# lfunc_search downloaded from the LMFDB on 30 May 2026.
# Search link: https://www.lmfdb.org/L/2/891
# Query "{'degree': 2, 'conductor': 891}" returned 22670 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.



"2-891-11.10-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"11.10"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	1.49992246792186455847727789153	["ModularForm/GL2/Q/holomorphic/891/1/c/a/406/1", "ModularForm/GL2/Q/holomorphic/891/1/c/a", "ArtinRepresentation/2.891.3t2.b.a", "ArtinRepresentation/2.891.3t2.b"]
"2-891-11.10-c0-0-1"	0.6668335071485274	0.4446669262560052	2	891	"11.10"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	1.85141390469645855415782041976	["ModularForm/GL2/Q/holomorphic/891/1/c/b/406/1", "ModularForm/GL2/Q/holomorphic/891/1/c/b", "ArtinRepresentation/2.891.6t3.a.a", "ArtinRepresentation/2.891.6t3.a"]
"2-891-297.142-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"297.142"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2037037037037037	0	2.18348318160314582980697635026	["ModularForm/GL2/Q/holomorphic/891/1/q/a/505/1"]
"2-891-297.175-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"297.175"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2037037037037037	0	1.05350538390653493851884988145	["ModularForm/GL2/Q/holomorphic/891/1/q/a/10/1"]
"2-891-297.241-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"297.241"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2037037037037037	0	2.04804590067180112763213581919	["ModularForm/GL2/Q/holomorphic/891/1/q/a/802/1"]
"2-891-297.274-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"297.274"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2037037037037037	0	1.19634339915372808604990390571	["ModularForm/GL2/Q/holomorphic/891/1/q/a/307/1"]
"2-891-297.43-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"297.43"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.12962962962962962	0	1.32085345870502991971871489209	["ModularForm/GL2/Q/holomorphic/891/1/q/a/208/1"]
"2-891-297.76-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"297.76"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.12962962962962962	0	1.83862428285239712791282220009	["ModularForm/GL2/Q/holomorphic/891/1/q/a/604/1"]
"2-891-891.142-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.142"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.16049382716049382	0	2.11740552308291910045713570026	["ModularForm/GL2/Q/holomorphic/891/1/w/a/142/1"]
"2-891-891.175-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.175"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.06172839506172839	0	1.41090792627585582851295528669	["ModularForm/GL2/Q/holomorphic/891/1/w/a/175/1"]
"2-891-891.241-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.241"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.06172839506172839	0	1.52393726560524912440329224508	["ModularForm/GL2/Q/holomorphic/891/1/w/a/241/1"]
"2-891-891.274-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.274"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.49382716049382713	0	0.48451313731335460588176354471	["ModularForm/GL2/Q/holomorphic/891/1/w/a/274/1"]
"2-891-891.340-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.340"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.3950617283950617	0	0.819334383861836829039973446073	["ModularForm/GL2/Q/holomorphic/891/1/w/a/340/1"]
"2-891-891.373-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.373"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.06172839506172839	0	1.32619109284606946527473059886	["ModularForm/GL2/Q/holomorphic/891/1/w/a/373/1"]
"2-891-891.43-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.43"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.06172839506172839	0	0.880169090426600098706291888498	["ModularForm/GL2/Q/holomorphic/891/1/w/a/43/1"]
"2-891-891.439-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.439"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.49382716049382713	0	2.48951332770732570860590077640	["ModularForm/GL2/Q/holomorphic/891/1/w/a/439/1"]
"2-891-891.472-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.472"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.06172839506172839	0	2.07365933194899567780148817166	["ModularForm/GL2/Q/holomorphic/891/1/w/a/472/1"]
"2-891-891.538-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.538"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.06172839506172839	0	1.46352397678991956493998675823	["ModularForm/GL2/Q/holomorphic/891/1/w/a/538/1"]
"2-891-891.571-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.571"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.16049382716049382	0	1.49356945343708438424020358453	["ModularForm/GL2/Q/holomorphic/891/1/w/a/571/1"]
"2-891-891.637-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.637"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2716049382716049	0	2.29678686298855693104059251311	["ModularForm/GL2/Q/holomorphic/891/1/w/a/637/1"]
"2-891-891.670-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.670"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2716049382716049	0	0.921198725571610961551579935935	["ModularForm/GL2/Q/holomorphic/891/1/w/a/670/1"]
"2-891-891.736-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.736"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.17283950617283952	0	1.52802690484097235992589155719	["ModularForm/GL2/Q/holomorphic/891/1/w/a/736/1"]
"2-891-891.76-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.76"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.3950617283950617	0	2.73181518156729620312675076254	["ModularForm/GL2/Q/holomorphic/891/1/w/a/76/1"]
"2-891-891.769-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.769"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.06172839506172839	0	1.78602992386665204530259078986	["ModularForm/GL2/Q/holomorphic/891/1/w/a/769/1"]
"2-891-891.835-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.835"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.06172839506172839	0	1.25054693167848562079219599332	["ModularForm/GL2/Q/holomorphic/891/1/w/a/835/1"]
"2-891-891.868-c0-0-0"	0.6668335071485274	0.4446669262560052	2	891	"891.868"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.17283950617283952	0	1.98018623062264757124164035638	["ModularForm/GL2/Q/holomorphic/891/1/w/a/868/1"]
"2-891-1.1-c1-0-0"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.45448446258251434250283040992	["ModularForm/GL2/Q/holomorphic/891/2/a/p/1/2"]
"2-891-1.1-c1-0-1"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.58535310119037990795018343052	["EllipticCurve/Q/891/d", "ModularForm/GL2/Q/holomorphic/891/2/a/d/1/1", "ModularForm/GL2/Q/holomorphic/891/2/a/d"]
"2-891-1.1-c1-0-10"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.03808763016450447486482474679	["ModularForm/GL2/Q/holomorphic/891/2/a/r/1/1"]
"2-891-1.1-c1-0-11"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.12563551526678805110021499722	["EllipticCurve/Q/891/f", "ModularForm/GL2/Q/holomorphic/891/2/a/f/1/1", "ModularForm/GL2/Q/holomorphic/891/2/a/f"]
"2-891-1.1-c1-0-12"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.18072091599964512308474894277	["ModularForm/GL2/Q/holomorphic/891/2/a/n/1/2"]
"2-891-1.1-c1-0-13"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.18617839694837518367140819035	["ModularForm/GL2/Q/holomorphic/891/2/a/p/1/1"]
"2-891-1.1-c1-0-14"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.22497281734807156992028915967	["ModularForm/GL2/Q/holomorphic/891/2/a/q/1/2"]
"2-891-1.1-c1-0-15"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.27714141478398604862661610384	["EllipticCurve/Q/891/g", "ModularForm/GL2/Q/holomorphic/891/2/a/g/1/1", "ModularForm/GL2/Q/holomorphic/891/2/a/g"]
"2-891-1.1-c1-0-16"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.28776879567314446521247512757	["ModularForm/GL2/Q/holomorphic/891/2/a/o/1/1"]
"2-891-1.1-c1-0-17"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.44671748168480109910232449024	["ModularForm/GL2/Q/holomorphic/891/2/a/o/1/2"]
"2-891-1.1-c1-0-18"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.47972613759800536285702242578	["ModularForm/GL2/Q/holomorphic/891/2/a/r/1/3"]
"2-891-1.1-c1-0-19"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.51886143024438886817171134055	["ModularForm/GL2/Q/holomorphic/891/2/a/i/1/1"]
"2-891-1.1-c1-0-2"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.61061057547310035274509742920	["ModularForm/GL2/Q/holomorphic/891/2/a/j/1/1"]
"2-891-1.1-c1-0-20"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.53865115269998686381095233957	["EllipticCurve/Q/891/b", "ModularForm/GL2/Q/holomorphic/891/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/891/2/a/b"]
"2-891-1.1-c1-0-21"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.56959324093876191654394122305	["ModularForm/GL2/Q/holomorphic/891/2/a/k/1/1"]
"2-891-1.1-c1-0-22"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.59029122202617954127435993087	["ModularForm/GL2/Q/holomorphic/891/2/a/q/1/4"]
"2-891-1.1-c1-0-23"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.64963475471670011121404588237	["ModularForm/GL2/Q/holomorphic/891/2/a/m/1/1"]
"2-891-1.1-c1-0-24"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.69877467674323381253483350367	["ModularForm/GL2/Q/holomorphic/891/2/a/n/1/3"]
"2-891-1.1-c1-0-25"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.71275901497551536766036693485	["ModularForm/GL2/Q/holomorphic/891/2/a/q/1/3"]
"2-891-1.1-c1-0-26"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.71354697264937956208438777903	["ModularForm/GL2/Q/holomorphic/891/2/a/k/1/2"]
"2-891-1.1-c1-0-27"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.73232800938446168341761808628	["EllipticCurve/Q/891/h", "ModularForm/GL2/Q/holomorphic/891/2/a/h/1/1", "ModularForm/GL2/Q/holomorphic/891/2/a/h"]
"2-891-1.1-c1-0-28"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.80248543682268758157709807156	["ModularForm/GL2/Q/holomorphic/891/2/a/m/1/2"]
"2-891-1.1-c1-0-29"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.82523763964115197775576835005	["ModularForm/GL2/Q/holomorphic/891/2/a/l/1/1"]
"2-891-1.1-c1-0-3"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.71019243271924120357558091045	["ModularForm/GL2/Q/holomorphic/891/2/a/r/1/2"]
"2-891-1.1-c1-0-30"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.90386177366371464256103671398	["ModularForm/GL2/Q/holomorphic/891/2/a/r/1/4"]
"2-891-1.1-c1-0-31"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.92872229089309196452290458560	["ModularForm/GL2/Q/holomorphic/891/2/a/p/1/4"]
"2-891-1.1-c1-0-32"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.95015074235929394309347079557	["ModularForm/GL2/Q/holomorphic/891/2/a/o/1/3"]
"2-891-1.1-c1-0-33"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.95088207045539380911267534362	["ModularForm/GL2/Q/holomorphic/891/2/a/j/1/2"]
"2-891-1.1-c1-0-34"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.97679894025303810451404739737	["ModularForm/GL2/Q/holomorphic/891/2/a/l/1/2"]
"2-891-1.1-c1-0-35"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.27002980518639592641975194195	["ModularForm/GL2/Q/holomorphic/891/2/a/o/1/4"]
"2-891-1.1-c1-0-36"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.37023065173205972269695666738	["ModularForm/GL2/Q/holomorphic/891/2/a/l/1/3"]
"2-891-1.1-c1-0-37"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.39291546337445751153946171653	["ModularForm/GL2/Q/holomorphic/891/2/a/i/1/2"]
"2-891-1.1-c1-0-38"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.51327556820106384030635696411	["ModularForm/GL2/Q/holomorphic/891/2/a/k/1/3"]
"2-891-1.1-c1-0-39"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.78366221376082730103963280331	["ModularForm/GL2/Q/holomorphic/891/2/a/m/1/3"]
"2-891-1.1-c1-0-4"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.73433714241970085875408554675	["ModularForm/GL2/Q/holomorphic/891/2/a/q/1/1"]
"2-891-1.1-c1-0-5"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.892194307395982919396068311152	["ModularForm/GL2/Q/holomorphic/891/2/a/p/1/3"]
"2-891-1.1-c1-0-6"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.912979561147814477356728990368	["EllipticCurve/Q/891/c", "ModularForm/GL2/Q/holomorphic/891/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/891/2/a/c"]
"2-891-1.1-c1-0-7"	2.66733402859411	7.1146708200960855	2	891	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.931362933455762091067918970399	["EllipticCurve/Q/891/a", "ModularForm/GL2/Q/holomorphic/891/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/891/2/a/a"]
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"2-891-1.1-c5-0-61"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.62323389921182872463425575942	["ModularForm/GL2/Q/holomorphic/891/6/a/i/1/11"]
"2-891-1.1-c5-0-62"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.62607718603616995019336284347	["ModularForm/GL2/Q/holomorphic/891/6/a/f/1/8"]
"2-891-1.1-c5-0-63"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.65247372488184801004149360399	["ModularForm/GL2/Q/holomorphic/891/6/a/j/1/17"]
"2-891-1.1-c5-0-64"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.65612436454993686586906205547	["ModularForm/GL2/Q/holomorphic/891/6/a/c/1/1"]
"2-891-1.1-c5-0-65"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.66889069696005382979149182084	["ModularForm/GL2/Q/holomorphic/891/6/a/f/1/1"]
"2-891-1.1-c5-0-66"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.67665401573056011419205433477	["ModularForm/GL2/Q/holomorphic/891/6/a/i/1/21"]
"2-891-1.1-c5-0-67"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.68887883600296269017811385595	["ModularForm/GL2/Q/holomorphic/891/6/a/h/1/7"]
"2-891-1.1-c5-0-68"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.69338253282939862216590039707	["ModularForm/GL2/Q/holomorphic/891/6/a/h/1/6"]
"2-891-1.1-c5-0-69"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.70038178643109121014636293504	["ModularForm/GL2/Q/holomorphic/891/6/a/j/1/22"]
"2-891-1.1-c5-0-7"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.17816903401448193031316650337	["ModularForm/GL2/Q/holomorphic/891/6/a/h/1/9"]
"2-891-1.1-c5-0-70"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.70660024999832051332920345724	["ModularForm/GL2/Q/holomorphic/891/6/a/j/1/16"]
"2-891-1.1-c5-0-71"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.71683213384295486709180576933	["ModularForm/GL2/Q/holomorphic/891/6/a/h/1/13"]
"2-891-1.1-c5-0-72"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.72332973387365413176357287871	["ModularForm/GL2/Q/holomorphic/891/6/a/i/1/3"]
"2-891-1.1-c5-0-73"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.73670064645489908678280479443	["ModularForm/GL2/Q/holomorphic/891/6/a/i/1/27"]
"2-891-1.1-c5-0-74"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.73953437168617975764935553782	["ModularForm/GL2/Q/holomorphic/891/6/a/a/1/8"]
"2-891-1.1-c5-0-75"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.74171467984034011214520141883	["ModularForm/GL2/Q/holomorphic/891/6/a/h/1/22"]
"2-891-1.1-c5-0-76"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.74777279670322347842171052320	["ModularForm/GL2/Q/holomorphic/891/6/a/e/1/14"]
"2-891-1.1-c5-0-77"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.74980672434544577410802798848	["ModularForm/GL2/Q/holomorphic/891/6/a/c/1/8"]
"2-891-1.1-c5-0-78"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.75072221087043821735739706607	["ModularForm/GL2/Q/holomorphic/891/6/a/c/1/6"]
"2-891-1.1-c5-0-79"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.75641900776422172823375667345	["ModularForm/GL2/Q/holomorphic/891/6/a/b/1/8"]
"2-891-1.1-c5-0-8"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.19626664849879832247512127564	["ModularForm/GL2/Q/holomorphic/891/6/a/i/1/6"]
"2-891-1.1-c5-0-80"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.77293748576006731630191347933	["ModularForm/GL2/Q/holomorphic/891/6/a/e/1/4"]
"2-891-1.1-c5-0-81"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.77502356407960111760832731820	["ModularForm/GL2/Q/holomorphic/891/6/a/d/1/5"]
"2-891-1.1-c5-0-82"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.78065431154459626445921540449	["ModularForm/GL2/Q/holomorphic/891/6/a/b/1/3"]
"2-891-1.1-c5-0-83"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.803637950398276600956890240720	["ModularForm/GL2/Q/holomorphic/891/6/a/j/1/11"]
"2-891-1.1-c5-0-84"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.808207756318732330198001003752	["ModularForm/GL2/Q/holomorphic/891/6/a/j/1/14"]
"2-891-1.1-c5-0-85"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.817032997938948023764674670465	["ModularForm/GL2/Q/holomorphic/891/6/a/c/1/10"]
"2-891-1.1-c5-0-86"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.833911045917444530527703721303	["ModularForm/GL2/Q/holomorphic/891/6/a/d/1/11"]
"2-891-1.1-c5-0-87"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.836538237508281136221014952499	["ModularForm/GL2/Q/holomorphic/891/6/a/i/1/9"]
"2-891-1.1-c5-0-88"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.842744300623977780540180573235	["ModularForm/GL2/Q/holomorphic/891/6/a/h/1/8"]
"2-891-1.1-c5-0-89"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.849218600606220941975387448553	["ModularForm/GL2/Q/holomorphic/891/6/a/j/1/15"]
"2-891-1.1-c5-0-9"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.21051433707530531045339887934	["ModularForm/GL2/Q/holomorphic/891/6/a/d/1/1"]
"2-891-1.1-c5-0-90"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.856822452896132863699499107105	["ModularForm/GL2/Q/holomorphic/891/6/a/f/1/14"]
"2-891-1.1-c5-0-91"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.862126268297418238552793158252	["ModularForm/GL2/Q/holomorphic/891/6/a/j/1/2"]
"2-891-1.1-c5-0-92"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.862855983815564529890965091026	["ModularForm/GL2/Q/holomorphic/891/6/a/c/1/13"]
"2-891-1.1-c5-0-93"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.864630078953320930281553083145	["ModularForm/GL2/Q/holomorphic/891/6/a/c/1/4"]
"2-891-1.1-c5-0-94"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.872330774837027992227330448200	["ModularForm/GL2/Q/holomorphic/891/6/a/e/1/3"]
"2-891-1.1-c5-0-95"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.873107179293618377360865455683	["ModularForm/GL2/Q/holomorphic/891/6/a/f/1/6"]
"2-891-1.1-c5-0-96"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.874875561994226603251471319174	["ModularForm/GL2/Q/holomorphic/891/6/a/i/1/23"]
"2-891-1.1-c5-0-97"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.876786174024559820889385548757	["ModularForm/GL2/Q/holomorphic/891/6/a/d/1/2"]
"2-891-1.1-c5-0-98"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.886857542700147085241560955003	["ModularForm/GL2/Q/holomorphic/891/6/a/j/1/21"]
"2-891-1.1-c5-0-99"	11.95416176289102	142.90198345336577	2	891	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	0.888202992369333190727739864475	["ModularForm/GL2/Q/holomorphic/891/6/a/e/1/7"]


# 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).