
# lfunc_search downloaded from the LMFDB on 30 May 2026.
# Search link: https://www.lmfdb.org/L/2/6^3/216.11/c1-0
# Query "{'degree': 2, 'conductor': 216, 'spectral_label': 'c1-0'}" returned 544 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.



"2-6e3-1.1-c1-0-0"	1.3133044900782367	1.7247686836596572	2	216	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.64081961055094255152301138209	["EllipticCurve/Q/216/b", "ModularForm/GL2/Q/holomorphic/216/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/216/2/a/b"]
"2-6e3-1.1-c1-0-1"	1.3133044900782367	1.7247686836596572	2	216	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.73582051333148490489274132763	["EllipticCurve/Q/216/c", "ModularForm/GL2/Q/holomorphic/216/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/216/2/a/c"]
"2-6e3-1.1-c1-0-2"	1.3133044900782367	1.7247686836596572	2	216	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.81832624891237728767312244270	["EllipticCurve/Q/216/d", "ModularForm/GL2/Q/holomorphic/216/2/a/d/1/1", "ModularForm/GL2/Q/holomorphic/216/2/a/d"]
"2-6e3-1.1-c1-0-3"	1.3133044900782367	1.7247686836596572	2	216	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	3.09788365205681643264055516753	["EllipticCurve/Q/216/a", "ModularForm/GL2/Q/holomorphic/216/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/216/2/a/a"]
"2-6e3-216.11-c1-0-0"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4211713875133685	0	0.02819849338131207927940388931	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/1"]
"2-6e3-216.11-c1-0-1"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.28548431838358723	0	0.06532386590356819459319581698	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/15"]
"2-6e3-216.11-c1-0-10"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.0031394882176779986	0	1.40273939972013847577273445814	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/14"]
"2-6e3-216.11-c1-0-11"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.28442215529798104	0	1.44822141215650242466982177337	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/28"]
"2-6e3-216.11-c1-0-12"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.09040560526915904	0	1.62915622453076410044855522441	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/30"]
"2-6e3-216.11-c1-0-13"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.34233809401507725	0	1.65210698665916350388922091792	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/18"]
"2-6e3-216.11-c1-0-14"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.0831405108673597	0	1.66518460925591149989187223347	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/2"]
"2-6e3-216.11-c1-0-15"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.06376234386552851	0	1.69271825619523422657578383690	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/5"]
"2-6e3-216.11-c1-0-16"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3403898112311186	0	1.79891137240838147427107772193	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/10"]
"2-6e3-216.11-c1-0-17"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.16068647284048834	0	1.81155771823139914855060780271	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/21"]
"2-6e3-216.11-c1-0-18"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.19504321716264883	0	1.88492126843989388520310866738	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/22"]
"2-6e3-216.11-c1-0-19"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.24817186609539071	0	1.88695271381678183793228062360	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/7"]
"2-6e3-216.11-c1-0-2"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2286723032782365	0	0.30372336005310850224830561492	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/3"]
"2-6e3-216.11-c1-0-20"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.06776658258365087	0	1.92219105726122991102996387828	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/11"]
"2-6e3-216.11-c1-0-21"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.11069914817535058	0	2.05016773101652453524154570506	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/31"]
"2-6e3-216.11-c1-0-22"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.03303508753580553	0	2.07790419153617926054218480636	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/26"]
"2-6e3-216.11-c1-0-23"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.22865089843289602	0	2.15325820908301983026435715940	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/16"]
"2-6e3-216.11-c1-0-24"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.23793176284477213	0	2.35465921742243513065280966660	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/8"]
"2-6e3-216.11-c1-0-25"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.12239742300843565	0	2.45703510623619484586395576517	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/24"]
"2-6e3-216.11-c1-0-26"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.16411715497196347	0	2.52185796971183232323530413213	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/25"]
"2-6e3-216.11-c1-0-27"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.17693595958782077	0	2.53050939657931399301769955468	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/29"]
"2-6e3-216.11-c1-0-28"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.48758343114144154	0	2.72716598406182984528772804874	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/9"]
"2-6e3-216.11-c1-0-29"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.0851740195693145	0	2.82600864886693515609129385609	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/32"]
"2-6e3-216.11-c1-0-3"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.0960441068435687	0	0.63701922363362367366180456321	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/13"]
"2-6e3-216.11-c1-0-30"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.32596356756279715	0	2.95146280993181150950201868877	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/17"]
"2-6e3-216.11-c1-0-31"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.42345369240479747	0	3.12514811423593178951422734535	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/27"]
"2-6e3-216.11-c1-0-32"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3309069510599925	0	3.23277142599543374205074813262	["ModularForm/GL2/Q/holomorphic/216/2/v/a/11/2"]
"2-6e3-216.11-c1-0-33"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3813443788713053	0	3.62176149216634885910735447432	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/19"]
"2-6e3-216.11-c1-0-4"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.44770031091663853	0	0.885269461971376804774059412786	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/23"]
"2-6e3-216.11-c1-0-5"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.26235376862467363	0	1.02122503609869474891670696693	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/4"]
"2-6e3-216.11-c1-0-6"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1695493845151286	0	1.23587853931797700042451828096	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/6"]
"2-6e3-216.11-c1-0-7"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2446576277074316	0	1.24663278940406614463887537537	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/20"]
"2-6e3-216.11-c1-0-8"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07710362360736732	0	1.26386817256927369984290598169	["ModularForm/GL2/Q/holomorphic/216/2/v/b/11/12"]
"2-6e3-216.11-c1-0-9"	1.3133044900782367	1.7247686836596572	2	216	"216.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.25683287698591845	0	1.30391266307259490174892650095	["ModularForm/GL2/Q/holomorphic/216/2/v/a/11/1"]
"2-6e3-216.13-c1-0-0"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3197413463516943	0	0.37273006083646312686736223407	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/6"]
"2-6e3-216.13-c1-0-1"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.40694758409762993	0	0.39258460730639900100475068046	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/9"]
"2-6e3-216.13-c1-0-10"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.13508170455705787	0	1.32214957660741767448731651577	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/14"]
"2-6e3-216.13-c1-0-11"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.09703961709082123	0	1.49920558869759316109100521178	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/4"]
"2-6e3-216.13-c1-0-12"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.08781444987617408	0	1.64326529537699049284403475472	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/2"]
"2-6e3-216.13-c1-0-13"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07650821357638148	0	1.67657688623850211807559109914	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/30"]
"2-6e3-216.13-c1-0-14"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.19450867674580388	0	1.77642633302074455090707160478	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/25"]
"2-6e3-216.13-c1-0-15"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2515923286061046	0	1.81899593655291541599096107636	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/26"]
"2-6e3-216.13-c1-0-16"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.15097659665447388	0	1.86627361150370726022256439971	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/11"]
"2-6e3-216.13-c1-0-17"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2347808334563278	0	1.99892054127417667242061212688	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/1"]
"2-6e3-216.13-c1-0-18"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.039652414230937544	0	2.02196492817986719416669174766	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/34"]
"2-6e3-216.13-c1-0-19"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07120761356371304	0	2.15242467540552866038409834861	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/19"]
"2-6e3-216.13-c1-0-2"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3986063358459729	0	0.46767461339973722197136391565	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/20"]
"2-6e3-216.13-c1-0-20"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.26347406434960946	0	2.17445437327796657953658156493	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/13"]
"2-6e3-216.13-c1-0-21"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.49608748372955613	0	2.26703352031219414160132914343	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/10"]
"2-6e3-216.13-c1-0-22"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.21943598276488588	0	2.32571648570850285303613826884	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/7"]
"2-6e3-216.13-c1-0-23"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11515382826294598	0	2.38754099649589315717441900747	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/29"]
"2-6e3-216.13-c1-0-24"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07263153629919072	0	2.40343069959966828428668004472	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/33"]
"2-6e3-216.13-c1-0-25"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.18124714686368684	0	2.47411307812522529977086783312	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/23"]
"2-6e3-216.13-c1-0-26"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2833080362369621	0	2.52859892422598959250006251490	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/17"]
"2-6e3-216.13-c1-0-27"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.04754771342585604	0	2.54814644185125516427538358639	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/31"]
"2-6e3-216.13-c1-0-28"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.0954564096457105	0	2.60645452442088088875490147122	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/32"]
"2-6e3-216.13-c1-0-29"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4602799814967011	0	2.67937720452654057488806137873	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/3"]
"2-6e3-216.13-c1-0-3"	1.3133044900782367	1.7247686836596572	2	216	"216.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.14825703054275227	0	0.858791981543322422675865456552	["ModularForm/GL2/Q/holomorphic/216/2/t/a/13/15"]
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"2-6e3-72.13-c1-0-3"	1.3133044900782367	1.7247686836596572	2	216	"72.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.20386375131299883	0	1.53582123941884095153597259643	["ModularForm/GL2/Q/holomorphic/216/2/n/b/37/7"]
"2-6e3-72.13-c1-0-4"	1.3133044900782367	1.7247686836596572	2	216	"72.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.14926896629806416	0	1.62023980263603489298278004554	["ModularForm/GL2/Q/holomorphic/216/2/n/b/37/4"]
"2-6e3-72.13-c1-0-5"	1.3133044900782367	1.7247686836596572	2	216	"72.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.06944444444444445	0	2.11554593785227139652540245546	["ModularForm/GL2/Q/holomorphic/216/2/n/a/37/2"]
"2-6e3-72.13-c1-0-6"	1.3133044900782367	1.7247686836596572	2	216	"72.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.06734113199142557	0	2.27448570432677294920759657740	["ModularForm/GL2/Q/holomorphic/216/2/n/b/37/8"]
"2-6e3-72.13-c1-0-7"	1.3133044900782367	1.7247686836596572	2	216	"72.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.18055555555555555	0	2.29880230993597420210544542444	["ModularForm/GL2/Q/holomorphic/216/2/n/a/37/1"]
"2-6e3-72.13-c1-0-8"	1.3133044900782367	1.7247686836596572	2	216	"72.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4415368915300981	0	2.74904789831606887210176424309	["ModularForm/GL2/Q/holomorphic/216/2/n/b/37/3"]
"2-6e3-72.13-c1-0-9"	1.3133044900782367	1.7247686836596572	2	216	"72.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.42198360109818905	0	3.26835906253130334969557043092	["ModularForm/GL2/Q/holomorphic/216/2/n/b/37/6"]
"2-6e3-72.59-c1-0-0"	1.3133044900782367	1.7247686836596572	2	216	"72.59"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.36421527085023436	0	0.34582365577185995921084818390	["ModularForm/GL2/Q/holomorphic/216/2/l/b/179/1"]
"2-6e3-72.59-c1-0-1"	1.3133044900782367	1.7247686836596572	2	216	"72.59"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.21320011127762414	0	0.45837559524099854475959997375	["ModularForm/GL2/Q/holomorphic/216/2/l/b/179/4"]
"2-6e3-72.59-c1-0-2"	1.3133044900782367	1.7247686836596572	2	216	"72.59"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.33669863488154417	0	1.12096017564893920421714367734	["ModularForm/GL2/Q/holomorphic/216/2/l/b/179/6"]
"2-6e3-72.59-c1-0-3"	1.3133044900782367	1.7247686836596572	2	216	"72.59"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.04240108245209626	0	1.47170040679629771130742550412	["ModularForm/GL2/Q/holomorphic/216/2/l/a/179/1"]
"2-6e3-72.59-c1-0-4"	1.3133044900782367	1.7247686836596572	2	216	"72.59"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.08369917117652946	0	1.74108316832948756750271787310	["ModularForm/GL2/Q/holomorphic/216/2/l/b/179/3"]
"2-6e3-72.59-c1-0-5"	1.3133044900782367	1.7247686836596572	2	216	"72.59"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.09494574357824218	0	1.77177590401366217256348352551	["ModularForm/GL2/Q/holomorphic/216/2/l/b/179/8"]
"2-6e3-72.59-c1-0-6"	1.3133044900782367	1.7247686836596572	2	216	"72.59"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2939383526056098	0	2.08995754414363346316245817379	["ModularForm/GL2/Q/holomorphic/216/2/l/b/179/2"]
"2-6e3-72.59-c1-0-7"	1.3133044900782367	1.7247686836596572	2	216	"72.59"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.08671897078822383	0	2.17788314410282264070507524753	["ModularForm/GL2/Q/holomorphic/216/2/l/b/179/7"]
"2-6e3-72.59-c1-0-8"	1.3133044900782367	1.7247686836596572	2	216	"72.59"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1535121935632074	0	2.46302574536800100006982858466	["ModularForm/GL2/Q/holomorphic/216/2/l/a/179/2"]
"2-6e3-72.59-c1-0-9"	1.3133044900782367	1.7247686836596572	2	216	"72.59"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.32998399439123277	0	2.86650321551862434045265358158	["ModularForm/GL2/Q/holomorphic/216/2/l/b/179/5"]
"2-6e3-72.61-c1-0-0"	1.3133044900782367	1.7247686836596572	2	216	"72.61"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4415368915300981	0	0.22735496729930546521910322768	["ModularForm/GL2/Q/holomorphic/216/2/n/b/181/3"]
"2-6e3-72.61-c1-0-1"	1.3133044900782367	1.7247686836596572	2	216	"72.61"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.18055555555555555	0	0.52493485583485650390044569946	["ModularForm/GL2/Q/holomorphic/216/2/n/a/181/1"]
"2-6e3-72.61-c1-0-2"	1.3133044900782367	1.7247686836596572	2	216	"72.61"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.42198360109818905	0	0.822201316537317741535202261830	["ModularForm/GL2/Q/holomorphic/216/2/n/b/181/6"]
"2-6e3-72.61-c1-0-3"	1.3133044900782367	1.7247686836596572	2	216	"72.61"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.14926896629806416	0	1.47155338009370854775886172198	["ModularForm/GL2/Q/holomorphic/216/2/n/b/181/4"]
"2-6e3-72.61-c1-0-4"	1.3133044900782367	1.7247686836596572	2	216	"72.61"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.13337204243801853	0	1.51608097079731405805175068206	["ModularForm/GL2/Q/holomorphic/216/2/n/b/181/2"]
"2-6e3-72.61-c1-0-5"	1.3133044900782367	1.7247686836596572	2	216	"72.61"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.08981095032482456	0	1.83115633734538758855093921274	["ModularForm/GL2/Q/holomorphic/216/2/n/b/181/1"]
"2-6e3-72.61-c1-0-6"	1.3133044900782367	1.7247686836596572	2	216	"72.61"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.06734113199142557	0	2.10449645220910708925499778287	["ModularForm/GL2/Q/holomorphic/216/2/n/b/181/8"]
"2-6e3-72.61-c1-0-7"	1.3133044900782367	1.7247686836596572	2	216	"72.61"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.06944444444444445	0	2.36332118847499301302913558219	["ModularForm/GL2/Q/holomorphic/216/2/n/a/181/2"]
"2-6e3-72.61-c1-0-8"	1.3133044900782367	1.7247686836596572	2	216	"72.61"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3255656193372943	0	2.46368104814122253318788757442	["ModularForm/GL2/Q/holomorphic/216/2/n/b/181/5"]
"2-6e3-72.61-c1-0-9"	1.3133044900782367	1.7247686836596572	2	216	"72.61"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.20386375131299883	0	2.54568166440474899826445236582	["ModularForm/GL2/Q/holomorphic/216/2/n/b/181/7"]
"2-6e3-8.5-c1-0-0"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.5	0	0.55514023329223631181035262769	["ModularForm/GL2/Q/holomorphic/216/2/d/a/109/4"]
"2-6e3-8.5-c1-0-1"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.351229953939019	0	0.61650717592624954793526747740	["ModularForm/GL2/Q/holomorphic/216/2/d/c/109/2"]
"2-6e3-8.5-c1-0-10"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	9.337125354100845e-62	0	2.09347155128834804444612063635	["ModularForm/GL2/Q/holomorphic/216/2/d/a/109/3"]
"2-6e3-8.5-c1-0-11"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07745990787803808	0	2.24793440843523719707062138465	["ModularForm/GL2/Q/holomorphic/216/2/d/b/109/3"]
"2-6e3-8.5-c1-0-12"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.351229953939019	0	2.33918178296509285885561530142	["ModularForm/GL2/Q/holomorphic/216/2/d/c/109/1"]
"2-6e3-8.5-c1-0-13"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.273770046060981	0	2.57940208782148185530571697162	["ModularForm/GL2/Q/holomorphic/216/2/d/c/109/5"]
"2-6e3-8.5-c1-0-14"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.148770046060981	0	3.02544171354141731788805282860	["ModularForm/GL2/Q/holomorphic/216/2/d/c/109/7"]
"2-6e3-8.5-c1-0-15"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.5	0	3.02891429392479997191239342200	["ModularForm/GL2/Q/holomorphic/216/2/d/a/109/1"]
"2-6e3-8.5-c1-0-2"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07745990787803808	0	1.09597606645478970806256319479	["ModularForm/GL2/Q/holomorphic/216/2/d/b/109/1"]
"2-6e3-8.5-c1-0-3"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.22622995393901907	0	1.19433220821260657188266070116	["ModularForm/GL2/Q/holomorphic/216/2/d/c/109/4"]
"2-6e3-8.5-c1-0-4"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	1.2253570962149904e-61	0	1.20357386349153630305809421009	["ModularForm/GL2/Q/holomorphic/216/2/d/a/109/2"]
"2-6e3-8.5-c1-0-5"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.273770046060981	0	1.39264991324237704461846571164	["ModularForm/GL2/Q/holomorphic/216/2/d/c/109/6"]
"2-6e3-8.5-c1-0-6"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.148770046060981	0	1.66349342426509532898164224007	["ModularForm/GL2/Q/holomorphic/216/2/d/c/109/8"]
"2-6e3-8.5-c1-0-7"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07745990787803808	0	1.75430672134053610056750135567	["ModularForm/GL2/Q/holomorphic/216/2/d/b/109/2"]
"2-6e3-8.5-c1-0-8"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.22622995393901907	0	1.80427050584664268243234755352	["ModularForm/GL2/Q/holomorphic/216/2/d/c/109/3"]
"2-6e3-8.5-c1-0-9"	1.3133044900782367	1.7247686836596572	2	216	"8.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07745990787803808	0	2.02578688338605839856043544083	["ModularForm/GL2/Q/holomorphic/216/2/d/b/109/4"]
"2-6e3-9.4-c1-0-0"	1.3133044900782367	1.7247686836596572	2	216	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.23117040310844345	0	0.937195734103419700344514845166	["ModularForm/GL2/Q/holomorphic/216/2/i/b/145/1"]
"2-6e3-9.4-c1-0-1"	1.3133044900782367	1.7247686836596572	2	216	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.11111111111111113	0	1.30484125328406603231345639004	["ModularForm/GL2/Q/holomorphic/216/2/i/a/145/1"]
"2-6e3-9.4-c1-0-2"	1.3133044900782367	1.7247686836596572	2	216	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1756148475528879	0	2.38292494937546658296639276730	["ModularForm/GL2/Q/holomorphic/216/2/i/b/145/2"]
"2-6e3-9.7-c1-0-0"	1.3133044900782367	1.7247686836596572	2	216	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1756148475528879	0	1.15616656276677850995285273223	["ModularForm/GL2/Q/holomorphic/216/2/i/b/73/2"]
"2-6e3-9.7-c1-0-1"	1.3133044900782367	1.7247686836596572	2	216	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11111111111111113	0	2.03593968508812365837195667138	["ModularForm/GL2/Q/holomorphic/216/2/i/a/73/1"]
"2-6e3-9.7-c1-0-2"	1.3133044900782367	1.7247686836596572	2	216	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.23117040310844345	0	2.42466392161486606974001286481	["ModularForm/GL2/Q/holomorphic/216/2/i/b/73/1"]


# 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).


