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_3241.3022'
a10	jsonb	[0.476262120839475, 0.8793033562164342]
a2	jsonb	[-0.9232276375115515, -0.3842534701662944]
a3	jsonb	[-0.3141861317770625, 0.9493614035755648]
a4	jsonb	[0.7046985413303214, 0.7095068469344868]
a5	jsonb	[-0.7775737186139037, -0.6287917875743494]
a6	jsonb	[0.6548607339452851, -0.7557495743542583]
a7	jsonb	[1.0, -2.8163065144692913e-30]
a8	jsonb	[-0.37796670142890654, -0.9258191900208981]
a9	jsonb	[-0.8025741491979327, -0.5965523740956988]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	348.2938212593797
analytic_normalization	numeric	0
bad_lfactors	jsonb	[[7, [1]], [463, [1]]]
bad_primes	bigint[]	[7, 463]
central_character	text	'3241.3022'
coeff_info	jsonb	['x^462 - 1', '0.999907521857918 + 0.0135995489615099*I', '\\\\zeta_{462}']
coefficient_field	text
conductor	numeric	3241
conductor_radical	integer	3241
conjugate	text	'dirichlet_L_3241.3167'
credit	text
degree	smallint	1
dirichlet_coefficients	jsonb	['a^0', 'a^260', 'a^139', 'a^58', 'a^281', 'a^399', 0, 'a^318', 'a^278', 'a^79', 'a^202', 'a^197', '...
euler_factors	jsonb	[[1, 'a^260'], [1, 'a^139'], [1, 'a^281'], [0], [1, 'a^202'], [1, 'a^99'], [1, 'a^103'], [1, 'a^251'...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[1], []]
group	text
index	smallint	0
label	text	'1-3241-3241.3022-r1-0-0'
leading_term	text	'0.0160192612410684037808310226721+0.315512924813191029842224233030*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/3241/3022'
plot_delta	numeric	0.3125
plot_values	jsonb	[-0.3159193290301876, -0.8785979164324316, -0.5442446040563195, 0.8152400142982785, 2.19990353703211...
positive_zeros	jsonb	['0.7711451339643471480795599457', '1.91149866520222614135708879204', '2.834983358160308298707575730...
precision	smallint
prelabel	text	'1-3241-3241.3022-r1-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	348.2938212593797
root_angle	double precision	-0.4838525965368134
root_number	text	'-0.994857638936445348305597943887-0.101283158766901323673890204517*I'
self_dual	boolean	False
sign_arg	numeric	-0.25
spectral_label	text	'r1-0'
st_group	text	'mu(462)'
symmetry_type	text	'unitary'
trace_hash	bigint
types	jsonb	['DIR']
values	jsonb	[[1, '0.461202203846283397639000630788+0.0991574298246695412087284359730*I']]
z1	numeric	0.771145133964
z2	numeric	1.9114986652
z3	numeric	2.83498335816

{'Lhash': '1922398428190780315258499508699', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.6457513110645905, 0.0], 'a6': [0.0, 0.0], 'a7': [-4.656843374720909, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.446453149448075, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 23], 'central_character': '3312.1', 'coefficient_field': 'CDF', 'conductor': 3312, 'conductor_radical': 138, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.6457513110645905, 0], [5.0, 0]], [[1.0, 0], [4.656843374720909, 0], [7.0, 0]], [[1.0, 0], [-3.5657607601127816, 0], [11.0, 0]], [[1.0, 0], [0.5546686964564629, 0], [13.0, 0]], [[1.0, 0], [-5.211512071177372, 0], [17.0, 0]], [[1.0, 0], [6.200420007521053, 0], [19.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [4.554668696456463, 0], [29.0, 0]], [[1.0, 0], [4.554668696456463, 0], [31.0, 0]], [[1.0, 0], [-3.5435766328001446, 0], [37.0, 0]], [[1.0, 0], [7.846171318585644, 0], [41.0, 0]], [[1.0, 0], [-9.331941527746617, 0], [43.0, 0]], [[1.0, 0], [11.313686749441818, 0], [47.0, 0]], [[1.0, 0], [-3.667935438377228, 0], [53.0, 0]], [[1.0, 0], [-11.159858068027463, 0], [59.0, 0]], [[1.0, 0], [1.5657607601127814, 0], [61.0, 0]], [[1.0, 0], [8.38258523673731, 0], [67.0, 0]], [[1.0, 0], [-3.846171318585644, 0], [71.0, 0]], [[1.0, 0], [8.977692838811206, 0], [73.0, 0]], [[1.0, 0], [9.766180767633834, 0], [79.0, 0]], [[1.0, 0], [0.4342392398872185, 0], [83.0, 0]], [[1.0, 0], [7.029346841961117, 0], [89.0, 0]], [[1.0, 0], [-4.022184127312637, 0], [97.0, 0]], [[1.0, 0], [17.86835544589828, 0], [101.0, 0]], [[1.0, 0], [15.788364894946472, 0], [103.0, 0]], [[1.0, 0], [9.587944887425419, 0], [107.0, 0]], [[1.0, 0], [-9.01724448414558, 0], [109.0, 0]], [[1.0, 0], [3.3936773003936276, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 19800973, 'index': 42, 'label': '2-3312-1.1-c1-0-42', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/3312/2/a/bg/1/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [-9.528992144224873e-61, 0.1760646942456577, 0.351537506514349, 0.5257770138588309, 0.6980459557562887, 0.867471166664943, 1.033012244145568, 1.1934408325508223, 1.3473317113363754, 1.4930661993685534, 1.6288477806473867, 1.7527293554306773, 1.862651132010909, 1.9564878879979961, 2.0321041251005267, 2.0874154944311964, 2.120454759360019, 2.1294404748141327, 2.112846487425413, 2.0694702981560336, 1.998498281131627, 1.8995657259718466, 1.7728096744077502, 1.6189125644366371, 1.4391347851741192, 1.2353343900496065, 1.0099724202253755, 0.7661025568876987, 0.5073441504812812, 0.23783806432213236, -0.03781478628276759, -0.31463182873860646, -0.5873432668534707, -0.8505011136478522, -1.0986008334805313, -1.3262130666300005, -1.5281224043681443, -1.6994697292169305, -1.8358942533490727, -1.9336710971790685, -1.989840067871033, -2.0023212393481757, -1.9700130140493208, -1.8928685710790043, -1.7719469801385954, -1.6094357854145733, -1.4086425328339893, -1.173953516604835, -0.9107589399273917, -0.6253446978693656, -0.32475207016263624, -0.016607726041020923, 0.2910724436480755, 0.5901010785775951, 0.8723531036484775, 1.1300090318672071, 1.3558006478514992, 1.5432513871906817, 1.6869034374794938, 1.7825235512527708, 1.827279797917044, 1.8198820011431287, 1.760679410467126, 1.6517102311107794, 1.4966989636078747, 1.300999053316358, 1.0714800776079707, 0.8163605543140009, 0.5449893795660655, 0.2675808307495211, -0.005090069245561839, -0.2620233090392105, -0.49235073900047477, -0.6857027546616905, -0.8325726614582765, -0.9246660698065534, -0.9552226037300086, -0.9192976003247046, -0.8139923418072526, -0.6386226897335191, -0.39481775695903043, -0.08654241338750031, 0.27996008489588026, 0.6963063046965383, 1.1521897325752475, 1.635671837388875, 2.1335392564015114, 2.6317165099030295, 3.1157211781348604, 3.571146394592455, 3.9841539211010883, 4.3419600575593105, 4.6332962692231074, 4.848826730644793, 4.981506006136607, 5.026861802525431, 4.983190102943871, 4.85165295381556, 4.636272637105551, 4.343819797633414, 3.9835971710675464, 3.567124716194458, 3.1077360287890192, 2.620099733555924, 2.1196829478967407, 1.622176729729669, 1.1429055217940383, 0.6962438716259294, 0.2950640548520704, -0.049762389840424956, -0.3297878030602397, -0.5393173577855498, -0.6756283750555744, -0.7390687333285719, -0.7330278914525284, -0.6637792605029889, -0.5401980923082138, -0.3733644754296945, -0.17606620735408848, 0.037778989069255114, 0.2537584380573011, 0.4576301061773451, 0.6359902221511836, 0.7769134833510039, 0.870536842150515, 0.9095595905992087, 0.8896354482628669, 0.8096365144369836, 0.671774125210673, 0.4815676594484236, 0.2476589226192501, -0.01852337457285672, -0.3032376363867007, -0.5910239163509481, -0.8653950228379552, -1.109595206609802, -1.3073935658411764, -1.4438768146571728, -1.5062051152415314, -1.4842953626640798, -1.371398654505461, -1.1645426165614277, -0.8648146574955163, -0.47746888266675536, -0.011847038366539244, 0.5188878446749592, 1.0981978537295305, 1.7067809069718454, 2.323322066685327, 2.925354663208568, 3.4901946145271503, 3.9959070645696233, 4.422262009610644, 4.751635102030966, 4.969811389629767, 5.066653346103668, 5.036600055324884, 4.8789716142669715, 4.598061414416915, 4.203008570917146, 3.7074529544392973, 3.128985564857936, 2.48841687247879, 1.8088947524880377, 1.114911292715662, 0.4312436593487616, -0.21812196853869179, -0.8110328707926102, -1.3281290628462432, -1.7536731434595743, -2.0762101769524866, -2.289024865974837, -2.3903728140190137, -2.383473529410377, -2.276264466720499, -2.080927267518182, -1.8132088556197177, -1.4915705732047515, -1.1362075594967826, -0.7679875841847039, -0.40736315609089707, -0.073312651020832, 0.21763470940620153, 0.45223895126432523, 0.6212098957631872, 0.7196524201837009, 0.7472715736057651, 0.7083250443892517, 0.6113236871380977, 0.46849420532686153, 0.2950309501430057, 0.1081754467941362, -0.0738279440820572, -0.23284443664737287, -0.3519689742711107, -0.4165924164085474, -0.4153539489985287, -0.34092506351044916, -0.19057864452568685, 0.03349243734667034, 0.32412984137155193, 0.6694455309603756, 1.0533317664126658, 1.4562231683366436, 1.8560744974016135, 2.229505279768449, 2.5530522959361925, 2.804463843152276, 2.963966026773048, 3.0154314043168786, 2.9473841702683803, 2.753783596836441, 2.4345382993248794, 1.9957175485122893, 1.4494416155822347, 0.8134501863585633, 0.11036531151408521, -0.633317781039122, -1.3884633333036156, -2.124689513930113, -2.811853202084847, -3.421547522841006, -3.928532609207794, -4.31202244284829, -4.556757273927541, -4.653801746662329, -4.601022939891007, -4.403219347426112, -4.07189048098053, -3.624656269561575, -3.084354679079433, -2.4778639047987414, -1.8347110730671208, -1.1855417181154984, -0.5605326338465509, 0.012165487488147154, 0.5078702069467389, 0.9066146588777961, 1.1941307661647595, 1.3625134475274379, 1.410528538792831, 1.3435470662578846, 1.1731096068994868, 0.9161455516430905, 0.5938919413479258, 0.23057401055175286, -0.14807638763482292, -0.516378546140691, -0.850246073873136, -1.128625075012354, -1.3347426133861855, -1.4570914243438229, -1.4900919714265057, -1.4343916914509647, -1.2967825675652915, -1.089740787547509, -0.8306148601424721], 'positive_zeros': ['1.51650496425802921948611881994897', '2.59257083136202314913881303275925', '3.55371863372842617624659151544060', '4.12598854398457937229316306075095', '5.52722622724377288708415664947854', '6.03413054557639676312114266690876', '6.64895122635829439767434510374805', '7.31369975395443123947227557774573', '8.412215605854165190638353748326064'], 'prelabel': '2-3312-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.142611510647881, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.51650496425802921948611881995', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.59257083136202314913881303276', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.55371863372842617624659151544', 'prec': 100}}