06314606745832592, 0.19530303452679607, 0.2990762298275455, 0.36047160847550785, 0.36748351428837595, 0.31074925914532353, 0.18409444456642557, -0.015059333873681196, -0.2854471424450616, -0.6218896125888408, -1.0154061654397846, -1.4535121991817443, -1.9206912103649372, -2.3990243169337773, -2.868951726328036, -3.31013374504775, -3.702373321524436, -4.026558164498532, -4.265578427024434, -4.405175950028873, -4.434683182116616, -4.347614095315008, -4.142075557380561, -3.8209754576774917, -3.392013081353445, -2.8674473732833756, -2.263649356486308, -1.6004555582995907, -0.9003493261835986, -0.1875058701143004, 0.5132557252190036, 1.177564829519786, 1.7825840884968454, 2.308034234251878, 2.737108329352048, 3.057229410798263, 3.260612431094415, 3.3446004435224475, 3.311755739931335, 3.169698614906955, 2.930699017048446, 2.6110389250666097, 2.2301752057050175, 1.8097433409146837, 1.3724511723854254, 0.9409182037884386, 0.5365196371580366, 0.1782949465788815, -0.1180216915246652, -0.34079732633794096, -0.48307909474093913, -0.5429234023343487, -0.5234555460695759, -0.43265393309799527, -0.28286765656775736, -0.09009060075632863, 0.12697131202913356, 0.34799139584224686, 0.5522143203150935, 0.7196850003133083, 0.8324471357416933, 0.8756448253055047, 0.838464860009463, 0.714864972227954, 0.5040441298269761, 0.21062439679139155, -0.15547074967306732, -0.5794402551891229, -1.042313340855129, -1.5219071644540116, -1.993985589912426, -2.4335582893668364, -2.8162504663078294, -3.119668255794112, -3.3246836985050807, -3.416566249597549, -3.385894987556464, -3.2291967145135354, -2.949269447550472, -2.5551676528563507, -2.0618440737306245, -1.4894621388192424, -0.8624116399917553, -0.20807757263691826, 0.444573270063433, 1.0665120467979388, 1.6301908463448453, 2.1110231524565735, 2.488718250802902, 2.748393019513041, 2.8813960089135264, 2.8857940828616337, 2.76649035170795, 2.534962668619788, 2.2086334394023925, 1.8099026868799584, 1.3648959830804854, 0.9019958493653709, 0.45023849409434313, 0.03766647499034874, -0.3102685444821534, -0.5721606218237429, -0.731876876838545, -0.779484602281648, -0.7118221457569807, -0.5326778185696018, -0.252563705848482, 0.11190506641582233, 0.5389916958449135, 1.0031241503869064, 1.4764125427957173, 1.930308861030681, 2.337311177151238, 2.672610896009872, 2.9155840854917106, 3.0510363902078965, 3.0701250460108693, 2.970900315612271, 2.75843118492691, 2.444505080932371, 2.046917212314674, 1.5883903310522687, 1.0951887172512282, 0.5955095609004609, 0.11774941217413162, -0.31124796466570376, -0.6678537871843564, -0.9331224235513884, -1.0939724279729184, -1.1440042229166354, -1.0839000482231569, -0.9213773053792789, -0.6706940670739253, -0.3517336051573855, 0.011278433305961988, 0.39134679641367165, 0.760472697806482, 1.091503109241452, 1.3599465064334328, 1.545638870541705, 1.634151654858764, 1.6178482816245872, 1.496516705005832, 1.277531430851576], 'positive_zeros': ['1.28727361565878232570871578635504', '2.52040323275803433634820376721619', '3.09701847766210319159419498885087', '3.97914144838994492148450285394084', '5.26837242631657484972213797180175', '5.71596944623108960803519351746809', '6.09046779922760816926680662828374', '7.22436649793845378276666263704444', '8.154112272917906908379276555982958', '8.552750276126042311274883243215286'], 'prelabel': '2-4608-24.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.065893606996912, 'root_angle': 0.4020433619923482, 'root_number': '-0.8164965809277260327324280249019637973219824935522233761 + 0.5773502691896257645091487805019574556476017512701268760*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.4020433619923482', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28727361565878232570871578636', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.52040323275803433634820376722', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.09701847766210319159419498885', 'prec': 100}}