Database - lfunc_lfunctions

Formats: - HTML - YAML - JSON - 2026-10-24T15:52:19.120357

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	'1784260303252347197728286458245'
a10	jsonb	[-1.3499038917513178, 0.0]
a2	jsonb	[-0.7908402801345485, 0.0]
a3	jsonb	[3.4452631302903614, 0.0]
a4	jsonb	[-1.3745716513167088, 0.0]
a5	jsonb	[1.7069235415293385, 0.0]
a6	jsonb	[-2.724652859096061, 0.0]
a7	jsonb	[0.45501960688608506, 0.0]
a8	jsonb	[2.668747190061412, 0.0]
a9	jsonb	[8.86983803693814, 0.0]
accuracy	smallint	100
algebraic	boolean	True
analytic_conductor	double precision	11.490472850862252
analytic_normalization	numeric	0.5
bad_lfactors	jsonb	[[1439, [[1.0, 0], [-1.0, 0]]]]
bad_primes	bigint[]	[1439]
central_character	text	'1439.1'
coeff_info	jsonb
coefficient_field	text	'CDF'
conductor	numeric	1439
conductor_radical	integer	1439
conjugate	text
credit	text
degree	smallint	2
dirichlet_coefficients	jsonb
euler_factors	jsonb	[[[1.0, 0], [0.7908402801345485, 0], [2.0, 0]], [[1.0, 0], [-3.4452631302903614, 0], [3.0, 0]], [[1....
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[], [0]]
group	text	'GL2'
index	smallint	70
label	text	'2-1439-1.1-c1-0-70'
leading_term	text	'2.71872519844307003136298359709'
load_key	text	'CMFs-workshop'
motivic_weight	smallint	1
mu_imag	numeric[]	[]
mu_real	smallint[]	[]
nu_imag	numeric[]	[0.0]
nu_real_doubled	smallint[]	[1]
order_of_vanishing	smallint	0
origin	text	'ModularForm/GL2/Q/holomorphic/1439/2/a/c/1/31'
plot_delta	numeric	0.05859375
plot_values	jsonb	[2.71872519844307, 2.7157742584220084, 2.7067781721716306, 2.69131693463309, 2.668722386716657, 2.63...
positive_zeros	jsonb	['1.40753319797356364472042955895613', '2.19695332759210733660072345860795', '3.39255115560497475886...
precision	smallint
prelabel	text	'2-1439-1.1-c1-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	3.3897599990061615
root_angle	double precision	0.0
root_number	text	'1'
self_dual	boolean	True
sign_arg	numeric	0
spectral_label	text	'c1-0'
st_group	text
symmetry_type	text
trace_hash	bigint
types	jsonb	['CMF']
values	jsonb
z1	numeric	1.40753319797356364472042955896
z2	numeric	2.19695332759210733660072345861
z3	numeric	3.39255115560497475886848833651

{'Lhash': '1004196061872366504977124066921', 'a10': [0.0, 0.0], 'a2': [-1.0, -1.0], 'a3': [-1.224744871391589, 1.224744871391589], 'a4': [0.0, 2.0], 'a5': [0.0, 0.0], 'a6': [2.449489742783178, 0.0], 'a7': [3.449489742783178, 3.449489742783178], 'a8': [2.0, -2.0], 'a9': [0.0, -3.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.791024121276825, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 1.0]]], [3, [[1.0, 0], [1.224744871391589, -1.224744871391589]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '600.557', 'coefficient_field': 'CDF', 'conductor': 600, 'conductor_radical': 30, 'conjugate': '1827322747499292193697084031998', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 1.0]], [[1.0, 0], [1.224744871391589, -1.224744871391589]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.449489742783178, -3.449489742783178], [0, 7.0]], [[1.0, 0], [-1.550510257216822, 0], [11.0, 0]], [[1.0, 0], [0, 0], [0, 13.0]], [[1.0, 0], [0, 0], [0, -17.0]], [[1.0, 0], [0, 0], [19.0, 0]], [[1.0, 0], [0, 0], [0, 23.0]], [[1.0, 0], [0, -5.3484692283495345], [-29.0, 0]], [[1.0, 0], [-4.898979485566356, 0], [31.0, 0]], [[1.0, 0], [0, 0], [0, -37.0]], [[1.0, 0], [0, 0], [-41.0, 0]], [[1.0, 0], [0, 0], [0, 43.0]], [[1.0, 0], [0, 0], [0, -47.0]], [[1.0, 0], [2.449489742783178, -2.449489742783178], [0, -53.0]], [[1.0, 0], [0, -15.348469228349535], [-59.0, 0]], [[1.0, 0], [0, 0], [-61.0, 0]], [[1.0, 0], [0, 0], [0, -67.0]], [[1.0, 0], [0, 0], [-71.0, 0]], [[1.0, 0], [11.898979485566356, -11.898979485566356], [0, -73.0]], [[1.0, 0], [0, 14.696938456699069], [-79.0, 0]], [[1.0, 0], [-4.0, 4.0], [0, -83.0]], [[1.0, 0], [0, 0], [89.0, 0]], [[1.0, 0], [8.797958971132712, 8.797958971132712], [0, 97.0]], [[1.0, 0], [-11.550510257216821, 0], [101.0, 0]], [[1.0, 0], [-0.3484692283495343, 0.3484692283495343], [0, -103.0]], [[1.0, 0], [-8.0, -8.0], [0, 107.0]], [[1.0, 0], [0, 0], [109.0, 0]], [[1.0, 0], [0, 0], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 11693684, 'index': 11, 'label': '2-600-120.77-c1-0-11', '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/600/2/w/b/557/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [0.8981781376043902, 0.8009261060435071, 0.6900494302671732, 0.5625955340325435, 0.415939698208173, 0.2493067908538984, 0.06509451297970346, -0.13013203198218878, -0.32503976324916783, -0.5033718735563485, -0.6442953050982914, -0.7233104821309614, -0.7137608225428689, -0.5889327802528475, -0.32466914220537524, 0.09766299657668429, 0.6880921256339886, 1.4451667920232274, 2.3536523171246224, 3.3831821942055407, 4.488214523424276, 5.609558573838989, 6.677598071468701, 7.617153827465165, 8.353714934588053, 8.820548840764614, 8.96600582671309, 8.760194903035945, 8.20015602668678, 7.312710840995247, 6.154351786891874, 4.807822184949689, 3.3754241616227443, 1.9695255280923363, 0.7011648021837061, -0.33198871170771205, -1.056838823025067, -1.4337110369285957, -1.461504345638162, -1.1781992661862764, -0.6563523051538973, 0.006101250110106803, 0.6987035877233606, 1.3133381216869087, 1.7590313410480338, 1.9744954318350538, 1.936426676483739, 1.6621254259286466, 1.2058325576626954, 0.6491698588847299, 0.08707198996704868, -0.38856764254286397, -0.7048069216330618, -0.8203281710985908, -0.7325131763333833, -0.4774472406048937, -0.12259894580972015, 0.24672693230350343, 0.5448272850972279, 0.7037114841272923, 0.6883410271788147, 0.5057920138387926, 0.2061257691577419, -0.1257437042705841, -0.3861372045196512, -0.47391911987045515, -0.3130280898023256, 0.12832465421748987, 0.8260143872188701, 1.698924622390377, 2.61950184195106, 3.4347034973775443, 3.9938618669901422, 4.178292847618727, 3.9267279344503043, 3.2510736389615076, 2.2386104400713993, 1.0392873864904182, -0.16021721425031465, -1.1711190016279958, -1.83916516900131, -2.07576928411427, -1.8768270592942609, -1.3246081633111153, -0.5714701593274755, 0.1920174698703725, 0.7784240119723229, 1.0457510361183282, 0.9314388953560021, 0.47014736335469665, -0.20950273344527062, -0.9096550234306602, -1.4050918884137824, -1.493871346051756, -1.045907273598447, -0.03852401706686669, 1.4296785019046072, 3.1509301695745418, 4.845061576220157, 6.214049275325176, 7.003131195665887, 7.055300670929097, 6.3468996574618055, 4.995776111331313, 3.2393185513317633, 1.3863770979719043, -0.2468897716992927, -1.403268702312919, -1.938031145933372, -1.8475116845619943, -1.2659669834209122, -0.4311717743910008, 0.373508259685952, 0.8872063095638031, 0.933879658978286, 0.46412639015381846, -0.4335104808295436, -1.5545280308414238, -2.6285088917248673, -3.385162451556449, -3.620336640622084, -3.2459199955932756, -2.311477919967946, -0.9924435271470246, 0.45200674443223315, 1.7407100335595926, 2.6363613407288375, 2.998998083950756, 2.813997831067057, 2.1881659468812793, 1.3158373263333931, 0.4247086902575947, -0.2837233405105046, -0.6831137187723807, -0.7478253455003995, -0.5490098578904707, -0.22348241748018102, 0.07466706435968856, 0.22495885847340957, 0.17856402038343192, -0.02794126265757422, -0.28723943016375575, -0.4598377194885191, -0.4245578118594611, -0.1249439673046295, 0.40368731414477343, 1.0363928742866007, 1.591073430292707, 1.8829092959328004, 1.7849666637973127, 1.276165100094781, 0.46036946847331756, -0.4519129865442329, -1.196896508377496, -1.5326869519087956, -1.3152917157384498, -0.5525256699995769, 0.582393106260785, 1.7852585399474163, 2.6974419071234874, 3.00591206741567, 2.53971511800097, 1.3348677891857677, -0.3534141117387696, -2.0987624788131614, -3.403102717780511, -3.8236625391545096, -3.094618129475819, -1.2101096400622287, 1.555726901576644, 4.699999654815339, 7.602877599594786, 9.672603634685615, 10.48668119638544, 9.892498686657483, 8.041020194857312, 5.3449001995850765, 2.3726145550612068, -0.29271116058256713, -2.191975431069625, -3.0899103311727587, -3.0112122625879576, -2.206489269593241, -1.0612669908107093, 0.023247024030969413, 0.7422076678003539, 0.9603645894152691, 0.7278792230190997, 0.23825134457737068, -0.25448171832294164, -0.5303506685563297, -0.47857896631553354, -0.12953188944651833, 0.36523236115659397, 0.7960677723145904, 0.9784635168180403, 0.8268405561049443, 0.3927612458429258, -0.14645244197767238, -0.545762442427457, -0.5780753251073741, -0.11856471900187743, 0.8016067569236687, 1.9918657866229492, 3.1523861035154237, 3.9631765283025637, 4.183974051385611, 3.73239537926615, 2.714117599932405, 1.3940532769970069, 0.11669070227049083, -0.7993308195976474, -1.158437247210629, -0.9453878228253091, -0.32370461832141256, 0.42425831766697136, 0.9956229058338815, 1.1706171145856192, 0.8863780365113262, 0.2555898275868171, -0.47676134324804875, -1.0239751017892158, -1.164356675393228, -0.826614493790506, -0.12308023127762231, 0.682600060698322, 1.263999965890361, 1.3472695720589967, 0.8134368644549956, -0.24911469515822332, -1.5626778744023382, -2.7455283885080064, -3.437556993384246, -3.424033448796609, -2.7141744889408352, -1.5451206791625938, -0.30669445131072426, 0.5902433698017013, 0.8583107850050993, 0.44095485524638933, -0.45686071291659125, -1.4294311155629915, -2.0064029179452505, -1.821203833630237, -0.7554765403860394, 0.9915688382365287, 2.9371466114837643, 4.447138036608877, 4.928456541400425, 4.021802497495027, 1.7324959424501511, -1.5450552111152536, -5.120770661873248, -8.194284222465983, -10.076699233077361, -10.381028748569491, -9.123289542237314], 'positive_zeros': ['0.792171014388010220229700700432450', '1.85002080543130363494218525620230', '4.33095519868326383186402466555601', '5.12390441831801024183499735026854', '6.27071516146700591994077048587515', '7.04057098920862255678748749342690', '7.82665556488751458369033807556203', '8.345695090598626871958649770158503', '9.732550975892989242542632221219070', '10.59192115481690591893328708552032'], 'prelabel': '2-600-120.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.188840816797061, 'root_angle': -0.16189590441260832, 'root_number': '0.5257311121191336 - 0.8506508083520399*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.161895904413', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.792171014388010220229700700432', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.85002080543130363494218525620', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.33095519868326383186402466556', 'prec': 100}}