# lfunc_search downloaded from the LMFDB on 25 May 2026.
# Search link: https://www.lmfdb.org/L/2/15^2/5.4
# Query "{'degree': 2, 'conductor': 225}" returned 8872 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.



"2-15e2-5.2-c0-0-0"	0.3350964455830971	0.11228962784242555	2	225	"5.2"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.0881040955873917	0	2.57334003132524961343902120842	["ModularForm/GL2/Q/holomorphic/225/1/g/a/82/1", "ArtinRepresentation/2.225.8t7.a.b"]
"2-15e2-5.3-c0-0-0"	0.3350964455830971	0.11228962784242555	2	225	"5.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.0881040955873917	0	1.82341514415177521088400579334	["ModularForm/GL2/Q/holomorphic/225/1/g/a/118/1", "ArtinRepresentation/2.225.8t7.a.a"]
"2-15e2-1.1-c1-0-0"	1.3403857823323886	1.7966340454788094	2	225	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.17988259436947085351712516811	["ModularForm/GL2/Q/holomorphic/225/2/a/f/1/1"]
"2-15e2-1.1-c1-0-1"	1.3403857823323886	1.7966340454788094	2	225	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.27025970316177507740293768624	["EllipticCurve/Q/225/b", "ModularForm/GL2/Q/holomorphic/225/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/225/2/a/b"]
"2-15e2-1.1-c1-0-2"	1.3403857823323886	1.7966340454788094	2	225	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.51470298744943699034589542418	["EllipticCurve/Q/225/d", "ModularForm/GL2/Q/holomorphic/225/2/a/d/1/1", "ModularForm/GL2/Q/holomorphic/225/2/a/d"]
"2-15e2-1.1-c1-0-3"	1.3403857823323886	1.7966340454788094	2	225	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.23186561512245260821665501913	["EllipticCurve/Q/225/a", "ModularForm/GL2/Q/holomorphic/225/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/225/2/a/a"]
"2-15e2-1.1-c1-0-4"	1.3403857823323886	1.7966340454788094	2	225	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	2.27079729708413704097834802658	["EllipticCurve/Q/225/e", "ModularForm/GL2/Q/holomorphic/225/2/a/e/1/1", "ModularForm/GL2/Q/holomorphic/225/2/a/e"]
"2-15e2-1.1-c1-0-5"	1.3403857823323886	1.7966340454788094	2	225	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.39073745840140963186525318063	["ModularForm/GL2/Q/holomorphic/225/2/a/f/1/2"]
"2-15e2-1.1-c1-0-6"	1.3403857823323886	1.7966340454788094	2	225	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.93248946372060750659719660133	["EllipticCurve/Q/225/c", "ModularForm/GL2/Q/holomorphic/225/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/225/2/a/c"]
"2-15e2-15.2-c1-0-0"	1.3403857823323886	1.7966340454788094	2	225	"15.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4200371793827998	0	0.71881077159523051674139860729	["ModularForm/GL2/Q/holomorphic/225/2/f/b/107/2"]
"2-15e2-15.2-c1-0-1"	1.3403857823323886	1.7966340454788094	2	225	"15.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3139392664049565	0	0.941842629029834829276222122057	["ModularForm/GL2/Q/holomorphic/225/2/f/a/107/1"]
"2-15e2-15.2-c1-0-2"	1.3403857823323886	1.7966340454788094	2	225	"15.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.009852542420260136	0	1.60237081858699516247308595620	["ModularForm/GL2/Q/holomorphic/225/2/f/a/107/2"]
"2-15e2-15.2-c1-0-3"	1.3403857823323886	1.7966340454788094	2	225	"15.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.006171011791983597	0	1.62844835723601809902365422192	["ModularForm/GL2/Q/holomorphic/225/2/f/b/107/1"]
"2-15e2-15.2-c1-0-4"	1.3403857823323886	1.7966340454788094	2	225	"15.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2758760966325039	0	2.85391935217092437432548227444	["ModularForm/GL2/Q/holomorphic/225/2/f/b/107/4"]
"2-15e2-15.2-c1-0-5"	1.3403857823323886	1.7966340454788094	2	225	"15.2"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2979157121927128	0	3.03483342554141363842389643997	["ModularForm/GL2/Q/holomorphic/225/2/f/b/107/3"]
"2-15e2-15.8-c1-0-0"	1.3403857823323886	1.7966340454788094	2	225	"15.8"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.006171011791983597	0	0.789909441807858349136943020977	["ModularForm/GL2/Q/holomorphic/225/2/f/b/143/1"]
"2-15e2-15.8-c1-0-1"	1.3403857823323886	1.7966340454788094	2	225	"15.8"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2979157121927128	0	1.66107925071076792843919169487	["ModularForm/GL2/Q/holomorphic/225/2/f/b/143/3"]
"2-15e2-15.8-c1-0-2"	1.3403857823323886	1.7966340454788094	2	225	"15.8"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2758760966325039	0	1.79318744664388340199161078881	["ModularForm/GL2/Q/holomorphic/225/2/f/b/143/4"]
"2-15e2-15.8-c1-0-3"	1.3403857823323886	1.7966340454788094	2	225	"15.8"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4200371793827998	0	1.91646681515026274660386773448	["ModularForm/GL2/Q/holomorphic/225/2/f/b/143/2"]
"2-15e2-15.8-c1-0-4"	1.3403857823323886	1.7966340454788094	2	225	"15.8"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.009852542420260136	0	2.15141207381034754334356551336	["ModularForm/GL2/Q/holomorphic/225/2/f/a/143/2"]
"2-15e2-15.8-c1-0-5"	1.3403857823323886	1.7966340454788094	2	225	"15.8"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3139392664049565	0	2.25848312992364474183984224563	["ModularForm/GL2/Q/holomorphic/225/2/f/a/143/1"]
"2-15e2-225.106-c1-0-0"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.48876297303193544	0	0.16146367930413292197339113739	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/9"]
"2-15e2-225.106-c1-0-1"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.19016201328155966	0	0.42650937331544843851679065490	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/11"]
"2-15e2-225.106-c1-0-10"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.006585776957501028	0	1.41366533242909221419533272451	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/10"]
"2-15e2-225.106-c1-0-11"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.058522109693759705	0	1.45712282725750327559973617840	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/3"]
"2-15e2-225.106-c1-0-12"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.05841546199986974	0	1.64042683439239307954911923750	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/15"]
"2-15e2-225.106-c1-0-13"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.14685701245514884	0	2.11550674966413175735722515466	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/24"]
"2-15e2-225.106-c1-0-14"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.40081662292260295	0	2.12305066177227185258105402451	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/1"]
"2-15e2-225.106-c1-0-15"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.13562335166429648	0	2.13328443864075057126307409750	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/25"]
"2-15e2-225.106-c1-0-16"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.013907908999657196	0	2.13554379682787695366777373556	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/26"]
"2-15e2-225.106-c1-0-17"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.08303827026596312	0	2.20406651588791962160571815918	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/28"]
"2-15e2-225.106-c1-0-18"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4306354792535804	0	2.24247818473773957300388158690	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/7"]
"2-15e2-225.106-c1-0-19"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.06598003715097173	0	2.25627862611603117238267629582	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/22"]
"2-15e2-225.106-c1-0-2"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.32729768000493953	0	0.44967044999245410217582355835	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/5"]
"2-15e2-225.106-c1-0-20"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.09571827129477481	0	2.31111364224100784476981310817	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/14"]
"2-15e2-225.106-c1-0-21"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.18456017680581077	0	2.44387237263487055907986965014	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/17"]
"2-15e2-225.106-c1-0-22"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.023394311416819073	0	2.50387077765487573436184945049	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/20"]
"2-15e2-225.106-c1-0-23"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.336287953684377	0	2.62577591904910876637164850117	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/19"]
"2-15e2-225.106-c1-0-24"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.004118597638903813	0	2.77967266079489783154697302563	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/27"]
"2-15e2-225.106-c1-0-25"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4214544790636577	0	2.86527859395438933830824810601	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/12"]
"2-15e2-225.106-c1-0-26"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.22432834080942327	0	3.04089537167170297036114826390	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/21"]
"2-15e2-225.106-c1-0-27"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4333353987987131	0	3.56412046273451583336705373170	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/16"]
"2-15e2-225.106-c1-0-3"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.38698151440929424	0	0.63382424947647006242713611932	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/18"]
"2-15e2-225.106-c1-0-4"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.03269943814916881	0	0.886822926074696129388715856988	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/6"]
"2-15e2-225.106-c1-0-5"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.0782559521082178	0	0.905369034657321267552485791033	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/2"]
"2-15e2-225.106-c1-0-6"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2073355059754009	0	1.09542682420657432822763358015	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/13"]
"2-15e2-225.106-c1-0-7"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2804417883867846	0	1.11762946934577242663088876464	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/23"]
"2-15e2-225.106-c1-0-8"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2614473960997005	0	1.21766169777927125396581284609	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/4"]
"2-15e2-225.106-c1-0-9"	1.3403857823323886	1.7966340454788094	2	225	"225.106"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.06835658480936367	0	1.27503814768059339124837710296	["ModularForm/GL2/Q/holomorphic/225/2/q/a/106/8"]
"2-15e2-225.113-c1-0-0"	1.3403857823323886	1.7966340454788094	2	225	"225.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3722851679057191	0	0.17042892620604310619172128534	["ModularForm/GL2/Q/holomorphic/225/2/w/a/113/8"]
"2-15e2-225.113-c1-0-1"	1.3403857823323886	1.7966340454788094	2	225	"225.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.45722781870669055	0	0.25886202776513221560554958325	["ModularForm/GL2/Q/holomorphic/225/2/w/a/113/10"]
"2-15e2-225.113-c1-0-10"	1.3403857823323886	1.7966340454788094	2	225	"225.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.09387908814339121	0	1.37476794510245418185732140194	["ModularForm/GL2/Q/holomorphic/225/2/w/a/113/4"]
"2-15e2-225.113-c1-0-11"	1.3403857823323886	1.7966340454788094	2	225	"225.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.041742806883707545	0	1.43262444925021446408340974917	["ModularForm/GL2/Q/holomorphic/225/2/w/a/113/23"]
"2-15e2-225.113-c1-0-12"	1.3403857823323886	1.7966340454788094	2	225	"225.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.0004382087558843079	0	1.43378941677616843891510925091	["ModularForm/GL2/Q/holomorphic/225/2/w/a/113/18"]
"2-15e2-225.113-c1-0-13"	1.3403857823323886	1.7966340454788094	2	225	"225.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.0304174184976328	0	1.44808415532521595918544328496	["ModularForm/GL2/Q/holomorphic/225/2/w/a/113/16"]
"2-15e2-225.113-c1-0-14"	1.3403857823323886	1.7966340454788094	2	225	"225.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1961609407366016	0	1.50210574666949396202904484259	["ModularForm/GL2/Q/holomorphic/225/2/w/a/113/3"]
"2-15e2-225.113-c1-0-15"	1.3403857823323886	1.7966340454788094	2	225	"225.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.10819052844168671	0	1.52792716321744562024607955959	["ModularForm/GL2/Q/holomorphic/225/2/w/a/113/19"]
"2-15e2-225.113-c1-0-16"	1.3403857823323886	1.7966340454788094	2	225	"225.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.11966013277604315	0	1.59861688006700564145552633742	["ModularForm/GL2/Q/holomorphic/225/2/w/a/113/15"]
"2-15e2-225.113-c1-0-17"	1.3403857823323886	1.7966340454788094	2	225	"225.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.007511515916699575	0	1.80819871641897393838203338623	["ModularForm/GL2/Q/holomorphic/225/2/w/a/113/11"]
"2-15e2-225.113-c1-0-18"	1.3403857823323886	1.7966340454788094	2	225	"225.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.21580553197032842	0	1.83093810083424727270663592307	["ModularForm/GL2/Q/holomorphic/225/2/w/a/113/12"]
"2-15e2-225.113-c1-0-19"	1.3403857823323886	1.7966340454788094	2	225	"225.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11989758733294059	0	1.97229028653815289897183069968	["ModularForm/GL2/Q/holomorphic/225/2/w/a/113/6"]
"2-15e2-225.113-c1-0-2"	1.3403857823323886	1.7966340454788094	2	225	"225.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3317458164255406	0	0.30969798073254559627175779850	["ModularForm/GL2/Q/holomorphic/225/2/w/a/113/20"]
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"2-15e2-1.1-c7-0-33"	8.38371222871631	70.28663073392742	2	225	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.21682688627180192237151884066	["ModularForm/GL2/Q/holomorphic/225/8/a/y/1/2"]
"2-15e2-1.1-c7-0-34"	8.38371222871631	70.28663073392742	2	225	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.22217531056249626651382245743	["ModularForm/GL2/Q/holomorphic/225/8/a/m/1/1"]
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"2-15e2-1.1-c7-0-36"	8.38371222871631	70.28663073392742	2	225	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.27164930615449706949041038097	["ModularForm/GL2/Q/holomorphic/225/8/a/y/1/1"]
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"2-15e2-3.2-c12-0-4"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.1520433619923482	0	0.05879042594076275056412643548	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/1"]
"2-15e2-3.2-c12-0-40"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.1520433619923482	0	0.64417643751737583642769615194	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/18"]
"2-15e2-3.2-c12-0-41"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.1520433619923482	0	0.64566243974217924178952447734	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/20"]
"2-15e2-3.2-c12-0-42"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.1520433619923482	0	0.66059059494779716466378027672	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/10"]
"2-15e2-3.2-c12-0-43"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3479566380076518	0	0.66590889143820280321820809206	["ModularForm/GL2/Q/holomorphic/225/13/c/d/26/5"]
"2-15e2-3.2-c12-0-44"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.1520433619923482	0	0.66948574562347152134209766073	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/12"]
"2-15e2-3.2-c12-0-45"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.3479566380076518	0	0.67267185574741876022582426223	["ModularForm/GL2/Q/holomorphic/225/13/c/c/26/10"]
"2-15e2-3.2-c12-0-46"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.3479566380076518	0	0.67726853333418238990098105845	["ModularForm/GL2/Q/holomorphic/225/13/c/c/26/13"]
"2-15e2-3.2-c12-0-47"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.3479566380076518	0	0.68048784446543106421781417996	["ModularForm/GL2/Q/holomorphic/225/13/c/d/26/1"]
"2-15e2-3.2-c12-0-48"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.1520433619923482	0	0.72572182410033200480840721248	["ModularForm/GL2/Q/holomorphic/225/13/c/e/26/5"]
"2-15e2-3.2-c12-0-49"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3479566380076518	0	0.76517174242076389761588886735	["ModularForm/GL2/Q/holomorphic/225/13/c/b/26/1"]
"2-15e2-3.2-c12-0-5"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3479566380076518	0	0.05904652919826835887509179228	["ModularForm/GL2/Q/holomorphic/225/13/c/d/26/14"]
"2-15e2-3.2-c12-0-50"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.1520433619923482	0	0.825478386714680196360430245913	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/24"]
"2-15e2-3.2-c12-0-51"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.1520433619923482	0	0.876745523991996378752462001829	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/17"]
"2-15e2-3.2-c12-0-52"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.1520433619923482	0	0.882220994684293485876185511671	["ModularForm/GL2/Q/holomorphic/225/13/c/e/26/13"]
"2-15e2-3.2-c12-0-53"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3479566380076518	0	0.882620065301358505166887686826	["ModularForm/GL2/Q/holomorphic/225/13/c/c/26/4"]
"2-15e2-3.2-c12-0-54"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.1520433619923482	0	0.901512850600553522766972916704	["ModularForm/GL2/Q/holomorphic/225/13/c/e/26/8"]
"2-15e2-3.2-c12-0-55"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.1520433619923482	0	0.965935510848391336723779564998	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/4"]
"2-15e2-3.2-c12-0-56"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.3479566380076518	0	1.04662988531544484137565702923	["ModularForm/GL2/Q/holomorphic/225/13/c/d/26/3"]
"2-15e2-3.2-c12-0-57"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.1520433619923482	0	1.05647057997610300144008602607	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/21"]
"2-15e2-3.2-c12-0-58"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.1520433619923482	0	1.07123091279212129856204592513	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/16"]
"2-15e2-3.2-c12-0-59"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3479566380076518	0	1.07594593775031772909934437329	["ModularForm/GL2/Q/holomorphic/225/13/c/d/26/6"]
"2-15e2-3.2-c12-0-6"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.1520433619923482	0	0.07194672012567577613044310799	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/13"]
"2-15e2-3.2-c12-0-60"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.1520433619923482	0	1.10729293379014809216188572395	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/8"]
"2-15e2-3.2-c12-0-61"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.1520433619923482	0	1.11946506680008455625674290395	["ModularForm/GL2/Q/holomorphic/225/13/c/e/26/12"]
"2-15e2-3.2-c12-0-62"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.1520433619923482	0	1.12258546530401883263066704765	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/23"]
"2-15e2-3.2-c12-0-63"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.3479566380076518	0	1.12392651287571945934659534130	["ModularForm/GL2/Q/holomorphic/225/13/c/a/26/1"]
"2-15e2-3.2-c12-0-64"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3479566380076518	0	1.16436922376395721987730348967	["ModularForm/GL2/Q/holomorphic/225/13/c/c/26/7"]
"2-15e2-3.2-c12-0-65"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.1520433619923482	0	1.16771826675717327938941252419	["ModularForm/GL2/Q/holomorphic/225/13/c/e/26/10"]
"2-15e2-3.2-c12-0-66"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.1520433619923482	0	1.20295034905867708474070359237	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/14"]
"2-15e2-3.2-c12-0-67"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.3479566380076518	0	1.25205048102146303498543187156	["ModularForm/GL2/Q/holomorphic/225/13/c/c/26/6"]
"2-15e2-3.2-c12-0-68"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3479566380076518	0	1.30714244002953240362163134951	["ModularForm/GL2/Q/holomorphic/225/13/c/c/26/8"]
"2-15e2-3.2-c12-0-69"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.1520433619923482	0	1.38725458421920021623180331945	["ModularForm/GL2/Q/holomorphic/225/13/c/e/26/16"]
"2-15e2-3.2-c12-0-7"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3479566380076518	0	0.084166424597873592655576414240	["ModularForm/GL2/Q/holomorphic/225/13/c/c/26/11"]
"2-15e2-3.2-c12-0-70"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3479566380076518	0	1.39008048288178086491812878534	["ModularForm/GL2/Q/holomorphic/225/13/c/d/26/8"]
"2-15e2-3.2-c12-0-71"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.3479566380076518	0	1.47778509381349281725328857595	["ModularForm/GL2/Q/holomorphic/225/13/c/d/26/4"]
"2-15e2-3.2-c12-0-72"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.3479566380076518	0	1.48755207487107507074258514465	["ModularForm/GL2/Q/holomorphic/225/13/c/d/26/7"]
"2-15e2-3.2-c12-0-73"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.3479566380076518	0	1.49003026327170973144423545409	["ModularForm/GL2/Q/holomorphic/225/13/c/c/26/5"]
"2-15e2-3.2-c12-0-74"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.1520433619923482	0	1.57008235287201009797220438208	["ModularForm/GL2/Q/holomorphic/225/13/c/f/26/5"]
"2-15e2-3.2-c12-0-75"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.1520433619923482	0	1.63116355406015399963411329236	["ModularForm/GL2/Q/holomorphic/225/13/c/e/26/3"]
"2-15e2-3.2-c12-0-8"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.1520433619923482	0	0.10925505115818929083964343402	["ModularForm/GL2/Q/holomorphic/225/13/c/e/26/14"]
"2-15e2-3.2-c12-0-9"	14.340453580245091	205.64860888716427	2	225	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3479566380076518	0	0.11801384115505754338065400697	["ModularForm/GL2/Q/holomorphic/225/13/c/c/26/12"]


# 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).