Database - lfunc_lfunctions

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Query: /api/lfunc_lfunctions/?_offset=0

Table lfunc_lfunctions

L-functions

Column	Type	Example
A10	numeric	0
A2	numeric	0
A3	numeric	0
A4	numeric	0
A5	numeric	0
A6	numeric	0
A7	numeric	1
A8	numeric	0
A9	numeric	0
Lhash	text	'937839280816519986'
a10	jsonb	[0.0, 0]
a2	jsonb	[0.0, 0]
a3	jsonb	[0.0, 0]
a4	jsonb	[0.0, 0]
a5	jsonb	[0.0, 0]
a6	jsonb	[0.0, 0]
a7	jsonb	[0.3779644730092272, 0]
a8	jsonb	[0.0, 0]
a9	jsonb	[0.0, 0]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	2080.6459553880995
analytic_normalization	numeric	0.5
bad_lfactors	jsonb	[[2, [1]], [3, [1]], [7, [1, -1]], [11, [1, 1]], [47, [1, 1]]]
bad_primes	bigint[]	[2, 3, 7, 11, 47]
central_character	text	'260568.1'
coeff_info	jsonb
coefficient_field	text	'1.1.1.1'
conductor	numeric	260568
conductor_radical	integer	21714
conjugate	text
credit	text
degree	smallint	2
dirichlet_coefficients	jsonb
euler_factors	jsonb	[[1], [1], [1, 0, 5], [1, -1], [1, 1], [1, -2, 13], [1, -2, 17], [1, 2, 19], [1, -4, 23], [1, 4, 29]...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[], [0]]
group	text
index	smallint	14
label	text	'2-260568-1.1-c1-0-14'
leading_term	text	'3.30729195132'
load_key	text	'Cremona'
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	'EllipticCurve/Q/260568/v'
plot_delta	numeric	0.25
plot_values	jsonb	[3.307291951316974, 2.440969203710684, 0.5010829332796827, -0.8247148349776016, -0.134755091878352, ...
positive_zeros	jsonb	['0.5678811620990073', '1.019230062117989', '1.888255209688585', '2.290144084645606', '3.01055969112...
precision	smallint
prelabel	text	'2-260568-1.1-c1-0'
primitive	boolean	True
rational	boolean	True
root_analytic_conductor	double precision	45.614098208647064
root_angle	double precision	0.0
root_number	text	'1'
self_dual	boolean	True
sign_arg	numeric
spectral_label	text	'c1-0'
st_group	text	'SU(2)'
symmetry_type	text
trace_hash	bigint	937839280816519986
types	jsonb
values	jsonb
z1	numeric	0.5678811620990073
z2	numeric	1.019230062117989
z3	numeric	1.888255209688585

{'Lhash': '2812974083869995825354483945426', 'a10': [0.40001903933453936, -0.6928533001223154], 'a2': [-0.6427876096865394, -0.766044443118978], 'a3': [1.4396926207859084, 1.2080455471101075], 'a4': [-0.17364817766693036, 0.984807753012208], 'a5': [0.27362913833239094, 0.7517898788730694], 'a6': [-4.7720212980954226e-61, -1.8793852415718169], 'a7': [-0.13844908042023066, 0.05039134423449164], 'a8': [0.8660254037844386, -0.5], 'a9': [0.09239626545204768, 0.5240052604587699], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0.6427876096865394, 0.766044443118978]]], [37, [[1.0, 0], [-6.082271935422356, -0.07725350201502051]]]], 'bad_primes': [2, 37], 'central_character': '74.25', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '3503516536742513163580713800535', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6427876096865394, 0.766044443118978]], [[1.0, 0], [-1.4396926207859084, -1.2080455471101075], [0.520944533000791, 2.9544232590366244]], [[1.0, 0], [-0.27362913833239094, -0.7517898788730694], [-3.83022221559489, 3.2139380484326967]], [[1.0, 0], [0.13844908042023066, -0.05039134423449164], [5.362311101832846, -4.499513267805775]], [[1.0, 0], [2.4056989852358077, 4.16679287014531], [-5.5, 9.526279441628825]], [[1.0, 0], [-1.9185827490183787, -0.33829790337375737], [12.216004070216808, 4.446261863233693]], [[1.0, 0], [3.4377878714737635, -0.6061747556931492], [15.974774553360442, -5.814342436536369]], [[1.0, 0], [4.336252938752023, -5.167745018154924], [-3.2993153756716764, -18.711347307231954]], [[1.0, 0], [3.616100232205718, 2.08775644248064], [11.5, 19.91858428704209]], [[1.0, 0], [-2.631340459211625, 1.519205122455385], [14.5, -25.11473670974872]], [[1.0, 0], [0, -8.137403480462693], [-31.0, 0]], [[1.0, 0], [-6.082271935422356, -0.07725350201502051]], [[1.0, 0], [-0.6768220035023037, 3.8384483235798488], [-38.527397452222246, -14.022825876352417]], [[1.0, 0], [0, 8.108523474992625], [-43.0, 0]], [[1.0, 0], [4.169109291350849, -7.221109114927148], [-23.5, -40.703193977868615]], [[1.0, 0], [-10.232709599873711, -3.7244017102440523], [40.60035548530583, 34.067743313386586]], [[1.0, 0], [2.9656894359362846, -8.148164758350058], [-45.196622144019706, -37.92446897150582]], [[1.0, 0], [0.3463442073242464, 0.06106982836335099], [57.32124986794041, 20.863228742865793]], [[1.0, 0], [2.254710391021458, -0.8206474692225209], [51.32497768897153, -43.066769848998135]], [[1.0, 0], [-5.349531328886567, -4.488789765040023], [12.329020614352055, 69.92135046386677]], [[1.0, 0], [-1.133990162145583, 0], [73.0, 0]], [[1.0, 0], [-0.6465098496384507, -1.7762712133366465], [-60.51751100639927, 50.780221165236604]], [[1.0, 0], [1.719968055341961, 9.75442356258409], [-77.9944875252304, 28.387671896030504]], [[1.0, 0], [3.459239031848524, -9.504181128499889], [-68.17795543758905, -57.208097262102]], [[1.0, 0], [-5.088120181471584, -2.937627556441787], [48.5, 84.00446416709055]], [[1.0, 0], [8.508655612704558, -14.73742382531039], [-50.5, -87.4685657822283]], [[1.0, 0], [-11.039095330213536, 6.373424660508726], [51.5, -89.20061658979718]], [[1.0, 0], [-2.4725178752759844, 14.022345674732497], [-100.5471104240922, -36.596155335846554]], [[1.0, 0], [12.719823569194958, 15.158895435752598], [-18.927651365695407, 107.34404507833068]], [[1.0, 0], [-5.464697245908875, -6.512572575251586], [-19.62224407636313, 111.28327609037952]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 9593061, 'index': 0, 'label': '2-74-37.25-c1-0-0', '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/74/2/h/a/25/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [0.9194528960990326, 0.9193581966336772, 0.9306991206244069, 0.9516345300840565, 0.9795409379498646, 1.0112029089639185, 1.0429734344615589, 1.0708847442123348, 1.0907210937355964, 1.0980782411607475, 1.0884334668714455, 1.0572431226884977, 1.0000771093026375, 0.9127932967292576, 0.7917498247625235, 0.6340490023150649, 0.4378027664400841, 0.2024061779597207, -0.07119775880573126, -0.3802813879299037, -0.7201452306833032, -1.0840027175477616, -1.4629587623052698, -1.8461020362928184, -2.220726856054815, -2.5726946899451204, -2.8869374667055814, -3.148095354680923, -3.3412708903353505, -3.4528698826370476, -3.4714882029636263, -3.3887933356994737, -3.200341454582635, -2.9062658647971156, -2.5117718966620237, -2.02737755899046, -1.4688489742177313, -0.856794945265708, -0.21590558895920545, 0.4261550784223405, 1.040164839952025, 1.5970006411900348, 2.069443525439951, 2.4340135844272024, 2.6727005867916804, 2.7744483279454286, 2.7362542952495152, 2.563762224569248, 2.271253811694786, 1.8809863357669387, 1.4218730862328484, 0.9275598500608775, 0.43400881247394846, -0.023244243535559744, -0.4119482556450264, -0.7058689870285904, -0.8871421579600361, -0.9480067615642518, -0.8917141168429604, -0.7324683083318124, -0.4943341371335346, -0.20914371163156004, 0.08646575017696707, 0.3546521965961026, 0.5602921136786425, 0.6748519298164749, 0.679805437326922, 0.5692077680475911, 0.35109132915887764, 0.04744478304359339, -0.307333529721256, -0.6694620599519584, -0.9900730520843904, -1.2204147303008064, -1.3174631274181223, -1.2493606852771013, -1.0000682415974897, -0.572652200111751, 0.009268222604198339, 0.7022231797614428, 1.4458384127492352, 2.167876152600119, 2.7909739184882674, 3.2404619259220606, 3.4524703416965523, 3.3814455304349105, 3.0061970353087117, 2.3337018005600236, 1.4000948899713963, 0.26856027726971077, -0.9758265228768686, -2.2338967194887998, -3.402088990565482, -4.383049428609015, -5.095965807009853, -5.485439884174187, -5.527812886397229, -5.234109139604003, -4.649128801757281, -3.846664194543597, -2.9212841893667743, -1.9775694802414545, -1.118030656296771, -0.4311509479365915, 0.018968400629978215, 0.20003401330367407, 0.11506114668982467, -0.19857366276214614, -0.6744896100364696, -1.2264508805648981, -1.7601712445398892, -2.18625010950945, -2.432520593738488, -2.454121603588017, -2.2398702029992057, -1.813981390489062, -1.232802972551774, -0.5769226869288564, 0.060331634444381534, 0.5864359801471237, 0.9233576175702791, 1.0194096483468424, 0.8575039500411306, 0.45850656115082233, -0.12092118335928513, -0.795818612046935, -1.4647864003844953, -2.0245616657140983, -2.3852029238952017, -2.483627227538376, -2.2934248826005597, -1.8293816995320842, -1.1459000047514787, -0.3294203437135833, 0.5141292289366849, 1.2750334607327882, 1.8562794474972324, 2.188290071133121, 2.2395660690786316, 2.0214880962368027, 1.5864138121561466, 1.0192551640590177, 0.42377461455619764, -0.09427447265463199, -0.4444693644869313, -0.5666616382306945, -0.4410203979044982, -0.09139800850582565, 0.418691753182337, 0.9969702920401116, 1.5384724009237507, 1.9441756420587306, 2.1390245208151963, 2.086184925790634, 1.7948974357559364, 1.3203049587177869, 0.7549592997796353, 0.2131490095247359, -0.18950503062742252, -0.3578000958850732, -0.2362655359016176, 0.17750196504765692, 0.8281581158072333, 1.6078915233465814, 2.371308863037349, 2.957889197378791, 3.218564600376324, 3.042104665214536, 2.3768062824806027, 1.2435785987723147, -0.26220254531953524, -1.9809088694854227, -3.7097783256233705, -5.231893780938727, -6.348548548430857, -6.909810929866198, -6.8382468734010775, -6.1417703653290205, -4.913316053163267, -3.3171885550964775, -1.5641738088818093, 0.12058727336670663, 1.5317049903433153, 2.5140020356888426, 2.9843086712773665, 2.94105405462791, 2.4602273202530083, 1.6786526655710368, 0.7677300856840735, -0.09756214897754863, -0.7688284743768675, -1.1482405642993423, -1.2022162248295458, -0.9626300616955996, -0.5157514746195313, 0.018587331860562037, 0.5132726380022935, 0.8603401408463062, 0.9923086241010072, 0.8942492531199744, 0.6043252212925143, 0.20289117378062302, -0.2074147875068956, -0.5262911461775641, -0.6798096320412141, -0.6386512769126795, -0.42648370431503413, -0.11644498523883853, 0.18381013652059058, 0.35559124188804914, 0.2963602730121554, -0.05514708443594426, -0.7014108163785201, -1.580368507278355, -2.5732289709665404, -3.5248856699522637, -4.273262342839178, -4.6818871889948435, -4.6690633011945, -4.227416566921135, -3.4293234314741325, -2.41644314798282, -1.3747772487415055, -0.4997098391428024, 0.04228629616419984, 0.14765089542662468, -0.2015934100340392, -0.9314870093872584, -1.8879359417417325, -2.864884523412983, -3.6436924149193017, -4.036123194415793, -3.9224045172057083, -3.27659241816308, -2.173854500941468, -0.7778320399969758, 0.6897512477302966, 1.9914118460291657, 2.9198022407576083, 3.337954223678812, 3.2056622890088846, 2.58653151287488, 1.6341249057031297, 0.5599407220707583, -0.4102612594342891, -1.082787485067016, -1.335370940815514, -1.1413328887233738, -0.57345682213722, 0.21326148753839863, 1.0163485280872626, 1.6306866362575008, 1.8938554819780051, 1.7222188806125014, 1.1299205339825138, 0.22658738887212002, -0.8058813410123674], 'positive_zeros': ['2.21904528216493128998787109743024', '4.79178088602117717488276735475569', '6.61823967574517458605710264106018', '7.71294215514688841880146913024217', '8.642476338286310745408090325821328', '9.748204993650154907114700562169607', '11.15261969697524827462867311358595', '12.99272645919101583618772894828403', '13.30577458533168828841334291439056', '14.73746883422659812102545661012063'], 'prelabel': '2-74-37.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': -0.0028035007153645267, 'root_number': '0.9998448614050147 - 0.017614003576328655*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00280350071536', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.21904528216493128998787109743', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '4.79178088602117717488276735476', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '6.61823967574517458605710264106', 'prec': 100}}