# lfunc_search downloaded from the LMFDB on 24 August 2026.
# Search link: https://www.lmfdb.org/L/2/605/1.1
# Query "{'degree': 2, 'conductor': 605}" returned 13402 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.



"2-605-5.2-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"5.2"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.16189590441260832	0	2.31090309747750861747671519750	["ModularForm/GL2/Q/holomorphic/605/1/f/a/122/1", "ArtinRepresentation/2.605.8t17.a.b"]
"2-605-5.3-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"5.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.16189590441260832	0	1.68645142704929817668356953408	["ModularForm/GL2/Q/holomorphic/605/1/f/a/243/1", "ArtinRepresentation/2.605.8t17.a.a"]
"2-605-55.19-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"55.19"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.19621626289782826	0	1.18772841557469463712064700282	["ModularForm/GL2/Q/holomorphic/605/1/h/a/239/1"]
"2-605-55.24-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"55.24"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.04271713006960679	0	1.93699773126312220587693635294	["ModularForm/GL2/Q/holomorphic/605/1/h/a/354/1"]
"2-605-55.27-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"55.27"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.19160322841561317	0	1.14395072034265558483809096537	["ModularForm/GL2/Q/holomorphic/605/1/l/a/27/1"]
"2-605-55.29-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"55.29"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.19621626289782826	0	2.32338853559295554678607845651	["ModularForm/GL2/Q/holomorphic/605/1/h/a/524/1"]
"2-605-55.3-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"55.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.3229625114451733	0	1.08259507175776341662098159118	["ModularForm/GL2/Q/holomorphic/605/1/l/a/3/1"]
"2-605-55.37-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"55.37"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.3229625114451733	0	2.51612685095028633135248256053	["ModularForm/GL2/Q/holomorphic/605/1/l/a/202/1"]
"2-605-55.38-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"55.38"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.4846049627591702	0	3.05004765402552925916788092080	["ModularForm/GL2/Q/holomorphic/605/1/l/a/148/1"]
"2-605-55.39-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"55.39"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.04271713006960679	0	1.54717661651294741362798882938	["ModularForm/GL2/Q/holomorphic/605/1/h/a/94/1"]
"2-605-55.42-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"55.42"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.4846049627591702	0	0.63173197566369554946515770389	["ModularForm/GL2/Q/holomorphic/605/1/l/a/372/1"]
"2-605-55.47-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"55.47"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.0008292973800433732	0	1.97738804122392864361554238037	["ModularForm/GL2/Q/holomorphic/605/1/l/a/487/1"]
"2-605-55.48-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"55.48"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.0008292973800433732	0	1.74476970960032848409458642893	["ModularForm/GL2/Q/holomorphic/605/1/l/a/323/1"]
"2-605-55.53-c0-0-0"	0.5494855163177338	0.3019343326429665	2	605	"55.53"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.19160322841561317	0	1.93346830409320891915823061122	["ModularForm/GL2/Q/holomorphic/605/1/l/a/493/1"]
"2-605-1.1-c1-0-0"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.33924701845223945894802940829	["ModularForm/GL2/Q/holomorphic/605/2/a/g/1/2"]
"2-605-1.1-c1-0-1"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.64500020425035326738338827898	["ModularForm/GL2/Q/holomorphic/605/2/a/d/1/1"]
"2-605-1.1-c1-0-10"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.16452410697109785082774396564	["ModularForm/GL2/Q/holomorphic/605/2/a/h/1/2"]
"2-605-1.1-c1-0-11"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.25138706605810035988356508603	["ModularForm/GL2/Q/holomorphic/605/2/a/m/1/1"]
"2-605-1.1-c1-0-12"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.33977056843985594276932931220	["ModularForm/GL2/Q/holomorphic/605/2/a/i/1/1"]
"2-605-1.1-c1-0-13"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.34412844528491965270904028569	["EllipticCurve/Q/605/a", "ModularForm/GL2/Q/holomorphic/605/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/605/2/a/a"]
"2-605-1.1-c1-0-14"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.35847909486953709471518764152	["ModularForm/GL2/Q/holomorphic/605/2/a/g/1/1"]
"2-605-1.1-c1-0-15"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.37217045192519409836679007673	["ModularForm/GL2/Q/holomorphic/605/2/a/j/1/2"]
"2-605-1.1-c1-0-16"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.41060291378352900714376948884	["ModularForm/GL2/Q/holomorphic/605/2/a/l/1/2"]
"2-605-1.1-c1-0-17"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.52320903738309950873819603485	["ModularForm/GL2/Q/holomorphic/605/2/a/d/1/2"]
"2-605-1.1-c1-0-18"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.53191520661976603474827760272	["ModularForm/GL2/Q/holomorphic/605/2/a/e/1/1"]
"2-605-1.1-c1-0-19"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.53956360492630326633157608259	["ModularForm/GL2/Q/holomorphic/605/2/a/m/1/2"]
"2-605-1.1-c1-0-2"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.66691259212154053818966833566	["ModularForm/GL2/Q/holomorphic/605/2/a/k/1/3"]
"2-605-1.1-c1-0-20"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.58891951458805395883110651479	["ModularForm/GL2/Q/holomorphic/605/2/a/l/1/4"]
"2-605-1.1-c1-0-21"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.86853886263346253357248352832	["EllipticCurve/Q/605/b", "ModularForm/GL2/Q/holomorphic/605/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/605/2/a/b"]
"2-605-1.1-c1-0-22"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.91615236151570534807396468396	["EllipticCurve/Q/605/c", "ModularForm/GL2/Q/holomorphic/605/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/605/2/a/c"]
"2-605-1.1-c1-0-23"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.94021034518507580190273520563	["ModularForm/GL2/Q/holomorphic/605/2/a/j/1/1"]
"2-605-1.1-c1-0-24"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.94863680280526318005072684132	["ModularForm/GL2/Q/holomorphic/605/2/a/i/1/2"]
"2-605-1.1-c1-0-25"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.95688892379934227145845556046	["ModularForm/GL2/Q/holomorphic/605/2/a/l/1/3"]
"2-605-1.1-c1-0-26"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.98505365307232056688200426516	["ModularForm/GL2/Q/holomorphic/605/2/a/m/1/5"]
"2-605-1.1-c1-0-27"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.99949519016452146689239223328	["ModularForm/GL2/Q/holomorphic/605/2/a/g/1/3"]
"2-605-1.1-c1-0-28"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.03825751663853670094581721175	["ModularForm/GL2/Q/holomorphic/605/2/a/k/1/4"]
"2-605-1.1-c1-0-29"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.06339272936782805230717687456	["ModularForm/GL2/Q/holomorphic/605/2/a/f/1/2"]
"2-605-1.1-c1-0-3"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.68176090390741789296398544915	["ModularForm/GL2/Q/holomorphic/605/2/a/h/1/1"]
"2-605-1.1-c1-0-30"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.26687467016727898820150766433	["ModularForm/GL2/Q/holomorphic/605/2/a/j/1/3"]
"2-605-1.1-c1-0-31"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.32863858932627955209568211674	["ModularForm/GL2/Q/holomorphic/605/2/a/h/1/3"]
"2-605-1.1-c1-0-32"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.33687375240713757191578207116	["ModularForm/GL2/Q/holomorphic/605/2/a/i/1/3"]
"2-605-1.1-c1-0-33"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.37840793565645615555423905524	["ModularForm/GL2/Q/holomorphic/605/2/a/m/1/6"]
"2-605-1.1-c1-0-34"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.57845760710912345016843008396	["ModularForm/GL2/Q/holomorphic/605/2/a/e/1/2"]
"2-605-1.1-c1-0-35"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.58738402693973646110576449948	["ModularForm/GL2/Q/holomorphic/605/2/a/i/1/4"]
"2-605-1.1-c1-0-36"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.85273387277794221626883106963	["ModularForm/GL2/Q/holomorphic/605/2/a/j/1/4"]
"2-605-1.1-c1-0-4"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.794318638946469023667388282742	["ModularForm/GL2/Q/holomorphic/605/2/a/m/1/3"]
"2-605-1.1-c1-0-5"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.853182081451121548450904398732	["ModularForm/GL2/Q/holomorphic/605/2/a/k/1/2"]
"2-605-1.1-c1-0-6"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.924614641754491117924675868799	["ModularForm/GL2/Q/holomorphic/605/2/a/m/1/4"]
"2-605-1.1-c1-0-7"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.948431305586601174813472817241	["ModularForm/GL2/Q/holomorphic/605/2/a/l/1/1"]
"2-605-1.1-c1-0-8"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.01759306538832874510871088712	["ModularForm/GL2/Q/holomorphic/605/2/a/k/1/1"]
"2-605-1.1-c1-0-9"	2.1979420652709356	4.8309493222874655	2	605	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.11646022545911958060614146128	["ModularForm/GL2/Q/holomorphic/605/2/a/f/1/1"]
"2-605-11.3-c1-0-0"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.38543426013921356	0	0.16418174527858703823356962315	["ModularForm/GL2/Q/holomorphic/605/2/g/f/366/1"]
"2-605-11.3-c1-0-1"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4389333929674351	0	0.24444803778015019238059081238	["ModularForm/GL2/Q/holomorphic/605/2/g/j/366/1"]
"2-605-11.3-c1-0-10"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2645864361830086	0	0.968743527746511937976207356399	["ModularForm/GL2/Q/holomorphic/605/2/g/q/366/1"]
"2-605-11.3-c1-0-11"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.03893339296743505	0	0.973221355226113801752617656343	["ModularForm/GL2/Q/holomorphic/605/2/g/k/366/1"]
"2-605-11.3-c1-0-12"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2645864361830086	0	0.992393588615408681186815768482	["ModularForm/GL2/Q/holomorphic/605/2/g/q/366/5"]
"2-605-11.3-c1-0-13"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.16106660703256495	0	1.01495658695033735725874075568	["ModularForm/GL2/Q/holomorphic/605/2/g/h/366/2"]
"2-605-11.3-c1-0-14"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.38543426013921356	0	1.03924756962418236090821263657	["ModularForm/GL2/Q/holomorphic/605/2/g/f/366/2"]
"2-605-11.3-c1-0-15"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2854342601392136	0	1.08286063106032696167277620798	["ModularForm/GL2/Q/holomorphic/605/2/g/e/366/1"]
"2-605-11.3-c1-0-16"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.03893339296743505	0	1.11801394251362155253791475136	["ModularForm/GL2/Q/holomorphic/605/2/g/p/366/2"]
"2-605-11.3-c1-0-17"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.00699826565644298	0	1.18136033200899559748551070424	["ModularForm/GL2/Q/holomorphic/605/2/g/c/366/1"]
"2-605-11.3-c1-0-18"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.16106660703256495	0	1.19232867376134542255304192006	["ModularForm/GL2/Q/holomorphic/605/2/g/h/366/1"]
"2-605-11.3-c1-0-19"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.21456573986078645	0	1.25263655192379891837087500494	["ModularForm/GL2/Q/holomorphic/605/2/g/g/366/1"]
"2-605-11.3-c1-0-2"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.18543426013921357	0	0.27669842401542515469935513239	["ModularForm/GL2/Q/holomorphic/605/2/g/d/366/1"]
"2-605-11.3-c1-0-20"	2.1979420652709356	4.8309493222874655	2	605	"11.3"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.061066607032564946	0	1.32575355927140503506158525281	["ModularForm/GL2/Q/holomorphic/605/2/g/m/366/2"]
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"2-605-1.1-c7-0-41"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.39885268030570043813490811802	["ModularForm/GL2/Q/holomorphic/605/8/a/h/1/4"]
"2-605-1.1-c7-0-42"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.41389375337849425798459822207	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/5"]
"2-605-1.1-c7-0-43"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.41458851463966786546660563788	["ModularForm/GL2/Q/holomorphic/605/8/a/h/1/3"]
"2-605-1.1-c7-0-44"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.41549831823866309812485707579	["ModularForm/GL2/Q/holomorphic/605/8/a/t/1/8"]
"2-605-1.1-c7-0-45"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.41942486324053644333122792833	["ModularForm/GL2/Q/holomorphic/605/8/a/j/1/5"]
"2-605-1.1-c7-0-46"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.42776598543686313537426137110	["ModularForm/GL2/Q/holomorphic/605/8/a/p/1/13"]
"2-605-1.1-c7-0-47"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.43121826755682336732735968428	["ModularForm/GL2/Q/holomorphic/605/8/a/n/1/1"]
"2-605-1.1-c7-0-48"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.43856683137156943162458699522	["ModularForm/GL2/Q/holomorphic/605/8/a/m/1/10"]
"2-605-1.1-c7-0-49"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.44303061969561933208110079368	["ModularForm/GL2/Q/holomorphic/605/8/a/n/1/2"]
"2-605-1.1-c7-0-5"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.080277251049989625862169440870	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/21"]
"2-605-1.1-c7-0-50"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.46424242983158402644701912908	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/6"]
"2-605-1.1-c7-0-51"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.47678344045924900738519463263	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/4"]
"2-605-1.1-c7-0-52"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.49200572669304750595002957366	["ModularForm/GL2/Q/holomorphic/605/8/a/g/1/2"]
"2-605-1.1-c7-0-53"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.49505539094287432793996692108	["ModularForm/GL2/Q/holomorphic/605/8/a/p/1/9"]
"2-605-1.1-c7-0-54"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	true	true	0.0	0	0.49943586700642653917223753955	["ModularForm/GL2/Q/holomorphic/605/8/a/b/1/1", "ModularForm/GL2/Q/holomorphic/605/8/a/b"]
"2-605-1.1-c7-0-55"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.50238155961651072995099595726	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/13"]
"2-605-1.1-c7-0-56"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.50265758095248198293877716680	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/20"]
"2-605-1.1-c7-0-57"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.51130939733327382278874491174	["ModularForm/GL2/Q/holomorphic/605/8/a/t/1/11"]
"2-605-1.1-c7-0-58"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.51434447519901039122835626023	["ModularForm/GL2/Q/holomorphic/605/8/a/t/1/17"]
"2-605-1.1-c7-0-59"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.51437915583541990122650471436	["ModularForm/GL2/Q/holomorphic/605/8/a/m/1/8"]
"2-605-1.1-c7-0-6"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.096173002584863905845591845149	["ModularForm/GL2/Q/holomorphic/605/8/a/p/1/15"]
"2-605-1.1-c7-0-60"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.51504889838086843718137924599	["ModularForm/GL2/Q/holomorphic/605/8/a/n/1/9"]
"2-605-1.1-c7-0-61"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.52089985818504113711667261466	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/24"]
"2-605-1.1-c7-0-62"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.53557739305091482511988108340	["ModularForm/GL2/Q/holomorphic/605/8/a/f/1/2"]
"2-605-1.1-c7-0-63"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.54006335031684566910448262701	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/18"]
"2-605-1.1-c7-0-64"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.54071203443492637829800992635	["ModularForm/GL2/Q/holomorphic/605/8/a/m/1/9"]
"2-605-1.1-c7-0-65"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.55192536945896793318382016476	["ModularForm/GL2/Q/holomorphic/605/8/a/m/1/7"]
"2-605-1.1-c7-0-66"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.55364890574257888230151132298	["ModularForm/GL2/Q/holomorphic/605/8/a/p/1/10"]
"2-605-1.1-c7-0-67"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.55585825011216957308019855455	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/9"]
"2-605-1.1-c7-0-68"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.55846275140775269540693917000	["ModularForm/GL2/Q/holomorphic/605/8/a/q/1/3"]
"2-605-1.1-c7-0-69"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.56069928237909888878503038721	["ModularForm/GL2/Q/holomorphic/605/8/a/t/1/16"]
"2-605-1.1-c7-0-7"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.10381998448318792340692824003	["ModularForm/GL2/Q/holomorphic/605/8/a/p/1/6"]
"2-605-1.1-c7-0-70"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.56366262281564917811030863390	["ModularForm/GL2/Q/holomorphic/605/8/a/p/1/21"]
"2-605-1.1-c7-0-71"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.56761127781868095662525569914	["ModularForm/GL2/Q/holomorphic/605/8/a/n/1/5"]
"2-605-1.1-c7-0-72"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.57075475026865100264229164245	["ModularForm/GL2/Q/holomorphic/605/8/a/j/1/7"]
"2-605-1.1-c7-0-73"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.59633146071735652891030282304	["ModularForm/GL2/Q/holomorphic/605/8/a/f/1/1"]
"2-605-1.1-c7-0-74"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.60201838741304819664134749736	["ModularForm/GL2/Q/holomorphic/605/8/a/m/1/12"]
"2-605-1.1-c7-0-75"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.60886529098361922567104850889	["ModularForm/GL2/Q/holomorphic/605/8/a/m/1/1"]
"2-605-1.1-c7-0-76"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.60894617548784086580428432446	["ModularForm/GL2/Q/holomorphic/605/8/a/p/1/19"]
"2-605-1.1-c7-0-77"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.61240224049652988504874691513	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/14"]
"2-605-1.1-c7-0-78"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.61647128758300960331022492846	["ModularForm/GL2/Q/holomorphic/605/8/a/t/1/9"]
"2-605-1.1-c7-0-79"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.61907331242029439947702323443	["ModularForm/GL2/Q/holomorphic/605/8/a/k/1/3"]
"2-605-1.1-c7-0-8"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.14284282606247871255383398226	["ModularForm/GL2/Q/holomorphic/605/8/a/j/1/2"]
"2-605-1.1-c7-0-80"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.62184996070312716358556435029	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/17"]
"2-605-1.1-c7-0-81"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.62380580306950691717178793484	["ModularForm/GL2/Q/holomorphic/605/8/a/j/1/4"]
"2-605-1.1-c7-0-82"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.62408025184250349696574982902	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/1"]
"2-605-1.1-c7-0-83"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.62959637719311965006140372074	["ModularForm/GL2/Q/holomorphic/605/8/a/t/1/24"]
"2-605-1.1-c7-0-84"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.63052770296743352138618357287	["ModularForm/GL2/Q/holomorphic/605/8/a/t/1/1"]
"2-605-1.1-c7-0-85"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.63306555041277400353931908875	["ModularForm/GL2/Q/holomorphic/605/8/a/l/1/3"]
"2-605-1.1-c7-0-86"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.63343125405466699149103416417	["ModularForm/GL2/Q/holomorphic/605/8/a/t/1/20"]
"2-605-1.1-c7-0-87"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.63526191931988220962892885637	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/19"]
"2-605-1.1-c7-0-88"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.64013638327197637008159916014	["ModularForm/GL2/Q/holomorphic/605/8/a/j/1/3"]
"2-605-1.1-c7-0-89"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.65038912830912555209906793154	["ModularForm/GL2/Q/holomorphic/605/8/a/s/1/9"]
"2-605-1.1-c7-0-9"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.14409800469764135154535820854	["ModularForm/GL2/Q/holomorphic/605/8/a/j/1/6"]
"2-605-1.1-c7-0-90"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.65163423408875645821363858044	["ModularForm/GL2/Q/holomorphic/605/8/a/n/1/3"]
"2-605-1.1-c7-0-91"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.66551435907479295930106634362	["ModularForm/GL2/Q/holomorphic/605/8/a/s/1/14"]
"2-605-1.1-c7-0-92"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.66593251796418643901535553983	["ModularForm/GL2/Q/holomorphic/605/8/a/p/1/4"]
"2-605-1.1-c7-0-93"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.66615414274531775442566393486	["ModularForm/GL2/Q/holomorphic/605/8/a/s/1/12"]
"2-605-1.1-c7-0-94"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.68606223773767320546652452072	["ModularForm/GL2/Q/holomorphic/605/8/a/l/1/1"]
"2-605-1.1-c7-0-95"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.68819539771210812458393588578	["ModularForm/GL2/Q/holomorphic/605/8/a/r/1/10"]
"2-605-1.1-c7-0-96"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.68992837540071206389444309242	["ModularForm/GL2/Q/holomorphic/605/8/a/h/1/7"]
"2-605-1.1-c7-0-97"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.69510656459861417781884165640	["ModularForm/GL2/Q/holomorphic/605/8/a/t/1/5"]
"2-605-1.1-c7-0-98"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.70680857035064812045423024198	["ModularForm/GL2/Q/holomorphic/605/8/a/m/1/3"]
"2-605-1.1-c7-0-99"	13.74747032795102	188.99294041789375	2	605	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.70699641742309325319269180757	["ModularForm/GL2/Q/holomorphic/605/8/a/s/1/19"]


# 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).