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_793.301'
a10	jsonb	[0.8090169943749475, 0.5877852522924731]
a2	jsonb	[-0.7431448254773942, -0.6691306063588582]
a3	jsonb	[-0.9781476007338057, -0.20791169081775934]
a4	jsonb	[0.10452846326765347, 0.9945218953682733]
a5	jsonb	[-0.9945218953682733, 0.10452846326765347]
a6	jsonb	[0.5877852522924731, 0.8090169943749475]
a7	jsonb	[0.9510565162951535, 0.30901699437494745]
a8	jsonb	[0.5877852522924731, -0.8090169943749475]
a9	jsonb	[0.9135454576426009, 0.4067366430758002]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	85.21968536213764
analytic_normalization	numeric	0
bad_lfactors	jsonb	[[13, [1]], [61, [1]]]
bad_primes	bigint[]	[13, 61]
central_character	text	'793.301'
coeff_info	jsonb	['x^60 - 1', '0.994521895368273 + 0.104528463267653*I', '\\\\zeta_{60}']
coefficient_field	text
conductor	numeric	793
conductor_radical	integer	793
conjugate	text	'dirichlet_L_793.137'
credit	text
degree	smallint	1
dirichlet_coefficients	jsonb	['a^0', 'a^37', 'a^32', 'a^14', 'a^29', 'a^9', 'a^3', 'a^51', 'a^4', 'a^6', 'a^35', 'a^46', 0, 'a^40...
euler_factors	jsonb	[[1, 'a^37'], [1, 'a^32'], [1, 'a^29'], [1, 'a^3'], [1, 'a^35'], [0], [1, 'a^14'], [1, 'a^17'], [1, ...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[1], []]
group	text
index	smallint	0
label	text	'1-793-793.301-r1-0-0'
leading_term	text	'0.362502900458560652432435125518+0.390320770840406033904430828912*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/793/301'
plot_delta	numeric	0.3125
plot_values	jsonb	[0.5326900196083248, 0.8791906419600944, 0.6881335483405103, 0.011101977426914588, -0.70350983368573...
positive_zeros	jsonb	['0.9418368730167824396077638829', '1.85740261469308225011009720894', '3.221098578673532866849834398...
precision	smallint
prelabel	text	'1-793-793.301-r1-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	85.21968536213764
root_angle	double precision	0.2617566393141821
root_number	text	'-0.0738019820459404943120194285544+0.997272915227366774458935496285*I'
self_dual	boolean	False
sign_arg	numeric	0.261756639314
spectral_label	text	'r1-0'
st_group	text	'mu(60)'
symmetry_type	text	'unitary'
trace_hash	bigint
types	jsonb	['DIR']
values	jsonb	[[1, '0.497065044235270616942562116673-0.0361554717208683160047047171458*I']]
z1	numeric	0.941836873017
z2	numeric	1.85740261469
z3	numeric	3.22109857867

{'Lhash': '1350799216113350769925956501499', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [2.6457513110645907, 0.0], 'a6': [0.0, 0.0], 'a7': [4.3778021186334675, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 20.697224203915887, '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': '2592.1', 'coefficient_field': 'CDF', 'conductor': 2592, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.6457513110645907, 0], [5.0, 0]], [[1.0, 0], [-4.3778021186334675, 0], [7.0, 0]], [[1.0, 0], [3.58257569495584, 0], [11.0, 0]], [[1.0, 0], [6.58257569495584, 0], [13.0, 0]], [[1.0, 0], [-1.7320508075688772, 0], [17.0, 0]], [[1.0, 0], [2.5504011116420413, 0], [19.0, 0]], [[1.0, 0], [-7.58257569495584, 0], [23.0, 0]], [[1.0, 0], [-6.109852926202345, 0], [29.0, 0]], [[1.0, 0], [-8.755604237266935, 0], [31.0, 0]], [[1.0, 0], [-2.58257569495584, 0], [37.0, 0]], [[1.0, 0], [1.8274010069914266, 0], [41.0, 0]], [[1.0, 0], [-2.5504011116420413, 0], [43.0, 0]], [[1.0, 0], [-8.0, 0], [47.0, 0]], [[1.0, 0], [-1.8274010069914266, 0], [53.0, 0]], [[1.0, 0], [-8.0, 0], [59.0, 0]], [[1.0, 0], [1.41742430504416, 0], [61.0, 0]], [[1.0, 0], [-2.5504011116420413, 0], [67.0, 0]], [[1.0, 0], [-0.41742430504416, 0], [71.0, 0]], [[1.0, 0], [6.16515138991168, 0], [73.0, 0]], [[1.0, 0], [-9.478604341917551, 0], [79.0, 0]], [[1.0, 0], [-15.16515138991168, 0], [83.0, 0]], [[1.0, 0], [12.31505605182724, 0], [89.0, 0]], [[1.0, 0], [5.16515138991168, 0], [97.0, 0]], [[1.0, 0], [-13.856406460551018, 0], [101.0, 0]], [[1.0, 0], [12.410406251249789, 0], [103.0, 0]], [[1.0, 0], [7.16515138991168, 0], [107.0, 0]], [[1.0, 0], [14.58257569495584, 0], [109.0, 0]], [[1.0, 0], [-19.24325928210275, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 19753447, 'index': 16, 'label': '2-2592-1.1-c1-0-16', 'leading_term': '2.57624957505545514100804858292', '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/2592/2/a/w/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 24}, 'plot_values': [2.576249575055455, 2.5711901977251728, 2.5559308410209023, 2.5302339266182927, 2.493723418868441, 2.445913394775562, 2.386245555149132, 2.3141335243178216, 2.2290115709727942, 2.1303853581301935, 2.0178824557791346, 1.891300573818324, 1.7506517448344812, 1.5962009657121745, 1.4284980678220227, 1.2484018156470367, 1.0570954326397901, 0.8560929278568298, 0.6472357582120497, 0.4326795204035608, 0.2148705336366792, -0.0034876435036102636, -0.21947751710297944, -0.43002031601788127, -0.6319372967149214, -0.8220187330077127, -0.9970993667053885, -1.1541388335476446, -1.2903053269866749, -1.4030605304890045, -1.4902436475454015, -1.5501521979401411, -1.5816171390573095, -1.584069821280418, -1.55759830484447, -1.5029906582057309, -1.4217630295357315, -1.3161705354880213, -1.1891993445559057, -1.0445387430135187, -0.8865324535995394, -0.7201090218103823, -0.5506916800687721, -0.3840887315263534, -0.22636614575560282, -0.08370470887254162, 0.037755300156101436, 0.13207834906674829, 0.19370272891533175, 0.21760995548606676, 0.19948965801730403, 0.13589491978205562, 0.024382980479704466, -0.13636368814897842, -0.3464406562382819, -0.6046534483786546, -0.9084817846197772, -1.2540790823632697, -1.636309250236275, -2.0488217793650096, -2.484165013013234, -2.93393628308166, -3.3889663768031, -3.839534578072987, -4.275609356695952, -4.687108698086054, -5.06417311807424, -5.397443633113297, -5.678336392613017, -5.89930535970917, -6.054084375311522, -6.137900175765339, -6.147648465818881, -6.082025974746366, -5.941612532746022, -5.728898574544895, -5.448255074163849, -5.105844695473135, -4.70947485468897, -4.268395372634832, -3.793045379623413, -3.294756053429199, -2.785417548671131, -2.277120042722366, -1.781780111537123, -1.3107645976569884, -0.8745246905522538, -0.48225306659350914, -0.14157660656563337, 0.14170358724546459, 0.3638144076491325, 0.523146415927636, 0.62031627686656, 0.6581516742846902, 0.6415970966499571, 0.5775417208208707, 0.47457352821149296, 0.3426666543265973, 0.19281168856338526, 0.03660109586121686, -0.11421598043494674, -0.24819365050668102, -0.35464698190404503, -0.4240900441434989, -0.44863704901098794, -0.42235020178451504, -0.34151940688850685, -0.20486113476737566, -0.013626495084684961, 0.22838821093384343, 0.514931578178221, 0.8374870853526535, 1.1855582772392008, 1.5470405196470751, 1.9086669976267248, 2.2565132868436617, 2.5765420036377185, 2.8551668655838074, 3.079814084280977, 3.2394584515441176, 3.3251118232532226, 3.330242970461623, 3.2511099358496436, 3.0869890475591926, 2.8402885064665813, 2.5165388464258975, 2.1242574082128147, 1.6746890796187162, 1.1814307307093306, 0.6599517986102901, 0.12702813276723637, -0.39988971024415604, -0.9033492260641073, -1.3665829096275688, -1.7741812221758542, -2.1127232678514756, -2.371337928774981, -2.5421704607562905, -2.620732938945676, -2.606121352076028, -2.5010874152297493, -2.311959100804605, -2.0484102363414047, -1.7230860205420597, -1.3510976841439197, -0.9494054859223668, -0.5361145108128983, -0.12971207376857183, 0.2517212895877605, 0.5912934200919864, 0.8740405025381065, 1.0875923039887365, 1.222732201964479, 1.2738255636360378, 1.2390953583012052, 1.1207302788403237, 0.9248178516464848, 0.6611027221713133, 0.34257817623901726, -0.015073360051425722, -0.3941679636506805, -0.7758068764754116, -1.1407280135996216, -1.4701845591094245, -1.7468109677482628, -1.955436559615019, -2.083808605549121, -2.123190316082149, -2.0688043446252884, -1.920099090919209, -1.6808229634544556, -1.3589004852930886, -0.9661133128185251, -0.5175984558474248, -0.03118480236314233, 0.4734029675877504, 0.9754372466129436, 1.454136147478898, 1.8896236405882183, 2.2638556572677575, 2.561467572555837, 2.770501588714639, 2.8829777125810554, 2.8952790473266794, 2.8083306975709172, 2.6275613280835834, 2.362646866212008, 2.027046496850293, 1.6373514445625137, 1.212476552266903, 0.7727328610736802, 0.33882583750832074, -0.06917177370390086, -0.4328215294015758, -0.7362449084086917, -0.9669256667446124, -1.1163471387640238, -1.1804304132038985, -1.1597488851060866, -1.0595056623633663, -0.8892721595276396, -0.662498355628686, -0.3958170136017776, -0.10817504624070702, 0.18016540826192431, 0.4487062797185233, 0.6778183857874337, 0.8498147530122344, 0.9499361353392992, 0.9671960713654368, 0.8950392580561114, 0.7317759669816621, 0.48076627296867025, 0.15034047021732366, -0.24654440954924545, -0.692898277357248, -1.1685148517725237, -1.6509725568133602, -2.116769999946604, -2.5425386872432663, -2.9062706152181406, -3.1884965519838033, -3.373352340203213, -3.449475402966821, -3.4106816163292875, -3.256383463710265, -2.9917233881353638, -2.6274108588365905, -2.179267121555214, -1.667497099548754, -1.1157226294882467, -0.5498243539655265, 0.003349579267156303, 0.5173419609597047, 0.967441557392417, 1.3319633914208624, 1.593385921760993, 1.7392834819852447, 1.7630024496070134, 1.664042634392915, 1.4481206452311037, 1.1269087242278462, 0.7174598398989818, 0.24134677679755018, -0.27644138088885617, -0.8087884718087907, -1.3278587096974388, -1.8065478588131474, -2.2199005762478947, -2.5464175175186865, -2.769181150070726, -2.876738523707319, -2.8636920450260326, -2.7309649310052206, -2.4857256436950346, -2.1409742783644656, -1.7148125638416472], 'positive_zeros': ['1.06559269239501104444819619025807', '2.31901180165068005305668461465057', '2.64945040223546785627414318880274', '4.49279648245163491476590927808305', '5.03935734986125837504910557106439', '5.48753397233011580630329976204461', '6.61368851286835753435581884405371', '7.48163028221718010838295218834450', '8.072155594231840799870282326905757', '8.839108134385151972460222952589029'], 'prelabel': '2-2592-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.549420205247685, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06559269239501104444819619026', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.31901180165068005305668461465', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.64945040223546785627414318880', 'prec': 100}}