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	'2188882612453410760035517440952'
a10	jsonb	[2.270828570762663, 0.0]
a2	jsonb	[1.2779731230060372, 0.0]
a3	jsonb	[1.8624470063598195, 0.0]
a4	jsonb	[-0.36678469687419635, 0.0]
a5	jsonb	[1.7768985355664133, 0.0]
a6	jsonb	[2.380157217150903, 0.0]
a7	jsonb	[-1.1880755835918095, 0.0]
a8	jsonb	[-3.0246872305472134, 0.0]
a9	jsonb	[0.46870885149865366, 0.0]
accuracy	smallint	100
algebraic	boolean	True
analytic_conductor	double precision	52.27805820333229
analytic_normalization	numeric	0.5
bad_lfactors	jsonb	[]
bad_primes	bigint[]	[6547]
central_character	text	'6547.1'
coeff_info	jsonb
coefficient_field	text	'CDF'
conductor	numeric	6547
conductor_radical	integer	6547
conjugate	text
credit	text
degree	smallint	2
dirichlet_coefficients	jsonb
euler_factors	jsonb	[[[1.0, 0], [-1.2779731230060372, 0], [2.0, 0]], [[1.0, 0], [-1.8624470063598195, 0], [3.0, 0]], [[1...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[], [0]]
group	text	'GL2'
index	smallint	505
label	text	'2-6547-1.1-c1-0-505'
leading_term	text
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	1
origin	text	'ModularForm/GL2/Q/holomorphic/6547/2/a/a/1/192'
plot_delta	numeric	0.046875
plot_values	jsonb	[2.2765053936394372e-60, 0.3547435884675497, 0.7085870146111389, 1.0605637983027572, 1.4095788697343...
positive_zeros	jsonb	['1.72672391908253078051102540869243', '2.61946690453040054269920374561104', '3.27613747168555296353...
precision	smallint
prelabel	text	'2-6547-1.1-c1-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	7.2303567134223945
root_angle	double precision	0.5
root_number	text	'-1'
self_dual	boolean	True
sign_arg	numeric	0.5
spectral_label	text	'c1-0'
st_group	text
symmetry_type	text
trace_hash	bigint
types	jsonb	['CMF']
values	jsonb
z1	numeric	1.72672391908253078051102540869
z2	numeric	2.61946690453040054269920374561
z3	numeric	3.27613747168555296353639703987

{'Lhash': '2881069966958736427705331868039', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, -1.4142135623730951], 'a6': [0.0, 0.0], 'a7': [0.0, -4.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.299691578212876, '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': '288.287', 'coefficient_field': 'CDF', 'conductor': 288, 'conductor_radical': 6, 'conjugate': '1158631306994367474132308092417', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-5.0, 0]], [[1.0, 0], [0, 4.0], [-7.0, 0]], [[1.0, 0], [5.656854249492381, 0], [11.0, 0]], [[1.0, 0], [-4.0, 0], [13.0, 0]], [[1.0, 0], [0, 4.242640687119285], [-17.0, 0]], [[1.0, 0], [0, 0], [-19.0, 0]], [[1.0, 0], [-5.656854249492381, 0], [23.0, 0]], [[1.0, 0], [0, -1.4142135623730951], [-29.0, 0]], [[1.0, 0], [0, 4.0], [-31.0, 0]], [[1.0, 0], [6.0, 0], [37.0, 0]], [[1.0, 0], [0, -9.899494936611665], [-41.0, 0]], [[1.0, 0], [0, -8.0], [-43.0, 0]], [[1.0, 0], [-5.656854249492381, 0], [47.0, 0]], [[1.0, 0], [0, 4.242640687119285], [-53.0, 0]], [[1.0, 0], [-11.313708498984761, 0], [59.0, 0]], [[1.0, 0], [2.0, 0], [61.0, 0]], [[1.0, 0], [0, -8.0], [-67.0, 0]], [[1.0, 0], [5.656854249492381, 0], [71.0, 0]], [[1.0, 0], [0, 0], [73.0, 0]], [[1.0, 0], [0, -4.0], [-79.0, 0]], [[1.0, 0], [-5.656854249492381, 0], [83.0, 0]], [[1.0, 0], [0, -4.242640687119285], [-89.0, 0]], [[1.0, 0], [8.0, 0], [97.0, 0]], [[1.0, 0], [0, 18.384776310850235], [-101.0, 0]], [[1.0, 0], [0, -4.0], [-103.0, 0]], [[1.0, 0], [0, 0], [107.0, 0]], [[1.0, 0], [-12.0, 0], [109.0, 0]], [[1.0, 0], [0, 1.4142135623730951], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 9818798, 'index': 3, 'label': '2-288-12.11-c1-0-3', '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/288/2/c/a/287/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [1.1595070426437273, 1.2773420248679765, 1.4008100722898424, 1.5300236756430647, 1.6622639438112632, 1.7922532616170401, 1.9126350675280708, 2.0145575967051763, 2.088317895986216, 2.124064607116156, 2.1125690774068926, 2.0460622340102366, 1.9191115719555667, 1.7294874934071558, 1.4789463629855246, 1.1738422004513196, 0.8254722261558163, 0.45006536916492557, 0.06833868321743701, -0.2954251003923893, -0.6147856032859497, -0.8629954766425212, -1.0151952993547761, -1.0507982822910689, -0.955860436641403, -0.7251952482661871, -0.36397572853460025, 0.11142295381347762, 0.6735462599265115, 1.28508235139676, 1.90121678687507, 2.4730314594323985, 2.9517277405407074, 3.2933269068504543, 3.4633955368203337, 3.4412765926288946, 3.2232931632221185, 2.824441634046737, 2.2782079229504575, 1.6343195218047006, 0.9544733735952141, 0.30633230418539065, -0.2436689635997861, -0.6379569433656874, -0.8350016345615877, -0.8151188998812264, -0.5840432109867131, -0.17362270757192283, 0.3606997922601863, 0.9455643645091591, 1.4980479809209717, 1.9358073651838374, 2.1877990696465437, 2.204178026715536, 1.9639677756764502, 1.4792870914441438, 0.7953019276025263, -0.01438825797954885, -0.856589011030973, -1.6305955930789728, -2.241996854241971, -2.616304071279805, -2.7103978268328617, -2.519968477902252, -2.0816017783740444, -1.4688824203816584, -0.782762503902618, -0.13734381475602253, 0.35698922326411897, 0.6106108246844102, 0.5692129018066271, 0.22345874036500826, -0.3880499891325418, -1.1832983713891108, -2.04850831050886, -2.8553581348389727, -3.4812114862097077, -3.8291567767834964, -3.8445208049763284, -3.5249411737320817, -2.922026998487766, -2.133976725311068, -1.2900474356546139, -0.5292255376666515, 0.023427683535324755, 0.2787112244963042, 0.1995736090126311, -0.1913433794566499, -0.8145774120346044, -1.5470004111867381, -2.2432482327354184, -2.761819086537187, -2.9912214111638438, -2.871346158518079, -2.405923125746165, -1.6634155373282915, -0.7657719507423744, 0.13327315467512368, 0.8766030283270302, 1.333646907068486, 1.4261526051462396, 1.1446986962436918, 0.5524345804147552, -0.22511504319421513, -1.0226672417618496, -1.6662125878623402, -2.0066507781702647, -1.949496372342349, -1.474673183947572, -0.6421893421026649, 0.41782534236675534, 1.5291394749383684, 2.50302540440457, 3.1748944803275725, 3.436596018676264, 3.2576950903255693, 2.691136269151247, 1.861821803803811, 0.9401677658328864, 0.10592000627159093, -0.49028217806928015, -0.7594224655523488, -0.6935744295563306, -0.36780078789649406, 0.07635726544704924, 0.462659447568962, 0.6206383416983683, 0.4260731857214582, -0.1675054971722472, -1.1135665685778926, -2.277519059987896, -3.46144078708989, -4.443797291523283, -5.025877830049565, -5.074928652241119, -4.554398987209677, -3.534309416839693, -2.17899348294228, -0.7144462703914188, 0.6178689066043141, 1.6107161024038477, 2.1332584595885633, 2.156188044880034, 1.754024747801737, 1.083946415255787, 0.3459293601774166, -0.266595896363242, -0.6139999033224944, -0.6443504695596737, -0.4056593377704118, -0.03321286742597304, 0.2853509494373272, 0.35911595312162187, 0.04537658424863662, -0.7090878907070716, -1.8474431583150734, -3.2086751860186116, -4.55937173385149, -5.644539327112151, -6.245745813889444, -6.232758693980072, -5.596047873345495, -4.451840796270458, -3.0178855487394096, -1.5651608696132226, -0.35673999548240043, 0.41163746634811127, 0.6549018943381352, 0.4152476971300554, -0.15221444772542725, -0.8213276303789389, -1.3539600016956748, -1.5615267657481997, -1.3534291298796581, -0.7600181285919375, 0.07595697135871397, 0.937447908911163, 1.5911405571217152, 1.850500888549161, 1.6273673108900661, 0.9583248380374211, -0.001559305500780817, -1.01664200081824, -1.8309170667884023, -2.2351253677736906, -2.1231933683731947, -1.5228489357113117, -0.591731948426089, 0.42077254102676537, 1.2366967607806283, 1.6215634184302008, 1.4465910015682637, 0.72447967581965, -0.3911058541417878, -1.6428099029071805, -2.7343349946747195, -3.4059463816192115, -3.5009093273993996, -3.00519272816297, -2.0497092638766587, -0.8742969538470391, 0.2370551336448986, 1.03236365042034, 1.358561356199625, 1.200863824946216, 0.6836740872361655, 0.03259443495607916, -0.4921250902448147, -0.6723094588658786, -0.3972806918424166, 0.30064144132075515, 1.2510810342726928, 2.190325132068176, 2.833954704524617, 2.957447002305028, 2.4621897434419453, 1.4080291013229904, 0.002542323185202738, -1.4507718995860077, -2.631592035966017, -3.287461688245232, -3.300466529287683, -2.7170562045579127, -1.7323493186982366, -0.6330626120008742, 0.2849810041654874, 0.8013849604951945, 0.8335385237291509, 0.458701570696312, -0.11087307497459911, -0.592956529851865, -0.7219416856972439, -0.33193580166513115, 0.588075575933911, 1.8836349544168103, 3.272678223171652, 4.421663059093691, 5.038443411628971, 4.955175142677915, 4.177085380470047, 2.8826042331424775, 1.3744072635334639, -0.00472527072739789, -0.9668968905044739, -1.3572368664755086, -1.192308509032527, -0.6475518926329854, 0.0023492207544761655, 0.47217221816769983, 0.5570668341614894, 0.19793733383535908, -0.49893909476087195, -1.294560336234756, -1.8927118877339002, -2.0356539693695863, -1.590702472374409, -0.6006510414021208], 'positive_zeros': ['2.27276346214013939093115467312824', '3.34792848021892115755775602455916', '5.19094359376972883526144959598995', '5.91809348584164147656764359400835', '7.12286463458675843000321819136525', '8.405246948675098042165002227671130', '8.926482804536720712728402979001129', '10.49308058682219561740548930110904', '10.82456005537774472019773432866534', '12.10557899429009744748115198640578'], 'prelabel': '2-288-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.516473401749228, 'root_angle': 0.22295663800765184, 'root_number': '0.16910197872576274 + 0.9855985596534887*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.222956638008', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.27276346214013939093115467313', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.34792848021892115755775602456', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.19094359376972883526144959599', 'prec': 100}}