# lfunc_search downloaded from the LMFDB on 18 April 2026.
# Search link: https://www.lmfdb.org/L/2/189/189.5
# Query "{'degree': 2, 'conductor': 189}" returned 8420 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.



"2-189-21.11-c0-0-0"	0.3071209653990386	0.09432328738763746	2	189	"21.11"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.07324685680636028	0	1.91255076604218535700168097614	["ModularForm/GL2/Q/holomorphic/189/1/q/a/53/1", "ArtinRepresentation/2.189.6t5.a.a"]
"2-189-21.2-c0-0-0"	0.3071209653990386	0.09432328738763746	2	189	"21.2"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.07324685680636028	0	2.55939948811483532521196998680	["ModularForm/GL2/Q/holomorphic/189/1/q/a/107/1", "ArtinRepresentation/2.189.6t5.a.b"]
"2-189-7.3-c0-0-0"	0.3071209653990386	0.09432328738763746	2	189	"7.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.06316038027938721	0	2.74706031030906967687092263124	["ModularForm/GL2/Q/holomorphic/189/1/m/a/136/1"]
"2-189-7.5-c0-0-0"	0.3071209653990386	0.09432328738763746	2	189	"7.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.06316038027938721	0	2.08500484518962646615119309951	["ModularForm/GL2/Q/holomorphic/189/1/m/a/82/1"]
"2-189-1.1-c1-0-0"	1.2284838615961546	1.5091725982022	2	189	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.19573202810142059571855967422	["ModularForm/GL2/Q/holomorphic/189/2/a/e/1/1"]
"2-189-1.1-c1-0-1"	1.2284838615961546	1.5091725982022	2	189	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.37701167359795407767938570487	["ModularForm/GL2/Q/holomorphic/189/2/a/f/1/1"]
"2-189-1.1-c1-0-2"	1.2284838615961546	1.5091725982022	2	189	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.69414023663856774565794959548	["EllipticCurve/Q/189/c", "ModularForm/GL2/Q/holomorphic/189/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/189/2/a/c"]
"2-189-1.1-c1-0-3"	1.2284838615961546	1.5091725982022	2	189	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.31763303042601749523987733960	["ModularForm/GL2/Q/holomorphic/189/2/a/e/1/2"]
"2-189-1.1-c1-0-4"	1.2284838615961546	1.5091725982022	2	189	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.34130595001443635884001685756	["EllipticCurve/Q/189/a", "ModularForm/GL2/Q/holomorphic/189/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/189/2/a/a"]
"2-189-1.1-c1-0-5"	1.2284838615961546	1.5091725982022	2	189	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	2.42236155159716987191201970387	["EllipticCurve/Q/189/d", "ModularForm/GL2/Q/holomorphic/189/2/a/d/1/1", "ModularForm/GL2/Q/holomorphic/189/2/a/d"]
"2-189-1.1-c1-0-6"	1.2284838615961546	1.5091725982022	2	189	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.74106997503221499804348918654	["ModularForm/GL2/Q/holomorphic/189/2/a/f/1/2"]
"2-189-1.1-c1-0-7"	1.2284838615961546	1.5091725982022	2	189	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	3.05701292571172651199468963397	["EllipticCurve/Q/189/b", "ModularForm/GL2/Q/holomorphic/189/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/189/2/a/b"]
"2-189-189.101-c1-0-0"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.49930931657973243	0	0.15924241250387371862464249774	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/8"]
"2-189-189.101-c1-0-1"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3242716143901525	0	0.35069715895337683308750955795	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/4"]
"2-189-189.101-c1-0-10"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.03150254520747681	0	1.66914650186055983857923072327	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/12"]
"2-189-189.101-c1-0-11"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.008830570891379171	0	1.70255150418066574753903759887	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/6"]
"2-189-189.101-c1-0-12"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1436863571321924	0	1.88721534736917274968966389007	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/5"]
"2-189-189.101-c1-0-13"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07723905628486148	0	2.06181851762054097184471879296	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/1"]
"2-189-189.101-c1-0-14"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.15665094793783554	0	2.07281348564212741926284495801	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/16"]
"2-189-189.101-c1-0-15"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.05567471527956918	0	2.15875758703812398201031099387	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/17"]
"2-189-189.101-c1-0-16"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.06200332926947391	0	2.34061196717170909444253951215	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/11"]
"2-189-189.101-c1-0-17"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.18160245843770031	0	2.45767576956587712689901178624	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/15"]
"2-189-189.101-c1-0-18"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.29820854240615613	0	2.92935547350536007070193442701	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/22"]
"2-189-189.101-c1-0-19"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2579461054450694	0	3.22655976314610917410075192893	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/20"]
"2-189-189.101-c1-0-2"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.32449916874889884	0	0.41681279251393353293675162520	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/3"]
"2-189-189.101-c1-0-20"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.32423018859139163	0	3.28032405396210625880611920173	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/19"]
"2-189-189.101-c1-0-21"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4579831919202464	0	3.81961180332311301157886471575	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/21"]
"2-189-189.101-c1-0-3"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3422620497534644	0	0.75754813847547919791296783365	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/7"]
"2-189-189.101-c1-0-4"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.19960076256354475	0	0.830965626818588458410407700782	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/14"]
"2-189-189.101-c1-0-5"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2843105017734971	0	0.852340565517255519102660794241	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/2"]
"2-189-189.101-c1-0-6"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.31598466075392756	0	1.25332310184182280441666623128	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/9"]
"2-189-189.101-c1-0-7"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.10603806843987275	0	1.29000546003868555407323154778	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/18"]
"2-189-189.101-c1-0-8"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.23349554758613533	0	1.42064565857742030824624060607	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/10"]
"2-189-189.101-c1-0-9"	1.2284838615961546	1.5091725982022	2	189	"189.101"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.12861547029050033	0	1.57120247218581575094770730900	["ModularForm/GL2/Q/holomorphic/189/2/ba/a/101/13"]
"2-189-189.104-c1-0-0"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3931809216737239	0	0.18628116788880523832285874561	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/5"]
"2-189-189.104-c1-0-1"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.27274493360978347	0	0.61504056698689675760766036149	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/1"]
"2-189-189.104-c1-0-10"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.022349285294455113	0	1.95607085145242010205044208988	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/3"]
"2-189-189.104-c1-0-11"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1625090680674694	0	1.98488217511651218881131303379	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/15"]
"2-189-189.104-c1-0-12"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.016175895420998017	0	2.12215285300381282511656673305	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/12"]
"2-189-189.104-c1-0-13"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.018139146901823947	0	2.25507898501513281775033542344	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/2"]
"2-189-189.104-c1-0-14"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.06209934070268537	0	2.26576693511251838110254722210	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/10"]
"2-189-189.104-c1-0-15"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.193552877418481	0	2.35267583813215529199681144286	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/20"]
"2-189-189.104-c1-0-16"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.026604481784181663	0	2.38897476155400260002639036517	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/14"]
"2-189-189.104-c1-0-17"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1969976383398533	0	2.46473636057687317526411836033	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/16"]
"2-189-189.104-c1-0-18"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.36350258645230615	0	3.04833762327746762751464674276	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/17"]
"2-189-189.104-c1-0-19"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.47292562488031503	0	3.18053582291439509574177122086	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/21"]
"2-189-189.104-c1-0-2"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3327359740462987	0	0.78162736925630196067782257656	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/11"]
"2-189-189.104-c1-0-20"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4908762723755072	0	3.38085059951216313799174021029	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/19"]
"2-189-189.104-c1-0-21"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.46428628866099103	0	3.89766894190991657579219031512	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/22"]
"2-189-189.104-c1-0-3"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2208373914844397	0	1.13243578284592558176413539513	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/7"]
"2-189-189.104-c1-0-4"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.44471870244457157	0	1.14080379051812746231651563492	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/6"]
"2-189-189.104-c1-0-5"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.33493321500288303	0	1.26383387478182645234470946005	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/9"]
"2-189-189.104-c1-0-6"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05917351775830339	0	1.32131213310530824579739072216	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/13"]
"2-189-189.104-c1-0-7"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.35521891320761506	0	1.34827219096548597625007484269	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/4"]
"2-189-189.104-c1-0-8"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.06684071564614057	0	1.43443342096684117114878974243	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/18"]
"2-189-189.104-c1-0-9"	1.2284838615961546	1.5091725982022	2	189	"189.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.30989288438371565	0	1.45575089749030488512322133253	["ModularForm/GL2/Q/holomorphic/189/2/be/a/104/8"]
"2-189-189.110-c1-0-0"	1.2284838615961546	1.5091725982022	2	189	"189.110"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.46575562440009227	0	0.48870943604134549751981404707	["ModularForm/GL2/Q/holomorphic/189/2/bd/a/110/6"]
"2-189-189.110-c1-0-1"	1.2284838615961546	1.5091725982022	2	189	"189.110"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4815648022042917	0	0.77190616398030414116192628744	["ModularForm/GL2/Q/holomorphic/189/2/bd/a/110/9"]
"2-189-189.110-c1-0-10"	1.2284838615961546	1.5091725982022	2	189	"189.110"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.054983539751695315	0	1.69974124936187307100175894235	["ModularForm/GL2/Q/holomorphic/189/2/bd/a/110/4"]
"2-189-189.110-c1-0-11"	1.2284838615961546	1.5091725982022	2	189	"189.110"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.13858525725278184	0	1.71906204158355675647727016922	["ModularForm/GL2/Q/holomorphic/189/2/bd/a/110/3"]
"2-189-189.110-c1-0-12"	1.2284838615961546	1.5091725982022	2	189	"189.110"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.08264479182435742	0	1.74083130704623337279900162125	["ModularForm/GL2/Q/holomorphic/189/2/bd/a/110/11"]
"2-189-189.110-c1-0-13"	1.2284838615961546	1.5091725982022	2	189	"189.110"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.08413909598369862	0	2.31322098877680511272423325466	["ModularForm/GL2/Q/holomorphic/189/2/bd/a/110/14"]
"2-189-189.110-c1-0-14"	1.2284838615961546	1.5091725982022	2	189	"189.110"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1970413751114474	0	2.37027064078092280727275673022	["ModularForm/GL2/Q/holomorphic/189/2/bd/a/110/5"]
"2-189-189.110-c1-0-15"	1.2284838615961546	1.5091725982022	2	189	"189.110"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.20895493963558906	0	2.62955845763440797692674697768	["ModularForm/GL2/Q/holomorphic/189/2/bd/a/110/15"]
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"2-189-1.1-c13-0-72"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.0	0	1.06808495951081158914170715710	["ModularForm/GL2/Q/holomorphic/189/14/a/g/1/14"]
"2-189-1.1-c13-0-73"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.08144777284507375211162529302	["ModularForm/GL2/Q/holomorphic/189/14/a/d/1/2"]
"2-189-1.1-c13-0-74"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.09549909717656594367690107820	["ModularForm/GL2/Q/holomorphic/189/14/a/a/1/10"]
"2-189-1.1-c13-0-75"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.10950007404326908136548055581	["ModularForm/GL2/Q/holomorphic/189/14/a/a/1/3"]
"2-189-1.1-c13-0-76"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.13174133270359948778842292000	["ModularForm/GL2/Q/holomorphic/189/14/a/b/1/1"]
"2-189-1.1-c13-0-77"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.13714486635695045687490525924	["ModularForm/GL2/Q/holomorphic/189/14/a/d/1/9"]
"2-189-1.1-c13-0-78"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.14294286397426665564675792242	["ModularForm/GL2/Q/holomorphic/189/14/a/a/1/5"]
"2-189-1.1-c13-0-79"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.15045979665888442961532460383	["ModularForm/GL2/Q/holomorphic/189/14/a/c/1/7"]
"2-189-1.1-c13-0-8"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.0	0	0.31052693335269404649000771002	["ModularForm/GL2/Q/holomorphic/189/14/a/f/1/4"]
"2-189-1.1-c13-0-80"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.16060819664293039233660608791	["ModularForm/GL2/Q/holomorphic/189/14/a/a/1/9"]
"2-189-1.1-c13-0-81"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.17175449489160127452434488433	["ModularForm/GL2/Q/holomorphic/189/14/a/d/1/4"]
"2-189-1.1-c13-0-82"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.18064618414832708115062375698	["ModularForm/GL2/Q/holomorphic/189/14/a/c/1/2"]
"2-189-1.1-c13-0-83"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.18896964345620110438996381097	["ModularForm/GL2/Q/holomorphic/189/14/a/c/1/8"]
"2-189-1.1-c13-0-84"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.21539587335595414994652305738	["ModularForm/GL2/Q/holomorphic/189/14/a/b/1/8"]
"2-189-1.1-c13-0-85"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.23341429998005882894067919308	["ModularForm/GL2/Q/holomorphic/189/14/a/a/1/7"]
"2-189-1.1-c13-0-86"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.0	0	1.27055220296478413811177438782	["ModularForm/GL2/Q/holomorphic/189/14/a/h/1/14"]
"2-189-1.1-c13-0-87"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.27778197600581140828968498821	["ModularForm/GL2/Q/holomorphic/189/14/a/b/1/6"]
"2-189-1.1-c13-0-88"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.29028420279135221375256720641	["ModularForm/GL2/Q/holomorphic/189/14/a/d/1/8"]
"2-189-1.1-c13-0-89"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.32020217811869852832162560518	["ModularForm/GL2/Q/holomorphic/189/14/a/c/1/4"]
"2-189-1.1-c13-0-9"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.0	0	0.31589225879560249690295043942	["ModularForm/GL2/Q/holomorphic/189/14/a/g/1/11"]
"2-189-1.1-c13-0-90"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.0	0	1.32515280663888712792687805709	["ModularForm/GL2/Q/holomorphic/189/14/a/f/1/13"]
"2-189-1.1-c13-0-91"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.36618561355716494774757886934	["ModularForm/GL2/Q/holomorphic/189/14/a/c/1/10"]
"2-189-1.1-c13-0-92"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.36857727176634804934654463258	["ModularForm/GL2/Q/holomorphic/189/14/a/d/1/11"]
"2-189-1.1-c13-0-93"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.37000190827367433563721410276	["ModularForm/GL2/Q/holomorphic/189/14/a/b/1/9"]
"2-189-1.1-c13-0-94"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.44984810463978398586801256654	["ModularForm/GL2/Q/holomorphic/189/14/a/c/1/12"]
"2-189-1.1-c13-0-95"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.53555826801465838789463326700	["ModularForm/GL2/Q/holomorphic/189/14/a/b/1/11"]
"2-189-1.1-c13-0-96"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.56985944892840662748242837543	["ModularForm/GL2/Q/holomorphic/189/14/a/b/1/10"]
"2-189-1.1-c13-0-97"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.65292142785561196769967538376	["ModularForm/GL2/Q/holomorphic/189/14/a/a/1/11"]
"2-189-1.1-c13-0-98"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.69404708261508656750350869078	["ModularForm/GL2/Q/holomorphic/189/14/a/d/1/13"]
"2-189-1.1-c13-0-99"	14.23609692714668	202.6664557191151	2	189	"1.1"	[]	[[6.5, 0.0]]	13	true	true	false	true	0.5	1	1.73099041296253661904769514824	["ModularForm/GL2/Q/holomorphic/189/14/a/a/1/12"]


# 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).