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_613.585'
a10	jsonb	[0.44573835577653825, 0.8951632913550623]
a2	jsonb	[-0.2736629900720829, -0.961825643172819]
a3	jsonb	[-0.9829730996839018, 0.18374951781657034]
a4	jsonb	[-0.8502171357296141, 0.5264321628773558]
a5	jsonb	[-0.9829730996839018, 0.18374951781657034]
a6	jsonb	[0.44573835577653825, 0.8951632913550623]
a7	jsonb	[-0.9829730996839018, -0.18374951781657034]
a8	jsonb	[0.7390089172206591, 0.6736956436465572]
a9	jsonb	[0.9324722294043558, -0.3612416661871529]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	2.8467600319702804
analytic_normalization	numeric	0
bad_lfactors	jsonb	[[613, [1]]]
bad_primes	bigint[]	[613]
central_character	text	'613.585'
coeff_info	jsonb	['x^17 - 1', '0.932472229404356 + 0.361241666187153*I', '\\\\zeta_{17}']
coefficient_field	text
conductor	numeric	613
conductor_radical	integer	613
conjugate	text	'dirichlet_L_613.197'
credit	text
degree	smallint	1
dirichlet_coefficients	jsonb	['a^0', 'a^12', 'a^8', 'a^7', 'a^8', 'a^3', 'a^9', 'a^2', 'a^16', 'a^3', 'a^14', 'a^15', 'a^9', 'a^4...
euler_factors	jsonb	[[1, 'a^12'], [1, 'a^8'], [1, 'a^8'], [1, 'a^9'], [1, 'a^14'], [1, 'a^9'], [1, 'a^11'], [1, 'a^16'],...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[0], []]
group	text
index	smallint	0
label	text	'1-613-613.585-r0-0-0'
leading_term	text	'0.0395179493695815113672549746273+0.0264144745368532296126783527514*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/613/585'
plot_delta	numeric	0.3125
plot_values	jsonb	[0.047533070460836865, 0.28934543161744264, 0.2737685877185373, -0.2829692187921239, -1.387092701107...
positive_zeros	jsonb	['0.820307831028739206859763334', '2.6791051681383047814856455619', '3.60546671788965667276233954355...
precision	smallint
prelabel	text	'1-613-613.585-r0-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	2.8467600319702804
root_angle	double precision	0.1875524783133508
root_number	text	'0.382378779875450228073387046068+0.924005664864107843236639516575*I'
self_dual	boolean	False
sign_arg	numeric	0.187552478313
spectral_label	text	'r0-0'
st_group	text	'mu(17)'
symmetry_type	text	'unitary'
trace_hash	bigint
types	jsonb	['DIR']
values	jsonb	[[1, '0.346924631253037386141420993720-0.185758354894085637465485784445*I']]
z1	numeric	0.820307831029
z2	numeric	2.67910516814
z3	numeric	3.60546671789

{'Lhash': '1366212912818863936116046871268', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.224744871391589, 0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.9403647691171135, 'analytic_normalization': 0, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3], 'central_character': '3888.161', 'coefficient_field': 'CDF', 'conductor': 3888, 'conductor_radical': 6, 'conjugate': '1903125741151059905421983205737', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.224744871391589, -0.7071067811865476], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-1.224744871391589, 0.7071067811865476], [0.5, -0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, -1.4142135623730951], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [1.224744871391589, 0.7071067811865476], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 1.4142135623730951], [-1.0, 0]], [[1.0, 0], [1.224744871391589, 0.7071067811865476], [0.5, 0.8660254037844386]], [[1.0, 0], [0.5, 0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0.5, -0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 1.4142135623730951], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [1.224744871391589, -0.7071067811865476], [0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-0.5, -0.8660254037844386], [-0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-0.5, 0.8660254037844386], [-0.5, -0.8660254037844386]], [[1.0, 0], [0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0], [1.0, 0]], [[1.0, 0], [0, 0], [0.5, 0.8660254037844386]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 19581218, 'index': 3, 'label': '2-3888-9.5-c0-0-3', 'leading_term': '1.7119741473746552073962371997604', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3888/1/q/d/161/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [1.7119741473746553, 1.683275547681903, 1.6634298562861984, 1.6503255478664287, 1.641239343776811, 1.6330929519458623, 1.622700002372432, 1.6069716398255205, 1.5830696065222805, 1.5485106792331431, 1.5012333950609722, 1.4396388978169317, 1.3626154382899833, 1.2695528638494362, 1.1603505523909157, 1.0354201027703864, 0.8956826946087905, 0.7425602295885894, 0.5779589998158592, 0.40424456163186995, 0.22420662838202277, 0.04101306741496745, -0.1418475487680929, -0.32063495976652906, -0.49143745721092896, -0.6502625107235174, -0.7931364460983845, -0.9162113544744608, -1.0158769497438787, -1.0888746722100033, -1.1324109760806458, -1.1442664529368878, -1.1228972481956345, -1.0675251366636211, -0.9782126483251512, -0.8559197855017441, -0.7025391530492289, -0.520906735924626, -0.3147861004273036, -0.08882445907579889, 0.15152018817549817, 0.4000807594402214, 0.6501106328676808, 0.8944390392644399, 1.125649332460917, 1.3362761996060029, 1.5190169666498947, 1.6669513420288793, 1.7737632602820483, 1.8339579714883343, 1.8430672032288822, 1.7978351257506346, 1.696377998509573, 1.53831078028654, 1.3248346500810273, 1.0587803071356443, 0.7446030809562794, 0.38832726118110744, -0.002561382222281122, -0.41927421989611713, -0.851927073727294, -1.2897919575284074, -1.7215872193172121, -2.1357983950987456, -2.521020597896788, -2.8663120214199864, -3.1615471967051936, -3.3977580563354577, -3.5674506781612174, -3.664885830002622, -3.6863121349859576, -3.630141823994598, -3.4970606197468483, -3.290065270873406, -3.0144245710016224, -2.677562287525044, -2.2888632027748788, -1.8594063395974163, -1.4016322974786684, -0.9289543524223103, -0.4553254605678663, 0.005224557908924202, 0.43906569370245024, 0.8334411783003419, 1.1769200359621008, 1.459811260474335, 1.6745229466799818, 1.8158512254835066, 1.8811860325912542, 1.8706235282899386, 1.7869782927709976, 1.6356921376682367, 1.4246403658188223, 1.1638404259231094, 0.8650719823339877, 0.5414212820159676, 0.20676618093553323, -0.12477887092650912, -0.43943633928691367, -0.7243346288806508, -0.9680491122169737, -1.1610920956601172, -1.2963300826278112, -1.3693090883670063, -1.3784720582268604, -1.32525653551721, -1.2140654704045832, -1.0521092775196352, -0.8491227282629115, -0.6169657750009042, -0.3691227081244772, -0.12011890213570454, 0.11512141765940548, 0.3219496710040794, 0.48667074819309375, 0.5971942238088063, 0.6436293057521068, 0.6187954865324219, 0.5186237905712756, 0.34242766005897696, 0.09302774879262997, -0.22327900031111372, -0.5969088793489246, -1.0153353399519818, -1.4635759946985851, -1.9248045393074231, -2.381063220506537, -2.8140461765806597, -3.2059198766968273, -3.5401442112699693, -3.802256710486042, -3.9805829944658133, -4.066838912923992, -4.056593860579985, -3.949570322103253, -3.7497615946163902, -3.4653575741128173, -3.1084771327270744, -2.6947145698348516, -2.242516476744483, -1.7724136886706339, -1.306140396457713, -0.8656785735554806, -0.4722703117704413, -0.14544319218512075, 0.09790573058853892, 0.24432346226605764, 0.2844721008036208, 0.2136232061408062, 0.031948988918694514, -0.2554071017030308, -0.6384876594838846, -1.1029030047072144, -1.6304229943441955, -2.199754330433162, -2.787469362332648, -3.36904446591127, -3.9199600603915945, -4.416810535176434, -4.838371045276819, -5.166569417437949, -5.38731528434712, -5.491144894734518, -5.473648568007828, -5.335658090428168, -5.083183001086597, -4.727097125763388, -4.282589268102341, -3.768404021130732, -3.205909589058857, -2.6180387238988883, -2.028155873199, -1.4589079972946273, -0.9311179679597816, -0.4627778720731094, -0.06819493744697325, 0.2426646436478829, 0.4645986575277189, 0.597335204016781, 0.6454324357341705, 0.6179158430729244, 0.5276713571580195, 0.3906259198755161, 0.2247590599297996, 0.048998747604092875, -0.11793818940977363, -0.25869695436082973, -0.3583624159472338, -0.4054020283633211, -0.39241909617499415, -0.31667109853254183, -0.1803201125801789, 0.009603250622500155, 0.24152531132854047, 0.49993096548706656, 0.7662125693245381, 1.0197227049812978, 1.2389751708084964, 1.4029290927490121, 1.4922850414416318, 1.490719870815778, 1.3859888706925034, 1.170829729945768, 0.843612494478041, 0.40869271497967447, -0.1235593438008583, -0.7370630387792299, -1.4106564117263731, -2.119022850331972, -2.8338710475362836, -3.5253089197634138, -4.163340124548542, -4.7194035554663, -5.167872228429346, -5.487428617613435, -5.662238806071942, -5.68285757668876, -5.546810317342421, -5.2588146476049955, -4.8306240893903745, -4.280496843411586, -3.6323136435377745, -2.9143885565848446, -2.1580343257231216, -1.39595837412221, -0.6605760094024974, 0.017666963870190826, 0.6118695075877854, 1.100060532299007, 1.4663158751050214, 1.7015433691950295, 1.8038905406854409, 1.7787505295918973, 1.6383645343712856, 1.4010421285941657, 1.0900428580545043, 0.7321822980019497, 0.35624204833868856, -0.008725029156879047, -0.33509642344879575, -0.5982895995776167, -0.77818566926658, -0.8602835890411387, -0.8365168440798885, -0.7056842170167952, -0.4734689245719248, -0.15204481076034437, 0.2407070288514072, 0.6823243311851646, 1.147164738350384, 1.6079971963422666, 2.0376870594679435, 2.4108720896965132, 2.70552655834078, 2.9043169537200684, 2.9956650594255643, 2.9744517106898702], 'positive_zeros': ['1.07775195513092428815528055892703', '1.99952525415419847654523341149708', '2.94499156292873590666922487480597', '4.11269110314432836324289300076821', '4.90647692300110461702931091386226', '5.66207671587129000373193480171657', '6.10978260143317395715461133130330', '7.34049805940935753179816963115067', '7.57308994276761512686756763634006', '8.896737668074040109132255012847385'], 'prelabel': '2-3888-9.5-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3929697660455929, 'root_angle': -0.11111111111111113, 'root_number': '0.76604444311897803520239265055524 - 0.64278760968653932632264340990740*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1111111111111111', 'prec': 54}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.07775195513092428815528055893', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.99952525415419847654523341150', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.94499156292873590666922487481', 'prec': 100}}