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_5717.972'
a10	jsonb	[-0.9898072154472762, 0.14241375020871158]
a2	jsonb	[0.6468950323634471, 0.7625790562974404]
a3	jsonb	[0.7004692060777273, 0.7136826264782115]
a4	jsonb	[-0.16305363420698932, 0.9866172066064393]
a5	jsonb	[-0.5316996274324006, 0.8469329998224455]
a6	jsonb	[-0.09110937406038352, 0.9958408918890231]
a7	jsonb	[0.7882513163921484, -0.6153534449452974]
a8	jsonb	[-0.8578522043180632, 0.5138964832985724]
a9	jsonb	[-0.01868578267367663, 0.99982540552132]
accuracy	smallint
algebraic	boolean	True
analytic_conductor	double precision	614.3769750508712
analytic_normalization	numeric	0
bad_lfactors	jsonb	[[5717, [1]]]
bad_primes	bigint[]	[5717]
central_character	text	'5717.972'
coeff_info	jsonb	['x^5716 - 1', '0.999999395849336 + 0.00109922743909191*I', '\\\\zeta_{5716}']
coefficient_field	text
conductor	numeric	5717
conductor_radical	integer	5717
conjugate	text	'dirichlet_L_5717.2088'
credit	text
degree	smallint	1
dirichlet_coefficients	jsonb	['a^0', 'a^789', 'a^723', 'a^1578', 'a^1939', 'a^1512', 'a^5113', 'a^2367', 'a^1446', 'a^2728', 'a^4...
euler_factors	jsonb	[[1, 'a^789'], [1, 'a^723'], [1, 'a^1939'], [1, 'a^5113'], [1, 'a^4933'], [1, 'a^2916'], [1, 'a^1521...
euler_factors_factorization	jsonb
gamma_factors	jsonb	[[1], []]
group	text
index	smallint	0
label	text	'1-5717-5717.972-r1-0-0'
leading_term	text	'2.19914913447619757443042728586+1.16672785177100694816148605749*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/5717/972'
plot_delta	numeric	0.3125
plot_values	jsonb	[2.489480025179071, -0.4713720989696992, -5.548718479119588, -9.766169079407714, -9.931871729519013,...
positive_zeros	jsonb	['0.27774901123438394732078853515', '1.86232745055069750750980825683', '2.74445491894457268082648766...
precision	smallint
prelabel	text	'1-5717-5717.972-r1-0'
primitive	boolean	True
rational	boolean	False
root_analytic_conductor	double precision	614.3769750508712
root_angle	double precision	0.15526423055860503
root_number	text	'0.560709476769849222202084910607+0.828012610206198439058154673597*I'
self_dual	boolean	False
sign_arg	numeric	-0.25
spectral_label	text	'r1-0'
st_group	text	'mu(5716)'
symmetry_type	text	'unitary'
trace_hash	bigint
types	jsonb	['DIR']
values	jsonb	[[1, '1.11823429191103285480885480015+1.04679983880479061141267074735*I']]
z1	numeric	0.277749011234
z2	numeric	1.86232745055
z3	numeric	2.74445491894

{'Lhash': '1607550960964974376483365343149', 'a10': [0.220469726348554, 0.0766855458545191], 'a2': [-1.2730184775366242, 0.6159739895891186], 'a3': [0.0, 1.0], 'a4': [1.2411520882993288, -1.5682925408578003], 'a5': [-0.11671286687766246, -0.11671286687766246], 'a6': [-0.6159739895891186, -1.2730184775366242], 'a7': [0.0, -4.08371947470112], 'a8': [-0.613982128603178, 2.760982786211444], 'a9': [-1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.090715699489701, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [1.2730184775366242, -0.6159739895891186]]], [3, [[1.0, 0], [0, -1.0]]], [37, [[1.0, 0], [2.554430394364117, 5.520406267689796]]]], 'bad_primes': [2, 3, 37], 'central_character': '888.475', 'coefficient_field': 'CDF', 'conductor': 888, 'conductor_radical': 222, 'conjugate': '813982079846907073049689751139', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.2730184775366242, -0.6159739895891186]], [[1.0, 0], [0, -1.0]], [[1.0, 0], [0.11671286687766246, 0.11671286687766246], [0, 5.0]], [[1.0, 0], [0, 4.08371947470112], [-7.0, 0]], [[1.0, 0], [0, -0.1923225261488571], [-11.0, 0]], [[1.0, 0], [-3.2180701547263317, -3.2180701547263317], [0, 13.0]], [[1.0, 0], [2.8102869287574763, -2.8102869287574763], [0, -17.0]], [[1.0, 0], [1.7987020512097995, -1.7987020512097995], [0, -19.0]], [[1.0, 0], [2.6634150557033394, 2.6634150557033394], [0, 23.0]], [[1.0, 0], [-7.171483640480455, 7.171483640480455], [0, -29.0]], [[1.0, 0], [-6.960705341162248, 6.960705341162248], [0, -31.0]], [[1.0, 0], [2.554430394364117, 5.520406267689796]], [[1.0, 0], [0, -2.3573869398879754], [-41.0, 0]], [[1.0, 0], [-6.406512326212717, 6.406512326212717], [0, -43.0]], [[1.0, 0], [0, -2.3687816651289735], [-47.0, 0]], [[1.0, 0], [0, 1.8756587762678758], [-53.0, 0]], [[1.0, 0], [-4.293550472140958, 4.293550472140958], [0, -59.0]], [[1.0, 0], [7.775299268383704, -7.775299268383704], [0, -61.0]], [[1.0, 0], [0, 3.9871489983068185], [-67.0, 0]], [[1.0, 0], [0, 12.30566096992547], [-71.0, 0]], [[1.0, 0], [0, -1.0828081825580251], [-73.0, 0]], [[1.0, 0], [-1.2950148148262801, -1.2950148148262801], [0, 79.0]], [[1.0, 0], [-14.570187490722217, 0], [83.0, 0]], [[1.0, 0], [-5.635914319995096, -5.635914319995096], [0, 89.0]], [[1.0, 0], [4.760264827068956, -4.760264827068956], [0, -97.0]], [[1.0, 0], [-11.271024190555298, 0], [101.0, 0]], [[1.0, 0], [-9.006291068136482, 9.006291068136482], [0, -103.0]], [[1.0, 0], [19.39252053149587, 0], [107.0, 0]], [[1.0, 0], [1.5048380234682075, 1.5048380234682075], [0, 109.0]], [[1.0, 0], [0.3712834170327783, 0.3712834170327783], [0, 113.0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'id': 16462810, 'index': 41, 'label': '2-888-296.179-c1-0-41', '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/888/2/r/e/475/5', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 10}, 'plot_values': [0.8963062347756439, 0.9763441342951782, 1.0306997639193631, 1.056356534848863, 1.0478398125732065, 0.9985548258065964, 0.9024817138495881, 0.7559264274645964, 0.55909896958305, 0.31733945090811644, 0.04182953678085765, -0.25036479183548194, -0.5370485493217679, -0.7925245852395907, -0.9900746870486221, -1.1051580360164361, -1.119055007143496, -1.0225531674350357, -0.8191684715943447, -0.5273424071452241, -0.18107678483947465, 0.1714234320141114, 0.47132904451484037, 0.6549372155687787, 0.6612108750121323, 0.44038039050426875, -0.037420331800076596, -0.7747124601299978, -1.7417031302945318, -2.8749237900995266, -4.080264735208021, -5.240662955533103, -6.228037534651159, -6.918358988245845, -7.208095509084452, -7.029817461160105, -6.364567416077916, -5.248789815328498, -3.7741840642868323, -2.0797560456523234, -0.33648801458175986, 1.2737389238248793, 2.58225191097531, 3.457255723450724, 3.823352191634099, 3.673557506970952, 3.071433396022221, 2.1424161610787436, 1.0551828842284916, -0.004352780134774916, -0.8623917237082595, -1.3851069666450264, -1.5001688260493187, -1.207986047254366, -0.5803864786483542, 0.25333604650650504, 1.1307374357936795, 1.8865915238671442, 2.383689462073761, 2.5381744853460604, 2.3343993063493342, 1.8262260331477063, 1.1243366902339453, 0.37197816480738016, -0.2859588034666042, -0.7340778501585264, -0.9111451377253103, -0.822796443571286, -0.5392407690102266, -0.17814693786472324, 0.1237680872718213, 0.24423871953830278, 0.10642267583170267, -0.29999524884665035, -0.9129227308506005, -1.609226756806128, -2.231397625496062, -2.623842250739821, -2.670573422028027, -2.3253266851726044, -1.6265142318435788, -0.6927058981966681, 0.30117398260906564, 1.1620545012401522, 1.7227071847166553, 1.8810715572971686, 1.6251373904144961, 1.0367321392278166, 0.27251355342136957, -0.4738981557952145, -1.0197822991975674, -1.2393729205332882, -1.096235941019483, -0.6530779715989475, -0.05554121244017943, 0.5068166948190509, 0.8529731048874613, 0.8628565468405238, 0.5154952972181485, -0.0983775797437658, -0.7943937397499178, -1.3405091145524837, -1.5203643198673185, -1.1981228931774053, -0.36729868111117275, 0.8309356842629914, 2.1274246438780597, 3.180646793379279, 3.6566121810565124, 3.3141896716182773, 2.0743075969372944, 0.054237020563241325, -2.4439977151705454, -4.99090473538309, -7.120649370247439, -8.434971285780813, -8.694684552229887, -7.875737193170355, -6.175035884898937, -3.9635848542908048, -1.697840469414946, 0.18894825224845155, 1.3882080268798476, 1.7846977299659093, 1.4750761450088978, 0.7321129318587751, -0.07546588837561037, -0.58582708796155, -0.5420035397555818, 0.14103299290188875, 1.3576014060013235, 2.8448869071404594, 4.2585067794583775, 5.268291871120882, 5.647284625992976, 5.329392686140811, 4.420518007574228, 3.1615767293990578, 1.8556716394632222, 0.7817301956515295, 0.12024238249477147, -0.08761264106888215, 0.06318690865322736, 0.3856372549920948, 0.6702519729483362, 0.7569547813652611, 0.5861077541704618, 0.2126821124971683, -0.22011514951877975, -0.5379836908982378, -0.6033961219190911, -0.37044913165163684, 0.09284602452561863, 0.6235349142158255, 1.018610792471377, 1.107843170998538, 0.8196103428106297, 0.2160792113334574, -0.5165215796238491, -1.1220801532348397, -1.3574746306800538, -1.0776159175824853, -0.293754790703272, 0.8166028373605856, 1.9548627781943664, 2.790186992405666, 3.0652611367618934, 2.6849013382493276, 1.7570015984169878, 0.5692512564008219, -0.49470905611209753, -1.0758141095245548, -0.9593955962073957, -0.15492343399126512, 1.0928913838146275, 2.3694285623254854, 3.2152814811171155, 3.2741970280200574, 2.417459682260493, 0.8034630657301426, -1.150138062101461, -2.8775404612668125, -3.8284220056137204, -3.635473074668713, -2.234127279422681, 0.10402647705094649, 2.8369241756464234, 5.299141128056014, 6.887258845076748, 7.227926815171343, 6.278003995857834, 4.327075523152444, 1.9029837069562883, -0.3888830060725852, -2.04161673106295, -2.7834562147979405, -2.634257557191956, -1.86774621376587, -0.8964032881855881, -0.12054233876779687, 0.20648192127425682, 0.0522274075848291, -0.4042340266366133, -0.8581726242154561, -1.008154107709382, -0.680313275595489, 0.0973034576276079, 1.0971249681917608, 1.970172831978547, 2.371623841430509, 2.08842725490126, 1.1227332390339595, -0.2994078936210445, -1.7979522703038398, -2.9631559790350663, -3.490582519391021, -3.2793427417987573, -2.4593177107213298, -1.3386326113407425, -0.29123140073122256, 0.37432119957735444, 0.517454709741968, 0.203353885413527, -0.336092165764898, -0.8015513756387667, -0.9469132082340121, -0.6749905910070991, -0.07185545959902524, 0.6328025403989898, 1.163227381152393, 1.3143354827950204, 1.0410483787754334, 0.4837890797551792, -0.08170215178006938, -0.352311525600501, -0.12185065370713086, 0.6275645801916309, 1.7050467468409138, 2.772721968178478, 3.468980258424483, 3.5471723909393367, 2.975554080678407, 1.9570670163242134, 0.8572214026842181, 0.06407545578639931, -0.16757842453258895, 0.173437358417333, 0.8367049900698, 1.397982809160213, 1.4253848963024447, 0.6640298043202104, -0.832235426992897, -2.6781560978624386, -4.261863236750814, -4.948492235936729, -4.314751679531252, -2.3303016674842634], 'positive_zeros': ['1.26813410625573710010870648154457', '2.56324695308040664029632799110137', '3.24222408539706369426126609275293', '5.02485499895459719699197062765629', '6.12444802610159861530111787253524', '6.83881654675125182461951237080877', '7.941849642391090724260912645216578', '8.692182993693068094122540867295845', '9.041387407447475863966166971272431', '10.21145348848852952510747462312858'], 'prelabel': '2-888-296.179-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6628397810401023, 'root_angle': 0.07770831624689113, 'root_number': '0.8831524047747463 + 0.4690861647294478*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0777083162469', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.26813410625573710010870648154', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.56324695308040664029632799110', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.24222408539706369426126609275', 'prec': 100}}