# lfunc_search downloaded from the LMFDB on 25 May 2026.
# Search link: https://www.lmfdb.org/L/2/567/189.104/c1-0
# Query "{'degree': 2, 'conductor': 567, 'spectral_label': 'c1-0'}" returned 8552 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.



"2-567-1.1-c1-0-0"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.67478738318070858054725244698	["ModularForm/GL2/Q/holomorphic/567/2/a/i/1/2"]
"2-567-1.1-c1-0-1"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.69247686109260914487240933215	["ModularForm/GL2/Q/holomorphic/567/2/a/e/1/1"]
"2-567-1.1-c1-0-10"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.56246823708341917748907078270	["ModularForm/GL2/Q/holomorphic/567/2/a/h/1/2"]
"2-567-1.1-c1-0-11"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.56542435205385803237484305376	["ModularForm/GL2/Q/holomorphic/567/2/a/d/1/1"]
"2-567-1.1-c1-0-12"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.67718686743966778762820678462	["ModularForm/GL2/Q/holomorphic/567/2/a/c/1/2"]
"2-567-1.1-c1-0-13"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.78483262292759609025059731828	["ModularForm/GL2/Q/holomorphic/567/2/a/i/1/4"]
"2-567-1.1-c1-0-14"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.85017468245371177253221244307	["ModularForm/GL2/Q/holomorphic/567/2/a/c/1/1"]
"2-567-1.1-c1-0-15"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.89538931356427475498208080000	["EllipticCurve/Q/567/a", "ModularForm/GL2/Q/holomorphic/567/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/567/2/a/a"]
"2-567-1.1-c1-0-16"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.92189327035101640534250179792	["ModularForm/GL2/Q/holomorphic/567/2/a/h/1/3"]
"2-567-1.1-c1-0-17"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.97327481307346946432861525220	["ModularForm/GL2/Q/holomorphic/567/2/a/e/1/3"]
"2-567-1.1-c1-0-18"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.07072477954214546651559024617	["ModularForm/GL2/Q/holomorphic/567/2/a/d/1/2"]
"2-567-1.1-c1-0-19"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.08165930963631097004582303146	["ModularForm/GL2/Q/holomorphic/567/2/a/f/1/3"]
"2-567-1.1-c1-0-2"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.836137487424588872797300600778	["ModularForm/GL2/Q/holomorphic/567/2/a/i/1/1"]
"2-567-1.1-c1-0-20"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.10742496733941490908995335729	["ModularForm/GL2/Q/holomorphic/567/2/a/g/1/3"]
"2-567-1.1-c1-0-21"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.38454120518082410602072645616	["ModularForm/GL2/Q/holomorphic/567/2/a/c/1/3"]
"2-567-1.1-c1-0-22"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.44493410532661624373120759375	["EllipticCurve/Q/567/b", "ModularForm/GL2/Q/holomorphic/567/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/567/2/a/b"]
"2-567-1.1-c1-0-23"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.78746966287949503706406316513	["ModularForm/GL2/Q/holomorphic/567/2/a/d/1/3"]
"2-567-1.1-c1-0-3"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.01347993391273402801437244725	["ModularForm/GL2/Q/holomorphic/567/2/a/g/1/2"]
"2-567-1.1-c1-0-4"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.06737710998401794297751551002	["ModularForm/GL2/Q/holomorphic/567/2/a/f/1/2"]
"2-567-1.1-c1-0-5"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.07966512384365140624752892278	["ModularForm/GL2/Q/holomorphic/567/2/a/h/1/1"]
"2-567-1.1-c1-0-6"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.13520287727974584344038223712	["ModularForm/GL2/Q/holomorphic/567/2/a/e/1/2"]
"2-567-1.1-c1-0-7"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.14553341242214246398375788316	["ModularForm/GL2/Q/holomorphic/567/2/a/f/1/1"]
"2-567-1.1-c1-0-8"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.19317538245399821070347558123	["ModularForm/GL2/Q/holomorphic/567/2/a/g/1/1"]
"2-567-1.1-c1-0-9"	2.1277964645629526	4.5275177946066	2	567	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.39233024194959116741180448877	["ModularForm/GL2/Q/holomorphic/567/2/a/i/1/3"]
"2-567-189.101-c1-0-0"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.18836800259739425	0	0.10105334363817669444513759141	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/1"]
"2-567-189.101-c1-0-1"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4326770040824998	0	0.18581588897146692395456655241	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/12"]
"2-567-189.101-c1-0-10"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05264393260932536	0	1.28099267870412349006290835261	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/7"]
"2-567-189.101-c1-0-11"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.12520916103103163	0	1.31958089627583693049720957317	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/6"]
"2-567-189.101-c1-0-12"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.12974743806714029	0	1.33568714533659100642811355412	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/5"]
"2-567-189.101-c1-0-13"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1248749939584231	0	1.45337346347671756736537846465	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/18"]
"2-567-189.101-c1-0-14"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.10664403252762036	0	1.55131551150344131214775577489	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/15"]
"2-567-189.101-c1-0-15"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07459358221558209	0	1.59782000530170614501307051586	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/16"]
"2-567-189.101-c1-0-16"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.212322791686633	0	1.71237254839738834220298166137	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/19"]
"2-567-189.101-c1-0-17"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.12330093015743077	0	1.74609253651154536065624750889	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/2"]
"2-567-189.101-c1-0-18"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07745980817690114	0	1.86278688305777841367503971781	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/10"]
"2-567-189.101-c1-0-19"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.37297296185649315	0	2.28145425400614852267215101764	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/21"]
"2-567-189.101-c1-0-2"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.226905750990982	0	0.41442405360295471212940593587	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/17"]
"2-567-189.101-c1-0-20"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.36755985297159227	0	2.52214965050431831530891602604	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/20"]
"2-567-189.101-c1-0-21"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4775381078074587	0	2.69080533452726133733537887327	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/22"]
"2-567-189.101-c1-0-3"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.44524444292841253	0	0.48182983884653254774562459056	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/9"]
"2-567-189.101-c1-0-4"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.44729420935032493	0	0.48793425857723350146972523019	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/3"]
"2-567-189.101-c1-0-5"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.38113344911363034	0	0.56576954116813990769640818519	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/8"]
"2-567-189.101-c1-0-6"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.365366277746906	0	0.63287548987250787324419281047	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/11"]
"2-567-189.101-c1-0-7"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.18647652009659818	0	0.77940904299551353733557515373	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/14"]
"2-567-189.101-c1-0-8"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2550776487634245	0	0.815437706579017695181028003545	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/13"]
"2-567-189.101-c1-0-9"	2.1277964645629526	4.5275177946066	2	567	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.18173077902550805	0	1.17642712091799465241832692403	["ModularForm/GL2/Q/holomorphic/567/2/ba/a/143/4"]
"2-567-189.104-c1-0-0"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.14699319777290362	0	0.18563888310864128349320131330	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/21"]
"2-567-189.104-c1-0-1"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4639625527997455	0	0.29170233864630120088462572004	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/6"]
"2-567-189.104-c1-0-10"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.14411784126415	0	1.24498697360249544815644899104	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/17"]
"2-567-189.104-c1-0-11"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.027670415554835657	0	1.28742466996855883880092502370	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/12"]
"2-567-189.104-c1-0-12"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.021151899999631896	0	1.39529206755886985430225572194	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/13"]
"2-567-189.104-c1-0-13"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.17360506730027012	0	1.41273846828360776971075805723	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/4"]
"2-567-189.104-c1-0-14"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.05066010085221308	0	1.64223453434055037304433458889	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/8"]
"2-567-189.104-c1-0-15"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.026501568484297147	0	1.66741323012275884133599345243	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/10"]
"2-567-189.104-c1-0-16"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.32474113686022865	0	1.67661295513340496149583814247	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/19"]
"2-567-189.104-c1-0-17"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.12411934429406349	0	1.71094004218397542352218835196	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/14"]
"2-567-189.104-c1-0-18"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3588090751745572	0	2.13256775181817699605715483833	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/16"]
"2-567-189.104-c1-0-19"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4471729383581585	0	2.28071676089057137069950696065	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/20"]
"2-567-189.104-c1-0-2"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.38833121665102033	0	0.36427923660775265729548725121	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/2"]
"2-567-189.104-c1-0-20"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4820174653824455	0	2.32565462482955329011097922757	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/18"]
"2-567-189.104-c1-0-21"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.35610911726129624	0	2.92171927894428998993197138870	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/22"]
"2-567-189.104-c1-0-3"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3943058548981922	0	0.46940828001061096680352140061	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/5"]
"2-567-189.104-c1-0-4"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3877204319732178	0	0.74680668380803112335870905920	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/9"]
"2-567-189.104-c1-0-5"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4838284694201708	0	0.78508029347627182461220253220	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/7"]
"2-567-189.104-c1-0-6"	2.1277964645629526	4.5275177946066	2	567	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.376281672343244	0	0.857688289764358318450164057563	["ModularForm/GL2/Q/holomorphic/567/2/be/a/503/3"]
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"2-567-9.4-c1-0-15"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2222222222222222	0	1.74278280528179097782973885708	["ModularForm/GL2/Q/holomorphic/567/2/f/d/190/1"]
"2-567-9.4-c1-0-16"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.11111111111111113	0	1.91384436702685900172554370375	["ModularForm/GL2/Q/holomorphic/567/2/f/m/190/3"]
"2-567-9.4-c1-0-17"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.05555555555555555	0	1.94369059287479573153554866939	["ModularForm/GL2/Q/holomorphic/567/2/f/g/190/1"]
"2-567-9.4-c1-0-18"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3888888888888889	0	1.97431014771842500510714112996	["ModularForm/GL2/Q/holomorphic/567/2/f/c/190/1"]
"2-567-9.4-c1-0-19"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1388888888888889	0	2.02655574121094565938772890379	["ModularForm/GL2/Q/holomorphic/567/2/f/n/190/3"]
"2-567-9.4-c1-0-2"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.11111111111111113	0	0.39620014345162603517039108289	["ModularForm/GL2/Q/holomorphic/567/2/f/k/190/1"]
"2-567-9.4-c1-0-20"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2222222222222222	0	2.03285933843507897008001771059	["ModularForm/GL2/Q/holomorphic/567/2/f/e/190/1"]
"2-567-9.4-c1-0-21"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2777777777777778	1	2.18277270191315355161761603580	["ModularForm/GL2/Q/holomorphic/567/2/f/a/190/1"]
"2-567-9.4-c1-0-22"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4444444444444444	0	2.31227417119174298209987017253	["ModularForm/GL2/Q/holomorphic/567/2/f/j/190/1"]
"2-567-9.4-c1-0-23"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3888888888888889	0	2.40776218169233389455132665265	["ModularForm/GL2/Q/holomorphic/567/2/f/l/190/2"]
"2-567-9.4-c1-0-3"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3888888888888889	0	0.66883297642523537982502379660	["ModularForm/GL2/Q/holomorphic/567/2/f/l/190/3"]
"2-567-9.4-c1-0-4"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3888888888888889	0	0.75660365681407308590198330003	["ModularForm/GL2/Q/holomorphic/567/2/f/i/190/2"]
"2-567-9.4-c1-0-5"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4444444444444444	0	0.77910926802181957947642901557	["ModularForm/GL2/Q/holomorphic/567/2/f/j/190/2"]
"2-567-9.4-c1-0-6"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1388888888888889	0	0.832746723388056974957765595927	["ModularForm/GL2/Q/holomorphic/567/2/f/n/190/1"]
"2-567-9.4-c1-0-7"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.05555555555555555	0	1.01961052068270479706967825022	["ModularForm/GL2/Q/holomorphic/567/2/f/b/190/1"]
"2-567-9.4-c1-0-8"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3611111111111111	0	1.11995985233995433737106232724	["ModularForm/GL2/Q/holomorphic/567/2/f/n/190/4"]
"2-567-9.4-c1-0-9"	2.1277964645629526	4.5275177946066	2	567	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.11111111111111113	0	1.12052124353740472277859379283	["ModularForm/GL2/Q/holomorphic/567/2/f/m/190/2"]
"2-567-9.7-c1-0-0"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3888888888888889	0	0.50382732868667070068770386961	["ModularForm/GL2/Q/holomorphic/567/2/f/l/379/1"]
"2-567-9.7-c1-0-1"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4444444444444444	0	0.62310919697730656263421114287	["ModularForm/GL2/Q/holomorphic/567/2/f/j/379/1"]
"2-567-9.7-c1-0-10"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11111111111111113	0	1.31046971586801636628892728414	["ModularForm/GL2/Q/holomorphic/567/2/f/m/379/3"]
"2-567-9.7-c1-0-11"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1388888888888889	0	1.33493768224810915073284609258	["ModularForm/GL2/Q/holomorphic/567/2/f/n/379/3"]
"2-567-9.7-c1-0-12"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11111111111111113	0	1.37114617351508921125778695066	["ModularForm/GL2/Q/holomorphic/567/2/f/k/379/2"]
"2-567-9.7-c1-0-13"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11111111111111113	0	1.49626899386113813250961403039	["ModularForm/GL2/Q/holomorphic/567/2/f/f/379/1"]
"2-567-9.7-c1-0-14"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11111111111111113	0	1.51980847526357409828092862039	["ModularForm/GL2/Q/holomorphic/567/2/f/m/379/2"]
"2-567-9.7-c1-0-15"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11111111111111113	0	1.54497310497130911948835887036	["ModularForm/GL2/Q/holomorphic/567/2/f/k/379/1"]
"2-567-9.7-c1-0-16"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11111111111111113	0	1.65155921756506443363791051498	["ModularForm/GL2/Q/holomorphic/567/2/f/m/379/1"]
"2-567-9.7-c1-0-17"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2777777777777778	0	1.79673254301043775437869586270	["ModularForm/GL2/Q/holomorphic/567/2/f/h/379/1"]
"2-567-9.7-c1-0-18"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2777777777777778	1	1.83052387424301387508268924935	["ModularForm/GL2/Q/holomorphic/567/2/f/a/379/1"]
"2-567-9.7-c1-0-19"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3611111111111111	0	2.01145159718181003928522683572	["ModularForm/GL2/Q/holomorphic/567/2/f/n/379/4"]
"2-567-9.7-c1-0-2"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2222222222222222	0	0.72277702127574534155772472532	["ModularForm/GL2/Q/holomorphic/567/2/f/d/379/1"]
"2-567-9.7-c1-0-20"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3611111111111111	0	2.16102763606980155098972098408	["ModularForm/GL2/Q/holomorphic/567/2/f/n/379/2"]
"2-567-9.7-c1-0-21"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4444444444444444	0	2.28847172101989537014774372157	["ModularForm/GL2/Q/holomorphic/567/2/f/j/379/2"]
"2-567-9.7-c1-0-22"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3888888888888889	0	2.95722146733724532710690750023	["ModularForm/GL2/Q/holomorphic/567/2/f/l/379/3"]
"2-567-9.7-c1-0-23"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3888888888888889	0	3.15808075737164071060245866665	["ModularForm/GL2/Q/holomorphic/567/2/f/i/379/2"]
"2-567-9.7-c1-0-3"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3888888888888889	0	0.72607937281851104768554051954	["ModularForm/GL2/Q/holomorphic/567/2/f/c/379/1"]
"2-567-9.7-c1-0-4"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3888888888888889	0	0.74048924406084730901836778466	["ModularForm/GL2/Q/holomorphic/567/2/f/l/379/2"]
"2-567-9.7-c1-0-5"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3888888888888889	0	0.940417049047063968904108612557	["ModularForm/GL2/Q/holomorphic/567/2/f/i/379/1"]
"2-567-9.7-c1-0-6"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1388888888888889	0	1.12299168323895143833583310758	["ModularForm/GL2/Q/holomorphic/567/2/f/n/379/1"]
"2-567-9.7-c1-0-7"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2222222222222222	0	1.13684157457683013998255757108	["ModularForm/GL2/Q/holomorphic/567/2/f/e/379/1"]
"2-567-9.7-c1-0-8"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05555555555555555	0	1.18238002414778718699540612194	["ModularForm/GL2/Q/holomorphic/567/2/f/g/379/1"]
"2-567-9.7-c1-0-9"	2.1277964645629526	4.5275177946066	2	567	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05555555555555555	0	1.28787422604450895769164124918	["ModularForm/GL2/Q/holomorphic/567/2/f/b/379/1"]


# 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).