# lfunc_search downloaded from the LMFDB on 28 July 2026.
# Search link: https://www.lmfdb.org/L/2/71
# Query "{'degree': 2, 'conductor': 71}" returned 14223 lfunc_searchs, sorted by root analytic conductor.

# Each entry in the following data list has the form:
#    [Label, $\alpha$, $A$, $d$, $N$, $\chi$, $\mu$, $\nu$, $w$, prim, arith, $\mathbb{Q}$, self-dual, $\operatorname{Arg}(\epsilon)$, $r$, First zero, Origin]
# For more details, see the definitions at the bottom of the file.



"2-71-71.70-c0-0-0"	0.1882381892628145	0.035433615896943174	2	71	"71.70"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	2.19448912992332732423794638884	["ModularForm/GL2/Q/holomorphic/71/1/b/a/70/1", "ArtinRepresentation/2.71.7t2.a.c"]
"2-71-71.70-c0-0-1"	0.1882381892628145	0.035433615896943174	2	71	"71.70"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	3.39979849702102685652285544820	["ModularForm/GL2/Q/holomorphic/71/1/b/a/70/2", "ArtinRepresentation/2.71.7t2.a.a"]
"2-71-71.70-c0-0-2"	0.1882381892628145	0.035433615896943174	2	71	"71.70"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	3.95531641366854447656333489742	["ModularForm/GL2/Q/holomorphic/71/1/b/a/70/3", "ArtinRepresentation/2.71.7t2.a.b"]
"2-71-1.1-c1-0-0"	0.7529527570512582	0.566937854351091	2	71	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.26812303783241273521302837971	["ModularForm/GL2/Q/holomorphic/71/2/a/b/1/1"]
"2-71-1.1-c1-0-1"	0.7529527570512582	0.566937854351091	2	71	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.05199077952259115106032887393	["ModularForm/GL2/Q/holomorphic/71/2/a/a/1/1"]
"2-71-1.1-c1-0-2"	0.7529527570512582	0.566937854351091	2	71	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.30588593320103744070894588986	["ModularForm/GL2/Q/holomorphic/71/2/a/a/1/2"]
"2-71-1.1-c1-0-3"	0.7529527570512582	0.566937854351091	2	71	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	3.08088599590281968403406987383	["ModularForm/GL2/Q/holomorphic/71/2/a/a/1/3"]
"2-71-1.1-c1-0-4"	0.7529527570512582	0.566937854351091	2	71	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	3.29794053663541918178362444025	["ModularForm/GL2/Q/holomorphic/71/2/a/b/1/3"]
"2-71-1.1-c1-0-5"	0.7529527570512582	0.566937854351091	2	71	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	3.36914581499645387434156530848	["ModularForm/GL2/Q/holomorphic/71/2/a/b/1/2"]
"2-71-71.10-c1-0-0"	0.7529527570512582	0.566937854351091	2	71	"71.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.28395828602351236	0	1.12012321968133748876735503586	["ModularForm/GL2/Q/holomorphic/71/2/g/a/10/2"]
"2-71-71.10-c1-0-1"	0.7529527570512582	0.566937854351091	2	71	"71.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.21434681802836428	0	1.19737804589314099882872835449	["ModularForm/GL2/Q/holomorphic/71/2/g/a/10/1"]
"2-71-71.10-c1-0-2"	0.7529527570512582	0.566937854351091	2	71	"71.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.030119722628940773	0	2.75879347602561312182711377485	["ModularForm/GL2/Q/holomorphic/71/2/g/a/10/5"]
"2-71-71.10-c1-0-3"	0.7529527570512582	0.566937854351091	2	71	"71.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.09984061675755519	0	3.36627685239139973320555476542	["ModularForm/GL2/Q/holomorphic/71/2/g/a/10/3"]
"2-71-71.10-c1-0-4"	0.7529527570512582	0.566937854351091	2	71	"71.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.10576663437507701	0	3.76526042190777589546207758867	["ModularForm/GL2/Q/holomorphic/71/2/g/a/10/4"]
"2-71-71.12-c1-0-0"	0.7529527570512582	0.566937854351091	2	71	"71.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.17146980387847768	0	2.60298646792661262992627362504	["ModularForm/GL2/Q/holomorphic/71/2/g/a/12/5"]
"2-71-71.12-c1-0-1"	0.7529527570512582	0.566937854351091	2	71	"71.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.14347691295192597	0	2.61860220967162330337517658416	["ModularForm/GL2/Q/holomorphic/71/2/g/a/12/2"]
"2-71-71.12-c1-0-2"	0.7529527570512582	0.566937854351091	2	71	"71.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.009977406152288456	0	3.10942514218036835316856979385	["ModularForm/GL2/Q/holomorphic/71/2/g/a/12/4"]
"2-71-71.12-c1-0-3"	0.7529527570512582	0.566937854351091	2	71	"71.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2937468676059463	0	3.61021847168725850569517794647	["ModularForm/GL2/Q/holomorphic/71/2/g/a/12/3"]
"2-71-71.12-c1-0-4"	0.7529527570512582	0.566937854351091	2	71	"71.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.31366347352028096	0	4.99659416335435403743600351846	["ModularForm/GL2/Q/holomorphic/71/2/g/a/12/1"]
"2-71-71.15-c1-0-0"	0.7529527570512582	0.566937854351091	2	71	"71.15"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.395004962345523	0	1.45024294668587798918381003040	["ModularForm/GL2/Q/holomorphic/71/2/g/a/15/1"]
"2-71-71.15-c1-0-1"	0.7529527570512582	0.566937854351091	2	71	"71.15"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.17433058443682894	0	2.35835351724345313939987369306	["ModularForm/GL2/Q/holomorphic/71/2/g/a/15/2"]
"2-71-71.15-c1-0-2"	0.7529527570512582	0.566937854351091	2	71	"71.15"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.010113174817233396	0	2.41933572842501425598137893375	["ModularForm/GL2/Q/holomorphic/71/2/g/a/15/3"]
"2-71-71.15-c1-0-3"	0.7529527570512582	0.566937854351091	2	71	"71.15"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.21620653046519447	0	3.86102612033339527346155613269	["ModularForm/GL2/Q/holomorphic/71/2/g/a/15/5"]
"2-71-71.15-c1-0-4"	0.7529527570512582	0.566937854351091	2	71	"71.15"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3407120309762113	0	4.20806712963640638181319480967	["ModularForm/GL2/Q/holomorphic/71/2/g/a/15/4"]
"2-71-71.16-c1-0-0"	0.7529527570512582	0.566937854351091	2	71	"71.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.18489968930982817	0	0.948617467263298194537120040255	["ModularForm/GL2/Q/holomorphic/71/2/g/a/16/1"]
"2-71-71.16-c1-0-1"	0.7529527570512582	0.566937854351091	2	71	"71.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.09395463909588622	0	2.63497387219329658279456496839	["ModularForm/GL2/Q/holomorphic/71/2/g/a/16/2"]
"2-71-71.16-c1-0-2"	0.7529527570512582	0.566937854351091	2	71	"71.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.06728737594295282	0	2.92917158021020873578250547458	["ModularForm/GL2/Q/holomorphic/71/2/g/a/16/5"]
"2-71-71.16-c1-0-3"	0.7529527570512582	0.566937854351091	2	71	"71.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2990211556681014	0	3.06426378338402208826292085238	["ModularForm/GL2/Q/holomorphic/71/2/g/a/16/3"]
"2-71-71.16-c1-0-4"	0.7529527570512582	0.566937854351091	2	71	"71.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.004559006195158205	0	3.14854463579830299302408403715	["ModularForm/GL2/Q/holomorphic/71/2/g/a/16/4"]
"2-71-71.18-c1-0-0"	0.7529527570512582	0.566937854351091	2	71	"71.18"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4955919370495039	0	0.43488487700746976454227933574	["ModularForm/GL2/Q/holomorphic/71/2/g/a/18/1"]
"2-71-71.18-c1-0-1"	0.7529527570512582	0.566937854351091	2	71	"71.18"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.08542447923281853	0	1.64493547072648967899120937298	["ModularForm/GL2/Q/holomorphic/71/2/g/a/18/2"]
"2-71-71.18-c1-0-2"	0.7529527570512582	0.566937854351091	2	71	"71.18"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.18830419401922163	0	1.72783365932276603986006976257	["ModularForm/GL2/Q/holomorphic/71/2/g/a/18/4"]
"2-71-71.18-c1-0-3"	0.7529527570512582	0.566937854351091	2	71	"71.18"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.03358711122849863	0	3.46385581346051263769017061319	["ModularForm/GL2/Q/holomorphic/71/2/g/a/18/5"]
"2-71-71.18-c1-0-4"	0.7529527570512582	0.566937854351091	2	71	"71.18"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.30021632420145505	0	3.67029620305546616850044424172	["ModularForm/GL2/Q/holomorphic/71/2/g/a/18/3"]
"2-71-71.19-c1-0-0"	0.7529527570512582	0.566937854351091	2	71	"71.19"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3407120309762113	0	1.42093127401725229603429736997	["ModularForm/GL2/Q/holomorphic/71/2/g/a/19/4"]
"2-71-71.19-c1-0-1"	0.7529527570512582	0.566937854351091	2	71	"71.19"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.010113174817233396	0	2.69010302283295469022832294942	["ModularForm/GL2/Q/holomorphic/71/2/g/a/19/3"]
"2-71-71.19-c1-0-2"	0.7529527570512582	0.566937854351091	2	71	"71.19"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.21620653046519447	0	2.79076349461045928980934240687	["ModularForm/GL2/Q/holomorphic/71/2/g/a/19/5"]
"2-71-71.19-c1-0-3"	0.7529527570512582	0.566937854351091	2	71	"71.19"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.17433058443682894	0	3.03441496665753651778186429294	["ModularForm/GL2/Q/holomorphic/71/2/g/a/19/2"]
"2-71-71.19-c1-0-4"	0.7529527570512582	0.566937854351091	2	71	"71.19"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.395004962345523	0	3.81515232127771226077433115585	["ModularForm/GL2/Q/holomorphic/71/2/g/a/19/1"]
"2-71-71.2-c1-0-0"	0.7529527570512582	0.566937854351091	2	71	"71.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3720954017573725	0	1.91417892293011410463655277914	["ModularForm/GL2/Q/holomorphic/71/2/g/a/2/1"]
"2-71-71.2-c1-0-1"	0.7529527570512582	0.566937854351091	2	71	"71.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.21864381759829707	0	1.94363854713858606004886116236	["ModularForm/GL2/Q/holomorphic/71/2/g/a/2/2"]
"2-71-71.2-c1-0-2"	0.7529527570512582	0.566937854351091	2	71	"71.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.10745718456020979	0	2.87020753756337001888424635394	["ModularForm/GL2/Q/holomorphic/71/2/g/a/2/4"]
"2-71-71.2-c1-0-3"	0.7529527570512582	0.566937854351091	2	71	"71.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1657241301696254	0	3.21434333943589672835919175617	["ModularForm/GL2/Q/holomorphic/71/2/g/a/2/3"]
"2-71-71.2-c1-0-4"	0.7529527570512582	0.566937854351091	2	71	"71.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.23435764762720812	0	3.43750685215308888425911336432	["ModularForm/GL2/Q/holomorphic/71/2/g/a/2/5"]
"2-71-71.20-c1-0-0"	0.7529527570512582	0.566937854351091	2	71	"71.20"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3278009330738928	0	1.78878284025837128870499305264	["ModularForm/GL2/Q/holomorphic/71/2/d/a/20/5"]
"2-71-71.20-c1-0-1"	0.7529527570512582	0.566937854351091	2	71	"71.20"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.012617037804039125	0	2.28352570042797769793434981136	["ModularForm/GL2/Q/holomorphic/71/2/d/a/20/3"]
"2-71-71.20-c1-0-2"	0.7529527570512582	0.566937854351091	2	71	"71.20"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.007171015628091952	0	2.93257205009479644072130769887	["ModularForm/GL2/Q/holomorphic/71/2/d/a/20/4"]
"2-71-71.20-c1-0-3"	0.7529527570512582	0.566937854351091	2	71	"71.20"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2863398582801385	0	3.64601277168255406099853554172	["ModularForm/GL2/Q/holomorphic/71/2/d/a/20/2"]
"2-71-71.20-c1-0-4"	0.7529527570512582	0.566937854351091	2	71	"71.20"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4335873448707345	0	4.87357857625262652394753936249	["ModularForm/GL2/Q/holomorphic/71/2/d/a/20/1"]
"2-71-71.24-c1-0-0"	0.7529527570512582	0.566937854351091	2	71	"71.24"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.34956589327973836	0	1.00394989430074700913269007743	["ModularForm/GL2/Q/holomorphic/71/2/g/a/24/2"]
"2-71-71.24-c1-0-1"	0.7529527570512582	0.566937854351091	2	71	"71.24"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3535744728436243	0	1.75875530600162743634763333646	["ModularForm/GL2/Q/holomorphic/71/2/g/a/24/1"]
"2-71-71.24-c1-0-2"	0.7529527570512582	0.566937854351091	2	71	"71.24"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.10446451261488451	0	2.11718572517770706731518622210	["ModularForm/GL2/Q/holomorphic/71/2/g/a/24/4"]
"2-71-71.24-c1-0-3"	0.7529527570512582	0.566937854351091	2	71	"71.24"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1938149660696205	0	3.01055663714212792583317302155	["ModularForm/GL2/Q/holomorphic/71/2/g/a/24/3"]
"2-71-71.24-c1-0-4"	0.7529527570512582	0.566937854351091	2	71	"71.24"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.19543909842380713	0	4.16099973836991005708294008426	["ModularForm/GL2/Q/holomorphic/71/2/g/a/24/5"]
"2-71-71.25-c1-0-0"	0.7529527570512582	0.566937854351091	2	71	"71.25"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3921747779287869	0	0.870737830100476689953827958645	["ModularForm/GL2/Q/holomorphic/71/2/c/a/25/2"]
"2-71-71.25-c1-0-1"	0.7529527570512582	0.566937854351091	2	71	"71.25"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.24726891681074492	0	1.23039057956880142318659054125	["ModularForm/GL2/Q/holomorphic/71/2/c/a/25/4"]
"2-71-71.25-c1-0-2"	0.7529527570512582	0.566937854351091	2	71	"71.25"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.09116013392254367	0	2.09012560064350587838274915855	["ModularForm/GL2/Q/holomorphic/71/2/c/a/25/3"]
"2-71-71.25-c1-0-3"	0.7529527570512582	0.566937854351091	2	71	"71.25"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.03161905106674498	0	2.77049752772748932450342951887	["ModularForm/GL2/Q/holomorphic/71/2/c/a/25/1"]
"2-71-71.25-c1-0-4"	0.7529527570512582	0.566937854351091	2	71	"71.25"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.09898477759533043	0	3.40442502883847188904352166878	["ModularForm/GL2/Q/holomorphic/71/2/c/a/25/5"]
"2-71-71.27-c1-0-0"	0.7529527570512582	0.566937854351091	2	71	"71.27"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.409536017543632	0	0.34745173103589585126910798132	["ModularForm/GL2/Q/holomorphic/71/2/g/a/27/1"]
"2-71-71.27-c1-0-1"	0.7529527570512582	0.566937854351091	2	71	"71.27"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1453993130893772	0	1.82281972604254060364928047932	["ModularForm/GL2/Q/holomorphic/71/2/g/a/27/3"]
"2-71-71.27-c1-0-2"	0.7529527570512582	0.566937854351091	2	71	"71.27"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.0779285964756878	0	2.77803399961095841509935828543	["ModularForm/GL2/Q/holomorphic/71/2/g/a/27/2"]
"2-71-71.27-c1-0-3"	0.7529527570512582	0.566937854351091	2	71	"71.27"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.10753896945178218	0	3.14558157786479768617983352585	["ModularForm/GL2/Q/holomorphic/71/2/g/a/27/4"]
"2-71-71.27-c1-0-4"	0.7529527570512582	0.566937854351091	2	71	"71.27"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.29990261218112607	0	4.60683600991522703572665823973	["ModularForm/GL2/Q/holomorphic/71/2/g/a/27/5"]
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"2-71-1.1-c21-0-74"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.0	0	0.929896994895546027734856652358	["ModularForm/GL2/Q/holomorphic/71/22/a/b/1/62"]
"2-71-1.1-c21-0-75"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	0.951064640197860563651679950056	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/21"]
"2-71-1.1-c21-0-76"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.01824858810888603623280944903	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/34"]
"2-71-1.1-c21-0-77"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.0	0	1.02142491686295191451001063382	["ModularForm/GL2/Q/holomorphic/71/22/a/b/1/17"]
"2-71-1.1-c21-0-78"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.02310884584827561061974933161	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/41"]
"2-71-1.1-c21-0-79"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.0	0	1.07167703587750318258472924641	["ModularForm/GL2/Q/holomorphic/71/22/a/b/1/65"]
"2-71-1.1-c21-0-8"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.0	0	0.16419011286144277212469646191	["ModularForm/GL2/Q/holomorphic/71/22/a/b/1/38"]
"2-71-1.1-c21-0-80"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.08502876368674540799428927861	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/27"]
"2-71-1.1-c21-0-81"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.09754560375748922269317614392	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/13"]
"2-71-1.1-c21-0-82"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.12648346350763780832476820034	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/22"]
"2-71-1.1-c21-0-83"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.14325868042617512231744667036	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/49"]
"2-71-1.1-c21-0-84"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.0	0	1.15149518761876941341554659508	["ModularForm/GL2/Q/holomorphic/71/22/a/b/1/49"]
"2-71-1.1-c21-0-85"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.15412191223816883906164524295	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/37"]
"2-71-1.1-c21-0-86"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.16659032108085367160489397974	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/28"]
"2-71-1.1-c21-0-87"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.16958443963039230080242476001	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/4"]
"2-71-1.1-c21-0-88"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.17500013776196703237155126600	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/40"]
"2-71-1.1-c21-0-89"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.0	0	1.18236154176640211660359596028	["ModularForm/GL2/Q/holomorphic/71/22/a/b/1/53"]
"2-71-1.1-c21-0-9"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.0	0	0.18119257208732941920087971684	["ModularForm/GL2/Q/holomorphic/71/22/a/b/1/34"]
"2-71-1.1-c21-0-90"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.18295711088258922165617710032	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/8"]
"2-71-1.1-c21-0-91"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.19309051498279324838582701313	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/38"]
"2-71-1.1-c21-0-92"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.22959415219591718537371634338	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/50"]
"2-71-1.1-c21-0-93"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.23227578873768298365476816891	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/20"]
"2-71-1.1-c21-0-94"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.0	0	1.23983596806297637842287403800	["ModularForm/GL2/Q/holomorphic/71/22/a/b/1/37"]
"2-71-1.1-c21-0-95"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.0	0	1.26430186306138356113858271684	["ModularForm/GL2/Q/holomorphic/71/22/a/b/1/59"]
"2-71-1.1-c21-0-96"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.27923604150580280302518876897	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/39"]
"2-71-1.1-c21-0-97"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.0	0	1.28194306381615662553017665032	["ModularForm/GL2/Q/holomorphic/71/22/a/b/1/63"]
"2-71-1.1-c21-0-98"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.28224752294951017881795885966	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/19"]
"2-71-1.1-c21-0-99"	14.086479845717811	198.4289144438141	2	71	"1.1"	[]	[[10.5, 0.0]]	21	true	true	false	true	0.5	1	1.30176246363968255370529993426	["ModularForm/GL2/Q/holomorphic/71/22/a/a/1/30"]


# Label --
#    Each L-function $L$ has a label of the form d-N-q.k-x-y-i, where

#     * $d$ is the degree of $L$.
#     * $N$ is the conductor of $L$.  When $N$ is a perfect power $m^n$ we write $N$ as $m$e$n$, since $N$ can be very large for some imprimitive L-functions.
#     * q.k is the label of the primitive Dirichlet character from which the central character is induced.
#     * x-y is the spectral label encoding the $\mu_j$ and $\nu_j$ in the analytically normalized functional equation.
#     * i is a non-negative integer disambiguating between L-functions that would otherwise have the same label.


#$\alpha$ (root_analytic_conductor) --
#    If $d$ is the degree of the L-function $L(s)$, the **root analytic conductor** $\alpha$ of $L$ is the $d$th root of the analytic conductor of $L$.  It plays a role analogous to the root discriminant for number fields.


#$A$ (analytic_conductor) --
#    The **analytic conductor** of an L-function $L(s)$ with infinity factor $L_{\infty}(s)$ and conductor $N$ is the real number
#    \[
#    A := \mathrm{exp}\left(2\mathrm{Re}\left(\frac{L_{\infty}'(1/2)}{L_{\infty}(1/2)}\right)\right)N.
#    \]



#$d$ (degree) --
#    The **degree** of an L-function is the number $J + 2K$ of Gamma factors occurring in its functional equation

#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s).
#    \]

#    The degree appears as the first component of the Selberg data of $L(s).$ In all known cases it is the degree of the polynomial of the inverse of the Euler factor at any prime not dividing the conductor.



#$N$ (conductor) --
#    The **conductor** of an L-function is the integer $N$  occurring in its functional equation

#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s).
#    \]


#    The conductor of an analytic L-function is the second component in the Selberg data. For a Dirichlet L-function
#     associated with a primitive Dirichlet character, the conductor of the L-function is the same as the conductor of the character. For a primitive L-function associated with a cusp form $\phi$ on $GL(2)/\mathbb Q$, the conductor of the L-function is the same as the level of $\phi$.

#    In the literature, the word _level_ is sometimes used instead of _conductor_.


#$\chi$ (central_character) --
#    An L-function has an Euler product of the form
#    $L(s) = \prod_p L_p(p^{-s})^{-1}$
#    where $L_p(x) = 1 + a_p x + \ldots + (-1)^d \chi(p) x^d$. The character $\chi$ is a Dirichlet character mod $N$ and is called **central character** of the L-function.
#    Here, $N$ is the conductor of $L$.


#$\mu$ (mus) --
#    All known analytic L-functions have a **functional equation** that can be written in the form
#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s),
#    \]
#    where $N$ is an integer, $\Gamma_{\mathbb R}$ and $\Gamma_{\mathbb C}$ are defined in terms of the $\Gamma$-function, $\mathrm{Re}(\mu_j) = 0 \ \mathrm{or} \ 1$ (assuming Selberg's eigenvalue conjecture), and $\mathrm{Re}(\nu_k)$ is a positive integer
#    or half-integer,
#    \[
#    \sum \mu_j + 2 \sum \nu_k \ \ \ \ \text{is real},
#    \]
#    and $\varepsilon$ is the sign of the functional equation.
#    With those restrictions on the spectral parameters, the
#    data in the functional equation is specified uniquely.  The integer $d = J + 2 K$
#    is the degree of the L-function. The integer $N$ is  the conductor (or level)
#    of the L-function.  The pair $[J,K]$ is the signature of the L-function.  The parameters
#    in the functional equation can be used to make up the 4-tuple called the Selberg data.


#    The axioms of the Selberg class are less restrictive than
#    given above.

#    Note that the functional equation above has the central point at $s=1/2$, and relates $s\leftrightarrow 1-s$.

#    For many L-functions there is another normalization which is natural. The corresponding functional equation relates $s\leftrightarrow w+1-s$ for some positive integer $w$,
#    called the motivic weight of the L-function. The central point is at $s=(w+1)/2$, and the arithmetically normalized Dirichlet coefficients $a_n n^{w/2}$ are algebraic integers.



#$\nu$ (nus) --
#    All known analytic L-functions have a **functional equation** that can be written in the form
#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s),
#    \]
#    where $N$ is an integer, $\Gamma_{\mathbb R}$ and $\Gamma_{\mathbb C}$ are defined in terms of the $\Gamma$-function, $\mathrm{Re}(\mu_j) = 0 \ \mathrm{or} \ 1$ (assuming Selberg's eigenvalue conjecture), and $\mathrm{Re}(\nu_k)$ is a positive integer
#    or half-integer,
#    \[
#    \sum \mu_j + 2 \sum \nu_k \ \ \ \ \text{is real},
#    \]
#    and $\varepsilon$ is the sign of the functional equation.
#    With those restrictions on the spectral parameters, the
#    data in the functional equation is specified uniquely.  The integer $d = J + 2 K$
#    is the degree of the L-function. The integer $N$ is  the conductor (or level)
#    of the L-function.  The pair $[J,K]$ is the signature of the L-function.  The parameters
#    in the functional equation can be used to make up the 4-tuple called the Selberg data.


#    The axioms of the Selberg class are less restrictive than
#    given above.

#    Note that the functional equation above has the central point at $s=1/2$, and relates $s\leftrightarrow 1-s$.

#    For many L-functions there is another normalization which is natural. The corresponding functional equation relates $s\leftrightarrow w+1-s$ for some positive integer $w$,
#    called the motivic weight of the L-function. The central point is at $s=(w+1)/2$, and the arithmetically normalized Dirichlet coefficients $a_n n^{w/2}$ are algebraic integers.



#$w$ (motivic_weight) --
#    The **motivic weight** (or **arithmetic weight**) of an arithmetic L-function with analytic normalization $L_{an}(s)=\sum_{n=1}^\infty a_nn^{-s}$ is the least nonnegative integer $w$ for which $a_nn^{w/2}$ is an algebraic integer for all $n\ge 1$.

#    If the L-function arises from a motive, then the weight of the motive has the
#    same parity as the motivic weight of the L-function, but the weight of the motive
#    could be larger.  This apparent discrepancy comes from the fact that a Tate twist
#    increases the weight of the motive.  This corresponds to the change of variables
#    $s \mapsto s + j$ in the L-function of the motive.


#prim (primitive) --
#    An L-function is <b>primitive</b> if it cannot be written as a product of nontrivial L-functions.  The "trivial L-function" is the constant function $1$.


#arith (algebraic) --
#    An L-function $L(s) = \sum_{n=1}^{\infty} a_n n^{-s}$  is called **arithmetic** if its Dirichlet coefficients $a_n$ are algebraic numbers.


#$\mathbb{Q}$ (rational) --
#    A **rational** L-function $L(s)$ is an arithmetic L-function with coefficient field $\Q$; equivalently, its Euler product in the arithmetic normalization can be written as a product over rational primes
#    \[
#    L(s)=\prod_pL_p(p^{-s})^{-1}
#    \]
#    with $L_p\in \Z[T]$.


#self-dual (self_dual) --
#    An L-function $L(s) = \sum_{n=1}^{\infty} \frac{a_n}{n^s}$ is called **self-dual** if its Dirichlet coefficients $a_n$ are real.


#$\operatorname{Arg}(\epsilon)$ (root_angle) --
#    The **root angle** of an L-function is the argument of its root number, as a real number $\alpha$ with $-0.5 < \alpha \le 0.5$.


#$r$ (order_of_vanishing) --
#    The **analytic rank** of an L-function $L(s)$ is its order of vanishing at its central point.

#    When the analytic rank $r$ is positive, the value listed in the LMFDB is typically an upper bound that is believed to be tight (in the sense that there are known to be $r$ zeroes located very near to the central point).


#First zero (z1) --
#    The **zeros** of an L-function $L(s)$ are the complex numbers $\rho$ for which $L(\rho)=0$.

#    Under the Riemann Hypothesis, every non-trivial zero $\rho$ lies on the critical line $\Re(s)=1/2$ (in the analytic normalization).

#    The **lowest zero** of an L-function $L(s)$ is the least $\gamma>0$ for which $L(1/2+i\gamma)=0$. Note that even when $L(1/2)=0$, the lowest zero is by definition a positive real number.


#Origin (instance_urls) --
#    L-functions arise from many different sources. Already in degree 2 we have examples of
#    L-functions associated with holomorphic cusp forms, with Maass forms, with elliptic curves, with characters of number fields (Hecke characters), and with 2-dimensional representations of the Galois group of a number field (Artin L-functions).

#    Sometimes an L-function may arise from more than one source. For example, the L-functions associated with elliptic curves are also associated with weight 2 cusp forms. A goal of the Langlands program ostensibly is to prove that any degree $d$ L-function is associated with an automorphic form on $\mathrm{GL}(d)$. Because of this representation theoretic genesis, one can associate an L-function not only to an automorphic representation but also to symmetric powers, or exterior powers of that representation, or to the tensor product of two representations (the Rankin-Selberg product of two L-functions).