# lfunc_search downloaded from the LMFDB on 24 October 2026.
# Search link: https://www.lmfdb.org/L/2/114/57.56
# Query "{'degree': 2, 'conductor': 114}" returned 3215 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.



"2-114-1.1-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.65254561433729232279648150469	["EllipticCurve/Q/114/a", "ModularForm/GL2/Q/holomorphic/114/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/114/2/a/a"]
"2-114-1.1-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	2.33973473634575001863443152397	["EllipticCurve/Q/114/b", "ModularForm/GL2/Q/holomorphic/114/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/114/2/a/b"]
"2-114-1.1-c1-0-2"	0.9540935923915415	0.9102945830425968	2	114	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	2.72251484544452322835217288408	["EllipticCurve/Q/114/c", "ModularForm/GL2/Q/holomorphic/114/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/114/2/a/c"]
"2-114-19.11-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"19.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.06775328806227679	0	2.70076862898533993905049973728	["ModularForm/GL2/Q/holomorphic/114/2/e/a/49/1"]
"2-114-19.11-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"19.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1978267572087798	0	3.03965187205450842041976789976	["ModularForm/GL2/Q/holomorphic/114/2/e/b/49/1"]
"2-114-19.16-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"19.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1424722119326779	0	1.07252988782449084960696443483	["ModularForm/GL2/Q/holomorphic/114/2/i/a/73/1"]
"2-114-19.16-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"19.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.18389548559253116	0	1.67591113988167962295001015136	["ModularForm/GL2/Q/holomorphic/114/2/i/b/73/1"]
"2-114-19.16-c1-0-2"	0.9540935923915415	0.9102945830425968	2	114	"19.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.12300395237937518	0	2.13048373333180802412150150202	["ModularForm/GL2/Q/holomorphic/114/2/i/c/73/1"]
"2-114-19.16-c1-0-3"	0.9540935923915415	0.9102945830425968	2	114	"19.16"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1665627857076632	0	2.47989876183043574185938126294	["ModularForm/GL2/Q/holomorphic/114/2/i/d/73/1"]
"2-114-19.17-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"19.17"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2900793912435025	0	1.31991710745951298477186348114	["ModularForm/GL2/Q/holomorphic/114/2/i/a/55/1"]
"2-114-19.17-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"19.17"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07964612933054084	0	1.93162657894447532058412909292	["ModularForm/GL2/Q/holomorphic/114/2/i/d/55/1"]
"2-114-19.17-c1-0-2"	0.9540935923915415	0.9102945830425968	2	114	"19.17"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11131887302911814	0	2.47686776152535551816621986439	["ModularForm/GL2/Q/holomorphic/114/2/i/b/55/1"]
"2-114-19.17-c1-0-3"	0.9540935923915415	0.9102945830425968	2	114	"19.17"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2708121419696535	0	2.96397647136189785474413584675	["ModularForm/GL2/Q/holomorphic/114/2/i/c/55/1"]
"2-114-19.4-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"19.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2704033697721928	0	0.861446573471696353256315581864	["ModularForm/GL2/Q/holomorphic/114/2/i/b/61/1"]
"2-114-19.4-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"19.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.13037836038496017	0	2.05466158097569299202966968004	["ModularForm/GL2/Q/holomorphic/114/2/i/a/61/1"]
"2-114-19.4-c1-0-2"	0.9540935923915415	0.9102945830425968	2	114	"19.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2101283706745045	0	2.42425829885683215657809595872	["ModularForm/GL2/Q/holomorphic/114/2/i/c/61/1"]
"2-114-19.4-c1-0-3"	0.9540935923915415	0.9102945830425968	2	114	"19.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.019163368314845542	0	2.62755000384875629765436946495	["ModularForm/GL2/Q/holomorphic/114/2/i/d/61/1"]
"2-114-19.5-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"19.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2101283706745045	0	1.28242763175821312831686930381	["ModularForm/GL2/Q/holomorphic/114/2/i/c/43/1"]
"2-114-19.5-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"19.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.019163368314845542	0	2.27016040909711471604506682140	["ModularForm/GL2/Q/holomorphic/114/2/i/d/43/1"]
"2-114-19.5-c1-0-2"	0.9540935923915415	0.9102945830425968	2	114	"19.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2704033697721928	0	2.95248436050377181495301089302	["ModularForm/GL2/Q/holomorphic/114/2/i/b/43/1"]
"2-114-19.5-c1-0-3"	0.9540935923915415	0.9102945830425968	2	114	"19.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.13037836038496017	0	3.05582050226642035351720467508	["ModularForm/GL2/Q/holomorphic/114/2/i/a/43/1"]
"2-114-19.6-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"19.6"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1665627857076632	0	1.64200822936618385186842858496	["ModularForm/GL2/Q/holomorphic/114/2/i/d/25/1"]
"2-114-19.6-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"19.6"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1424722119326779	0	2.36041807562599896617885482882	["ModularForm/GL2/Q/holomorphic/114/2/i/a/25/1"]
"2-114-19.6-c1-0-2"	0.9540935923915415	0.9102945830425968	2	114	"19.6"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.18389548559253116	0	2.87768604156883120626606761591	["ModularForm/GL2/Q/holomorphic/114/2/i/b/25/1"]
"2-114-19.6-c1-0-3"	0.9540935923915415	0.9102945830425968	2	114	"19.6"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.12300395237937518	0	3.14228509481876831132742873618	["ModularForm/GL2/Q/holomorphic/114/2/i/c/25/1"]
"2-114-19.7-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"19.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.06775328806227679	0	1.54913072358068928721326785821	["ModularForm/GL2/Q/holomorphic/114/2/e/a/7/1"]
"2-114-19.7-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"19.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1978267572087798	0	1.88720241946061314769023443231	["ModularForm/GL2/Q/holomorphic/114/2/e/b/7/1"]
"2-114-19.9-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"19.9"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2708121419696535	0	1.42302436248626201470600860177	["ModularForm/GL2/Q/holomorphic/114/2/i/c/85/1"]
"2-114-19.9-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"19.9"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.07964612933054084	0	1.98266696372122383748274164302	["ModularForm/GL2/Q/holomorphic/114/2/i/d/85/1"]
"2-114-19.9-c1-0-2"	0.9540935923915415	0.9102945830425968	2	114	"19.9"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.11131887302911814	0	2.11885032600494272846516133560	["ModularForm/GL2/Q/holomorphic/114/2/i/b/85/1"]
"2-114-19.9-c1-0-3"	0.9540935923915415	0.9102945830425968	2	114	"19.9"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2900793912435025	0	3.13064920329042396182175552699	["ModularForm/GL2/Q/holomorphic/114/2/i/a/85/1"]
"2-114-57.14-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"57.14"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.27837525536188173	0	0.70143382369172338886617560540	["ModularForm/GL2/Q/holomorphic/114/2/l/b/71/1"]
"2-114-57.14-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"57.14"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.11682451404748416	0	1.85814406342591140448233541344	["ModularForm/GL2/Q/holomorphic/114/2/l/b/71/2"]
"2-114-57.14-c1-0-2"	0.9540935923915415	0.9102945830425968	2	114	"57.14"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.04903818110771284	0	2.28623865492916084271664319142	["ModularForm/GL2/Q/holomorphic/114/2/l/a/71/2"]
"2-114-57.14-c1-0-3"	0.9540935923915415	0.9102945830425968	2	114	"57.14"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.0666377445677677	0	2.42817775325617408845565512561	["ModularForm/GL2/Q/holomorphic/114/2/l/a/71/1"]
"2-114-57.14-c1-0-4"	0.9540935923915415	0.9102945830425968	2	114	"57.14"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11132312537822751	0	2.51589671024885738769020426549	["ModularForm/GL2/Q/holomorphic/114/2/l/b/71/3"]
"2-114-57.14-c1-0-5"	0.9540935923915415	0.9102945830425968	2	114	"57.14"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.08741268139769563	0	2.92918833894696729200818734994	["ModularForm/GL2/Q/holomorphic/114/2/l/a/71/3"]
"2-114-57.2-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"57.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3349954165381758	0	1.33964862873533353556297718732	["ModularForm/GL2/Q/holomorphic/114/2/l/a/59/2"]
"2-114-57.2-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"57.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.09486507933850569	0	2.15103675785412170099445699019	["ModularForm/GL2/Q/holomorphic/114/2/l/a/59/3"]
"2-114-57.2-c1-0-2"	0.9540935923915415	0.9102945830425968	2	114	"57.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.05949964347007176	0	2.34059615826681349755095999868	["ModularForm/GL2/Q/holomorphic/114/2/l/b/59/3"]
"2-114-57.2-c1-0-3"	0.9540935923915415	0.9102945830425968	2	114	"57.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.20153940740109869	0	3.04200396488313173551979424880	["ModularForm/GL2/Q/holomorphic/114/2/l/a/59/1"]
"2-114-57.2-c1-0-4"	0.9540935923915415	0.9102945830425968	2	114	"57.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.37705975089694943	0	3.20806724500156506145965291447	["ModularForm/GL2/Q/holomorphic/114/2/l/b/59/1"]
"2-114-57.2-c1-0-5"	0.9540935923915415	0.9102945830425968	2	114	"57.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.27956396160184044	0	3.34483724372996788864475836307	["ModularForm/GL2/Q/holomorphic/114/2/l/b/59/2"]
"2-114-57.29-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"57.29"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.37705975089694943	0	0.811678746607932647894916086709	["ModularForm/GL2/Q/holomorphic/114/2/l/b/29/1"]
"2-114-57.29-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"57.29"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.20153940740109869	0	0.968620835113525867493081073357	["ModularForm/GL2/Q/holomorphic/114/2/l/a/29/1"]
"2-114-57.29-c1-0-2"	0.9540935923915415	0.9102945830425968	2	114	"57.29"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.27956396160184044	0	1.61950410827600855092488691341	["ModularForm/GL2/Q/holomorphic/114/2/l/b/29/2"]
"2-114-57.29-c1-0-3"	0.9540935923915415	0.9102945830425968	2	114	"57.29"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.09486507933850569	0	2.38956251176692016356981997063	["ModularForm/GL2/Q/holomorphic/114/2/l/a/29/3"]
"2-114-57.29-c1-0-4"	0.9540935923915415	0.9102945830425968	2	114	"57.29"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05949964347007176	0	2.71487538198983525595867719210	["ModularForm/GL2/Q/holomorphic/114/2/l/b/29/3"]
"2-114-57.29-c1-0-5"	0.9540935923915415	0.9102945830425968	2	114	"57.29"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3349954165381758	0	3.37288811449141544272358512240	["ModularForm/GL2/Q/holomorphic/114/2/l/a/29/2"]
"2-114-57.32-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"57.32"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4621815702697645	0	0.56398526482336628179128257017	["ModularForm/GL2/Q/holomorphic/114/2/l/a/89/2"]
"2-114-57.32-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"57.32"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.027682507912054784	0	1.87347750818937264734849717211	["ModularForm/GL2/Q/holomorphic/114/2/l/a/89/1"]
"2-114-57.32-c1-0-2"	0.9540935923915415	0.9102945830425968	2	114	"57.32"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.013381160495609957	0	2.16018919362293811871625935937	["ModularForm/GL2/Q/holomorphic/114/2/l/b/89/2"]
"2-114-57.32-c1-0-3"	0.9540935923915415	0.9102945830425968	2	114	"57.32"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.0038465158333741405	0	2.30814860113295529854540136606	["ModularForm/GL2/Q/holomorphic/114/2/l/a/89/3"]
"2-114-57.32-c1-0-4"	0.9540935923915415	0.9102945830425968	2	114	"57.32"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.054387480756107366	0	2.71185842033480500845573931040	["ModularForm/GL2/Q/holomorphic/114/2/l/b/89/3"]
"2-114-57.32-c1-0-5"	0.9540935923915415	0.9102945830425968	2	114	"57.32"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.242870323770641	0	3.30090229005543295211359344759	["ModularForm/GL2/Q/holomorphic/114/2/l/b/89/1"]
"2-114-57.41-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"57.41"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.027682507912054784	0	1.40020863190698779221597899941	["ModularForm/GL2/Q/holomorphic/114/2/l/a/41/1"]
"2-114-57.41-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"57.41"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.242870323770641	0	1.59828000032087878682008238102	["ModularForm/GL2/Q/holomorphic/114/2/l/b/41/1"]
"2-114-57.41-c1-0-2"	0.9540935923915415	0.9102945830425968	2	114	"57.41"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.0038465158333741405	0	1.95500344041229009937522224334	["ModularForm/GL2/Q/holomorphic/114/2/l/a/41/3"]
"2-114-57.41-c1-0-3"	0.9540935923915415	0.9102945830425968	2	114	"57.41"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.054387480756107366	0	2.55037531086282043472881374126	["ModularForm/GL2/Q/holomorphic/114/2/l/b/41/3"]
"2-114-57.41-c1-0-4"	0.9540935923915415	0.9102945830425968	2	114	"57.41"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.013381160495609957	0	2.57545820937354260546543606300	["ModularForm/GL2/Q/holomorphic/114/2/l/b/41/2"]
"2-114-57.41-c1-0-5"	0.9540935923915415	0.9102945830425968	2	114	"57.41"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4621815702697645	0	3.39694726692243166288556302507	["ModularForm/GL2/Q/holomorphic/114/2/l/a/41/2"]
"2-114-57.50-c1-0-0"	0.9540935923915415	0.9102945830425968	2	114	"57.50"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3827900226355283	0	0.925932476813854479131803856221	["ModularForm/GL2/Q/holomorphic/114/2/h/c/107/1"]
"2-114-57.50-c1-0-1"	0.9540935923915415	0.9102945830425968	2	114	"57.50"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.03588402609299761	0	1.71825552365282122115149657755	["ModularForm/GL2/Q/holomorphic/114/2/h/e/107/2"]
"2-114-57.50-c1-0-2"	0.9540935923915415	0.9102945830425968	2	114	"57.50"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.21612335596886162	0	1.95196628564662745654120187475	["ModularForm/GL2/Q/holomorphic/114/2/h/d/107/1"]
"2-114-57.50-c1-0-3"	0.9540935923915415	0.9102945830425968	2	114	"57.50"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11720997736447172	0	1.95603494038211965070339268295	["ModularForm/GL2/Q/holomorphic/114/2/h/b/107/1"]
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"2-114-1.1-c17-0-13"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.67114109088343394003346074482	["ModularForm/GL2/Q/holomorphic/114/18/a/g/1/5"]
"2-114-1.1-c17-0-14"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.67606469114995490234359468627	["ModularForm/GL2/Q/holomorphic/114/18/a/f/1/7"]
"2-114-1.1-c17-0-15"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.71531743096227475973189370033	["ModularForm/GL2/Q/holomorphic/114/18/a/c/1/5"]
"2-114-1.1-c17-0-16"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.74843557576593842239247476021	["ModularForm/GL2/Q/holomorphic/114/18/a/c/1/3"]
"2-114-1.1-c17-0-17"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.809973833794810773258463440956	["ModularForm/GL2/Q/holomorphic/114/18/a/h/1/3"]
"2-114-1.1-c17-0-18"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.826354064844867510264149297797	["ModularForm/GL2/Q/holomorphic/114/18/a/g/1/3"]
"2-114-1.1-c17-0-19"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.840116389204312268204792321798	["ModularForm/GL2/Q/holomorphic/114/18/a/h/1/2"]
"2-114-1.1-c17-0-2"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.23437959087658107883942188053	["ModularForm/GL2/Q/holomorphic/114/18/a/c/1/1"]
"2-114-1.1-c17-0-20"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	0.846857861144969597026031712938	["ModularForm/GL2/Q/holomorphic/114/18/a/a/1/2"]
"2-114-1.1-c17-0-21"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	0.854562876660866501264973841392	["ModularForm/GL2/Q/holomorphic/114/18/a/a/1/5"]
"2-114-1.1-c17-0-22"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.855089484512154884326822879130	["ModularForm/GL2/Q/holomorphic/114/18/a/h/1/6"]
"2-114-1.1-c17-0-23"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.894315292026341427285368786188	["ModularForm/GL2/Q/holomorphic/114/18/a/g/1/6"]
"2-114-1.1-c17-0-24"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	0.902964208764232166425780617003	["ModularForm/GL2/Q/holomorphic/114/18/a/b/1/4"]
"2-114-1.1-c17-0-25"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	0.916609269892968494083917398831	["ModularForm/GL2/Q/holomorphic/114/18/a/b/1/1"]
"2-114-1.1-c17-0-26"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	0.921707749534684605665743131182	["ModularForm/GL2/Q/holomorphic/114/18/a/d/1/2"]
"2-114-1.1-c17-0-27"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	0.970545899186304391505246630292	["ModularForm/GL2/Q/holomorphic/114/18/a/a/1/3"]
"2-114-1.1-c17-0-28"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.993177651159015808560170018959	["ModularForm/GL2/Q/holomorphic/114/18/a/f/1/6"]
"2-114-1.1-c17-0-29"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	1.00143501085310084885913329061	["ModularForm/GL2/Q/holomorphic/114/18/a/g/1/7"]
"2-114-1.1-c17-0-3"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.24214464214668225434621276332	["ModularForm/GL2/Q/holomorphic/114/18/a/f/1/1"]
"2-114-1.1-c17-0-30"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	1.02762029313952959826643243140	["ModularForm/GL2/Q/holomorphic/114/18/a/c/1/6"]
"2-114-1.1-c17-0-31"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.07104071139346730057881749883	["ModularForm/GL2/Q/holomorphic/114/18/a/a/1/1"]
"2-114-1.1-c17-0-32"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.08205651666187940210863858746	["ModularForm/GL2/Q/holomorphic/114/18/a/d/1/1"]
"2-114-1.1-c17-0-33"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	1.09258129596351561540533114836	["ModularForm/GL2/Q/holomorphic/114/18/a/h/1/7"]
"2-114-1.1-c17-0-34"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.11788635891779516486617771838	["ModularForm/GL2/Q/holomorphic/114/18/a/d/1/3"]
"2-114-1.1-c17-0-35"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.15620876415518574279604729614	["ModularForm/GL2/Q/holomorphic/114/18/a/b/1/3"]
"2-114-1.1-c17-0-36"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.16778910691375462090547233577	["ModularForm/GL2/Q/holomorphic/114/18/a/b/1/2"]
"2-114-1.1-c17-0-37"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	1.16922302664084453277793421000	["ModularForm/GL2/Q/holomorphic/114/18/a/h/1/5"]
"2-114-1.1-c17-0-38"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.23748451429469221995982012693	["ModularForm/GL2/Q/holomorphic/114/18/a/a/1/4"]
"2-114-1.1-c17-0-39"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	1.32943844301798148550360537613	["ModularForm/GL2/Q/holomorphic/114/18/a/h/1/8"]
"2-114-1.1-c17-0-4"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.36188590702082477248659341659	["ModularForm/GL2/Q/holomorphic/114/18/a/g/1/1"]
"2-114-1.1-c17-0-40"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.33785860517202748440521802822	["ModularForm/GL2/Q/holomorphic/114/18/a/a/1/6"]
"2-114-1.1-c17-0-41"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.34877035119352986895985348471	["ModularForm/GL2/Q/holomorphic/114/18/a/d/1/5"]
"2-114-1.1-c17-0-42"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.35068177041296825092598568136	["ModularForm/GL2/Q/holomorphic/114/18/a/d/1/6"]
"2-114-1.1-c17-0-43"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.35167723753663416815530792891	["ModularForm/GL2/Q/holomorphic/114/18/a/b/1/6"]
"2-114-1.1-c17-0-44"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.35967187617486231469548942750	["ModularForm/GL2/Q/holomorphic/114/18/a/e/1/1"]
"2-114-1.1-c17-0-45"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.41108564524407247157312787518	["ModularForm/GL2/Q/holomorphic/114/18/a/e/1/4"]
"2-114-1.1-c17-0-46"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.43917570376855195756071481485	["ModularForm/GL2/Q/holomorphic/114/18/a/e/1/3"]
"2-114-1.1-c17-0-47"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.52940681457054982872409100613	["ModularForm/GL2/Q/holomorphic/114/18/a/e/1/2"]
"2-114-1.1-c17-0-48"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.56602287418104224784253668521	["ModularForm/GL2/Q/holomorphic/114/18/a/b/1/5"]
"2-114-1.1-c17-0-49"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.60205995830306669526964328786	["ModularForm/GL2/Q/holomorphic/114/18/a/d/1/4"]
"2-114-1.1-c17-0-5"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.38394403461603903352489797455	["ModularForm/GL2/Q/holomorphic/114/18/a/f/1/4"]
"2-114-1.1-c17-0-50"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.67638266448278006876907566933	["ModularForm/GL2/Q/holomorphic/114/18/a/e/1/5"]
"2-114-1.1-c17-0-51"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.5	1	1.79895792791327522560387905526	["ModularForm/GL2/Q/holomorphic/114/18/a/e/1/6"]
"2-114-1.1-c17-0-6"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.39656680123290835834024746718	["ModularForm/GL2/Q/holomorphic/114/18/a/c/1/2"]
"2-114-1.1-c17-0-7"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.40057000317829548244084283793	["ModularForm/GL2/Q/holomorphic/114/18/a/c/1/4"]
"2-114-1.1-c17-0-8"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.40463739013792985022180656720	["ModularForm/GL2/Q/holomorphic/114/18/a/g/1/4"]
"2-114-1.1-c17-0-9"	14.452445453029677	208.87317957279816	2	114	"1.1"	[]	[[8.5, 0.0]]	17	true	true	false	true	0.0	0	0.45821652849994595448145022028	["ModularForm/GL2/Q/holomorphic/114/18/a/g/1/2"]


# 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).