
# lfunc_search downloaded from the LMFDB on 21 September 2026.
# Search link: https://www.lmfdb.org/L/2/23^2
# Query "{'degree': 2, 'conductor': 529}" returned 11925 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.



"2-23e2-23.10-c0-0-0"	0.5138145498940823	0.2640053916828583	2	529	"23.10"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.020852994586112145	0	1.98832976613431978869891846814	["ModularForm/GL2/Q/holomorphic/529/1/d/a/263/1", "ArtinRepresentation/2.529.33t2.a.f"]
"2-23e2-23.11-c0-0-0"	0.5138145498940823	0.2640053916828583	2	529	"23.11"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.05189780921049788	0	1.61711021586480188255228548776	["ModularForm/GL2/Q/holomorphic/529/1/d/a/195/1", "ArtinRepresentation/2.529.33t2.a.a"]
"2-23e2-23.14-c0-0-0"	0.5138145498940823	0.2640053916828583	2	529	"23.14"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.06450999300237818	0	1.90660409659246277446888356648	["ModularForm/GL2/Q/holomorphic/529/1/d/a/359/1", "ArtinRepresentation/2.529.33t2.a.b"]
"2-23e2-23.15-c0-0-0"	0.5138145498940823	0.2640053916828583	2	529	"23.15"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.3577832225927045	0	2.41459347363938636346834332744	["ModularForm/GL2/Q/holomorphic/529/1/d/a/130/1", "ArtinRepresentation/2.529.33t2.a.g"]
"2-23e2-23.17-c0-0-0"	0.5138145498940823	0.2640053916828583	2	529	"23.17"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2767155967392572	0	1.49090835484882860715703639907	["ModularForm/GL2/Q/holomorphic/529/1/d/a/63/1", "ArtinRepresentation/2.529.33t2.a.d"]
"2-23e2-23.19-c0-0-0"	0.5138145498940823	0.2640053916828583	2	529	"23.19"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2767155967392572	0	2.39033656988996553716550406438	["ModularForm/GL2/Q/holomorphic/529/1/d/a/42/1", "ArtinRepresentation/2.529.33t2.a.j"]
"2-23e2-23.20-c0-0-0"	0.5138145498940823	0.2640053916828583	2	529	"23.20"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.3577832225927045	0	1.33377017719317223005252703081	["ModularForm/GL2/Q/holomorphic/529/1/d/a/411/1", "ArtinRepresentation/2.529.33t2.a.h"]
"2-23e2-23.21-c0-0-0"	0.5138145498940823	0.2640053916828583	2	529	"23.21"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.05189780921049788	0	1.18544133226214076330003986811	["ModularForm/GL2/Q/holomorphic/529/1/d/a/274/1", "ArtinRepresentation/2.529.33t2.a.e"]
"2-23e2-23.5-c0-0-0"	0.5138145498940823	0.2640053916828583	2	529	"23.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.06450999300237818	0	2.53146292675253785001350500437	["ModularForm/GL2/Q/holomorphic/529/1/d/a/28/1", "ArtinRepresentation/2.529.33t2.a.c"]
"2-23e2-23.7-c0-0-0"	0.5138145498940823	0.2640053916828583	2	529	"23.7"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.020852994586112145	0	1.37860327792291508325272120362	["ModularForm/GL2/Q/holomorphic/529/1/d/a/352/1", "ArtinRepresentation/2.529.33t2.a.i"]
"2-23e2-1.1-c1-0-0"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.46169135144493053484300961322	["ModularForm/GL2/Q/holomorphic/529/2/a/d/1/1"]
"2-23e2-1.1-c1-0-1"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.49920237583885349159921848571	["ModularForm/GL2/Q/holomorphic/529/2/a/b/1/1"]
"2-23e2-1.1-c1-0-10"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.49016673478495051464534578056	["ModularForm/GL2/Q/holomorphic/529/2/a/f/1/2"]
"2-23e2-1.1-c1-0-11"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.49465548609043917645375106068	["ModularForm/GL2/Q/holomorphic/529/2/a/g/1/2"]
"2-23e2-1.1-c1-0-12"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.49690512660288956306866357673	["ModularForm/GL2/Q/holomorphic/529/2/a/j/1/5"]
"2-23e2-1.1-c1-0-13"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.56365816364982184781730230291	["ModularForm/GL2/Q/holomorphic/529/2/a/a/1/1"]
"2-23e2-1.1-c1-0-14"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.76006738066196025050284465933	["ModularForm/GL2/Q/holomorphic/529/2/a/j/1/4"]
"2-23e2-1.1-c1-0-15"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.76334727895928243218831617601	["ModularForm/GL2/Q/holomorphic/529/2/a/h/1/2"]
"2-23e2-1.1-c1-0-16"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.76404544998069086067921299653	["ModularForm/GL2/Q/holomorphic/529/2/a/j/1/3"]
"2-23e2-1.1-c1-0-17"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.97063682105558982080825942545	["ModularForm/GL2/Q/holomorphic/529/2/a/f/1/3"]
"2-23e2-1.1-c1-0-18"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.99996768572415531730373731592	["ModularForm/GL2/Q/holomorphic/529/2/a/c/1/2"]
"2-23e2-1.1-c1-0-19"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.01506044436354445135578328805	["ModularForm/GL2/Q/holomorphic/529/2/a/i/1/1"]
"2-23e2-1.1-c1-0-2"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.59260081307978610649595977547	["ModularForm/GL2/Q/holomorphic/529/2/a/f/1/1"]
"2-23e2-1.1-c1-0-20"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.01512607632177681093065860064	["ModularForm/GL2/Q/holomorphic/529/2/a/g/1/4"]
"2-23e2-1.1-c1-0-21"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.03467548871439129106540968832	["ModularForm/GL2/Q/holomorphic/529/2/a/g/1/3"]
"2-23e2-1.1-c1-0-22"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.17649186729030247357100323608	["ModularForm/GL2/Q/holomorphic/529/2/a/e/1/2"]
"2-23e2-1.1-c1-0-23"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.21808488822614578032609200091	["ModularForm/GL2/Q/holomorphic/529/2/a/b/1/2"]
"2-23e2-1.1-c1-0-24"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.35330474570925320964803744568	["ModularForm/GL2/Q/holomorphic/529/2/a/d/1/2"]
"2-23e2-1.1-c1-0-25"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.40017925819501907480454259775	["ModularForm/GL2/Q/holomorphic/529/2/a/i/1/2"]
"2-23e2-1.1-c1-0-26"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.42509230813021361471041893921	["ModularForm/GL2/Q/holomorphic/529/2/a/h/1/3"]
"2-23e2-1.1-c1-0-27"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.62440851308220145119535988552	["ModularForm/GL2/Q/holomorphic/529/2/a/h/1/4"]
"2-23e2-1.1-c1-0-28"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.62972098991262961586525701908	["ModularForm/GL2/Q/holomorphic/529/2/a/i/1/5"]
"2-23e2-1.1-c1-0-29"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.73137396143199116245389615121	["ModularForm/GL2/Q/holomorphic/529/2/a/i/1/3"]
"2-23e2-1.1-c1-0-3"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.73170715735506229020222124456	["ModularForm/GL2/Q/holomorphic/529/2/a/a/1/2"]
"2-23e2-1.1-c1-0-30"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.96429008421902837505163149886	["ModularForm/GL2/Q/holomorphic/529/2/a/i/1/4"]
"2-23e2-1.1-c1-0-4"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.06124492686432802058530837298	["ModularForm/GL2/Q/holomorphic/529/2/a/e/1/1"]
"2-23e2-1.1-c1-0-5"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.13042339474823028193423544641	["ModularForm/GL2/Q/holomorphic/529/2/a/c/1/1"]
"2-23e2-1.1-c1-0-6"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.14401939920308373601966596737	["ModularForm/GL2/Q/holomorphic/529/2/a/j/1/2"]
"2-23e2-1.1-c1-0-7"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.21261031455514073487963443334	["ModularForm/GL2/Q/holomorphic/529/2/a/j/1/1"]
"2-23e2-1.1-c1-0-8"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.38266411121798212320661941798	["ModularForm/GL2/Q/holomorphic/529/2/a/g/1/1"]
"2-23e2-1.1-c1-0-9"	2.0552581995763295	4.224086266925735	2	529	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.44107315565445325210518686302	["ModularForm/GL2/Q/holomorphic/529/2/a/h/1/1"]
"2-23e2-23.12-c1-0-0"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3648437879623498	0	0.13798227531959051401540816796	["ModularForm/GL2/Q/holomorphic/529/2/c/e/334/1"]
"2-23e2-23.12-c1-0-1"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3077502304138813	0	0.33459424238967101657750385079	["ModularForm/GL2/Q/holomorphic/529/2/c/p/334/2"]
"2-23e2-23.12-c1-0-10"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.18611354355322485	0	0.966014050898413966737217564831	["ModularForm/GL2/Q/holomorphic/529/2/c/c/334/1"]
"2-23e2-23.12-c1-0-11"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.05099742260757029	0	1.10695804844631226782539337448	["ModularForm/GL2/Q/holomorphic/529/2/c/n/334/1"]
"2-23e2-23.12-c1-0-12"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.14936330924034807	0	1.15002151225890468734445522054	["ModularForm/GL2/Q/holomorphic/529/2/c/m/334/1"]
"2-23e2-23.12-c1-0-13"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.007621861721658871	0	1.18141832459102416664128241395	["ModularForm/GL2/Q/holomorphic/529/2/c/q/334/3"]
"2-23e2-23.12-c1-0-14"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.14936330924034807	0	1.21431067146667675330557548248	["ModularForm/GL2/Q/holomorphic/529/2/c/l/334/2"]
"2-23e2-23.12-c1-0-15"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.27452481976555215	0	1.23078077759071882129107289710	["ModularForm/GL2/Q/holomorphic/529/2/c/d/334/1"]
"2-23e2-23.12-c1-0-16"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.18302560614416793	0	1.29288331730868199345027450475	["ModularForm/GL2/Q/holomorphic/529/2/c/j/334/1"]
"2-23e2-23.12-c1-0-17"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.19903763869461957	0	1.29389337680302002655326590226	["ModularForm/GL2/Q/holomorphic/529/2/c/q/334/1"]
"2-23e2-23.12-c1-0-18"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.05099742260757029	0	1.31917870162363831082873095293	["ModularForm/GL2/Q/holomorphic/529/2/c/n/334/2"]
"2-23e2-23.12-c1-0-19"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.007621861721658871	0	1.37954789270278804019988678212	["ModularForm/GL2/Q/holomorphic/529/2/c/q/334/2"]
"2-23e2-23.12-c1-0-2"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3196591461286614	0	0.39511814938081448023955791248	["ModularForm/GL2/Q/holomorphic/529/2/c/l/334/1"]
"2-23e2-23.12-c1-0-20"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.08655663162942047	0	1.48561504345615982818675164948	["ModularForm/GL2/Q/holomorphic/529/2/c/r/334/2"]
"2-23e2-23.12-c1-0-21"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.04365699841626604	0	1.49426065786858479941649268094	["ModularForm/GL2/Q/holomorphic/529/2/c/k/334/2"]
"2-23e2-23.12-c1-0-22"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.04365699841626604	0	1.49940369594443123071675567444	["ModularForm/GL2/Q/holomorphic/529/2/c/k/334/1"]
"2-23e2-23.12-c1-0-23"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.06045439899699847	0	1.65410079992449208821522923255	["ModularForm/GL2/Q/holomorphic/529/2/c/g/334/1"]
"2-23e2-23.12-c1-0-24"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3077502304138813	0	1.75495895108579828853419774781	["ModularForm/GL2/Q/holomorphic/529/2/c/p/334/1"]
"2-23e2-23.12-c1-0-25"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.19903763869461957	0	1.86695511659577554206763257898	["ModularForm/GL2/Q/holomorphic/529/2/c/q/334/4"]
"2-23e2-23.12-c1-0-26"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.37272741292210504	0	2.09209050852227310625309427939	["ModularForm/GL2/Q/holomorphic/529/2/c/r/334/4"]
"2-23e2-23.12-c1-0-27"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.18302560614416793	0	2.15497778894469365018046707304	["ModularForm/GL2/Q/holomorphic/529/2/c/j/334/2"]
"2-23e2-23.12-c1-0-28"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3077502304138813	0	2.56142807072159652223019338048	["ModularForm/GL2/Q/holomorphic/529/2/c/p/334/3"]
"2-23e2-23.12-c1-0-29"	2.0552581995763295	4.224086266925735	2	529	"23.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.44720180418657457	0	2.65006932074301751933721650524	["ModularForm/GL2/Q/holomorphic/529/2/c/o/334/2"]
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"2-23e2-1.1-c7-0-55"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.43634863316263629969576911239	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/3"]
"2-23e2-1.1-c7-0-56"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.43881315560689200384436897219	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/46"]
"2-23e2-1.1-c7-0-57"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.43892986401110118623183824517	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/35"]
"2-23e2-1.1-c7-0-58"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.44568898242136893761388964268	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/33"]
"2-23e2-1.1-c7-0-59"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.44596621165169410144080394528	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/18"]
"2-23e2-1.1-c7-0-6"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.05092858245056958613044765773	["ModularForm/GL2/Q/holomorphic/529/8/a/h/1/13"]
"2-23e2-1.1-c7-0-60"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.44685931642261872471571115170	["ModularForm/GL2/Q/holomorphic/529/8/a/h/1/6"]
"2-23e2-1.1-c7-0-61"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.44811934092740059621004951232	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/27"]
"2-23e2-1.1-c7-0-62"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.44981710309865159929780719698	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/53"]
"2-23e2-1.1-c7-0-63"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.45098466713385295048309097803	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/40"]
"2-23e2-1.1-c7-0-64"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.45133708182588476613176136267	["ModularForm/GL2/Q/holomorphic/529/8/a/g/1/7"]
"2-23e2-1.1-c7-0-65"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.45969690684929307867564972699	["ModularForm/GL2/Q/holomorphic/529/8/a/j/1/43"]
"2-23e2-1.1-c7-0-66"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.46184441203024361626579791652	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/27"]
"2-23e2-1.1-c7-0-67"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.47578910850313261007776495671	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/4"]
"2-23e2-1.1-c7-0-68"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.47832887153579954904196627800	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/38"]
"2-23e2-1.1-c7-0-69"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.48108608802918211695265756019	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/9"]
"2-23e2-1.1-c7-0-7"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.06879865186533647611290338427	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/5"]
"2-23e2-1.1-c7-0-70"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.48283323094186314755091274897	["ModularForm/GL2/Q/holomorphic/529/8/a/h/1/17"]
"2-23e2-1.1-c7-0-71"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.48503870401011124017995776583	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/58"]
"2-23e2-1.1-c7-0-72"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.48652759317662335108796255832	["ModularForm/GL2/Q/holomorphic/529/8/a/c/1/5"]
"2-23e2-1.1-c7-0-73"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.49302211589746445280382295294	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/16"]
"2-23e2-1.1-c7-0-74"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.49884154982933945746273374404	["ModularForm/GL2/Q/holomorphic/529/8/a/h/1/23"]
"2-23e2-1.1-c7-0-75"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.50069481480383268081888224116	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/21"]
"2-23e2-1.1-c7-0-76"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.50480606945288607010205770115	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/20"]
"2-23e2-1.1-c7-0-77"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.51386162202228064641902430922	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/40"]
"2-23e2-1.1-c7-0-78"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.52303601762635602203655509473	["ModularForm/GL2/Q/holomorphic/529/8/a/b/1/1"]
"2-23e2-1.1-c7-0-79"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.53734832847516881726974947098	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/6"]
"2-23e2-1.1-c7-0-8"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.10045172903295286392291922189	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/20"]
"2-23e2-1.1-c7-0-80"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.53773417584281841318064455776	["ModularForm/GL2/Q/holomorphic/529/8/a/e/1/5"]
"2-23e2-1.1-c7-0-81"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.54717566334872069143905951805	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/38"]
"2-23e2-1.1-c7-0-82"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.54723815222957518530924801096	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/29"]
"2-23e2-1.1-c7-0-83"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.54934601600879711338185709747	["ModularForm/GL2/Q/holomorphic/529/8/a/h/1/2"]
"2-23e2-1.1-c7-0-84"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.55663962483735272852560648638	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/19"]
"2-23e2-1.1-c7-0-85"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.58230402258468296934311748102	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/14"]
"2-23e2-1.1-c7-0-86"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.58321886013354389622836801242	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/56"]
"2-23e2-1.1-c7-0-87"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.58531225957395997613585958068	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/4"]
"2-23e2-1.1-c7-0-88"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.59018396228694376131765191089	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/35"]
"2-23e2-1.1-c7-0-89"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.60840127416819124992214379880	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/15"]
"2-23e2-1.1-c7-0-9"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.10675610207413112785385506477	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/24"]
"2-23e2-1.1-c7-0-90"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.61306010758467065463772803813	["ModularForm/GL2/Q/holomorphic/529/8/a/j/1/21"]
"2-23e2-1.1-c7-0-91"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.61511611988288148297897919830	["ModularForm/GL2/Q/holomorphic/529/8/a/j/1/36"]
"2-23e2-1.1-c7-0-92"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.61623529186709092341060550244	["ModularForm/GL2/Q/holomorphic/529/8/a/h/1/11"]
"2-23e2-1.1-c7-0-93"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.61836582038380443464211380631	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/5"]
"2-23e2-1.1-c7-0-94"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.62311590878136428225288415247	["ModularForm/GL2/Q/holomorphic/529/8/a/j/1/18"]
"2-23e2-1.1-c7-0-95"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.62512535935649487650300239707	["ModularForm/GL2/Q/holomorphic/529/8/a/h/1/12"]
"2-23e2-1.1-c7-0-96"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.62646683431120390222924551365	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/43"]
"2-23e2-1.1-c7-0-97"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.63036206289453243919527944271	["ModularForm/GL2/Q/holomorphic/529/8/a/j/1/14"]
"2-23e2-1.1-c7-0-98"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.63205474640356343647805630831	["ModularForm/GL2/Q/holomorphic/529/8/a/k/1/33"]
"2-23e2-1.1-c7-0-99"	12.855025417365011	165.25167848110047	2	529	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.63262713632152033226666362103	["ModularForm/GL2/Q/holomorphic/529/8/a/i/1/1"]


# 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).


