# lfunc_search downloaded from the LMFDB on 16 April 2026.
# Search link: https://www.lmfdb.org/L/2/230/115.107
# Query "{'degree': 2, 'conductor': 230}" returned 3983 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.



"2-230-1.1-c1-0-0"	1.355197124587213	1.8365592464894498	2	230	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.911793692957645258149635391835	["ModularForm/GL2/Q/holomorphic/230/2/a/a/1/1"]
"2-230-1.1-c1-0-1"	1.355197124587213	1.8365592464894498	2	230	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.43901946297639245435214581985	["ModularForm/GL2/Q/holomorphic/230/2/a/d/1/1"]
"2-230-1.1-c1-0-2"	1.355197124587213	1.8365592464894498	2	230	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.46438094505397839462929047850	["ModularForm/GL2/Q/holomorphic/230/2/a/b/1/1"]
"2-230-1.1-c1-0-3"	1.355197124587213	1.8365592464894498	2	230	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.69968985125155088025702730602	["ModularForm/GL2/Q/holomorphic/230/2/a/a/1/2"]
"2-230-1.1-c1-0-4"	1.355197124587213	1.8365592464894498	2	230	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.89317783414266679508333114377	["ModularForm/GL2/Q/holomorphic/230/2/a/c/1/1"]
"2-230-1.1-c1-0-5"	1.355197124587213	1.8365592464894498	2	230	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.11808372085269199478702255532	["ModularForm/GL2/Q/holomorphic/230/2/a/b/1/2"]
"2-230-1.1-c1-0-6"	1.355197124587213	1.8365592464894498	2	230	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.22861792377438448870645236794	["ModularForm/GL2/Q/holomorphic/230/2/a/d/1/2"]
"2-230-1.1-c1-0-7"	1.355197124587213	1.8365592464894498	2	230	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.38964411962337051053951412739	["ModularForm/GL2/Q/holomorphic/230/2/a/c/1/2"]
"2-230-1.1-c1-0-8"	1.355197124587213	1.8365592464894498	2	230	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.41708781421801947228034811566	["ModularForm/GL2/Q/holomorphic/230/2/a/d/1/3"]
"2-230-115.102-c1-0-0"	1.355197124587213	1.8365592464894498	2	230	"115.102"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.29068079701349164	0	0.05972176614707039496505172027	["ModularForm/GL2/Q/holomorphic/230/2/l/a/217/1"]
"2-230-115.102-c1-0-1"	1.355197124587213	1.8365592464894498	2	230	"115.102"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3620654971349792	0	0.11938569489401101145208009549	["ModularForm/GL2/Q/holomorphic/230/2/l/a/217/10"]
"2-230-115.102-c1-0-10"	1.355197124587213	1.8365592464894498	2	230	"115.102"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1968339794583775	0	2.48030604816635136006562899559	["ModularForm/GL2/Q/holomorphic/230/2/l/a/217/12"]
"2-230-115.102-c1-0-11"	1.355197124587213	1.8365592464894498	2	230	"115.102"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.46930537082922824	0	2.84583974136973075078289341902	["ModularForm/GL2/Q/holomorphic/230/2/l/a/217/9"]
"2-230-115.102-c1-0-2"	1.355197124587213	1.8365592464894498	2	230	"115.102"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.45861179825995146	0	0.50684901059920367048518778352	["ModularForm/GL2/Q/holomorphic/230/2/l/a/217/4"]
"2-230-115.102-c1-0-3"	1.355197124587213	1.8365592464894498	2	230	"115.102"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.16825452673332222	0	0.65091536933177783831979574352	["ModularForm/GL2/Q/holomorphic/230/2/l/a/217/8"]
"2-230-115.102-c1-0-4"	1.355197124587213	1.8365592464894498	2	230	"115.102"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.04506245970106798	0	0.994737132796726042927782944520	["ModularForm/GL2/Q/holomorphic/230/2/l/a/217/7"]
"2-230-115.102-c1-0-5"	1.355197124587213	1.8365592464894498	2	230	"115.102"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.19977453463015116	0	1.29674872469290547821606179248	["ModularForm/GL2/Q/holomorphic/230/2/l/a/217/3"]
"2-230-115.102-c1-0-6"	1.355197124587213	1.8365592464894498	2	230	"115.102"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.12908811213025873	0	1.81599112121407061806726802777	["ModularForm/GL2/Q/holomorphic/230/2/l/a/217/2"]
"2-230-115.102-c1-0-7"	1.355197124587213	1.8365592464894498	2	230	"115.102"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11922159540715863	0	1.88028691838139407587713470880	["ModularForm/GL2/Q/holomorphic/230/2/l/a/217/11"]
"2-230-115.102-c1-0-8"	1.355197124587213	1.8365592464894498	2	230	"115.102"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1340134459971061	0	1.93388243174552360137120013682	["ModularForm/GL2/Q/holomorphic/230/2/l/a/217/6"]
"2-230-115.102-c1-0-9"	1.355197124587213	1.8365592464894498	2	230	"115.102"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.027075197195863206	0	2.20669086572034364108860092444	["ModularForm/GL2/Q/holomorphic/230/2/l/a/217/5"]
"2-230-115.103-c1-0-0"	1.355197124587213	1.8365592464894498	2	230	"115.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2897490572919511	0	0.35741362753006433679789395294	["ModularForm/GL2/Q/holomorphic/230/2/l/a/103/8"]
"2-230-115.103-c1-0-1"	1.355197124587213	1.8365592464894498	2	230	"115.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.46451643741017407	0	0.51437516737733704647182893347	["ModularForm/GL2/Q/holomorphic/230/2/l/a/103/3"]
"2-230-115.103-c1-0-10"	1.355197124587213	1.8365592464894498	2	230	"115.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.32884539494558174	0	2.74171319137302312466030036132	["ModularForm/GL2/Q/holomorphic/230/2/l/a/103/10"]
"2-230-115.103-c1-0-11"	1.355197124587213	1.8365592464894498	2	230	"115.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3057624330799308	0	3.04428243140719078536068957490	["ModularForm/GL2/Q/holomorphic/230/2/l/a/103/12"]
"2-230-115.103-c1-0-2"	1.355197124587213	1.8365592464894498	2	230	"115.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3364612360585661	0	0.810527960986368746907402475954	["ModularForm/GL2/Q/holomorphic/230/2/l/a/103/2"]
"2-230-115.103-c1-0-3"	1.355197124587213	1.8365592464894498	2	230	"115.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.10097686098496862	0	1.02548930958865414580761736695	["ModularForm/GL2/Q/holomorphic/230/2/l/a/103/9"]
"2-230-115.103-c1-0-4"	1.355197124587213	1.8365592464894498	2	230	"115.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.18727347080785184	0	1.60963296110582117537289811241	["ModularForm/GL2/Q/holomorphic/230/2/l/a/103/7"]
"2-230-115.103-c1-0-5"	1.355197124587213	1.8365592464894498	2	230	"115.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.08795269969446845	0	1.79397802587328088344708277885	["ModularForm/GL2/Q/holomorphic/230/2/l/a/103/6"]
"2-230-115.103-c1-0-6"	1.355197124587213	1.8365592464894498	2	230	"115.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.053536324716331976	0	1.86843579737884240791286186715	["ModularForm/GL2/Q/holomorphic/230/2/l/a/103/4"]
"2-230-115.103-c1-0-7"	1.355197124587213	1.8365592464894498	2	230	"115.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.12994490298182335	0	1.89452277759974449213203058374	["ModularForm/GL2/Q/holomorphic/230/2/l/a/103/1"]
"2-230-115.103-c1-0-8"	1.355197124587213	1.8365592464894498	2	230	"115.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2209189037813589	0	2.38651264398381558122430788186	["ModularForm/GL2/Q/holomorphic/230/2/l/a/103/11"]
"2-230-115.103-c1-0-9"	1.355197124587213	1.8365592464894498	2	230	"115.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11606866877790739	0	2.54027026166940410042290934874	["ModularForm/GL2/Q/holomorphic/230/2/l/a/103/5"]
"2-230-115.104-c1-0-0"	1.355197124587213	1.8365592464894498	2	230	"115.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.09169734252073601	0	0.58980086463494942367848424443	["ModularForm/GL2/Q/holomorphic/230/2/j/a/219/2"]
"2-230-115.104-c1-0-1"	1.355197124587213	1.8365592464894498	2	230	"115.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3078625110212195	0	1.03094634020148820241300319803	["ModularForm/GL2/Q/holomorphic/230/2/j/a/219/9"]
"2-230-115.104-c1-0-10"	1.355197124587213	1.8365592464894498	2	230	"115.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4378125933526454	0	2.67613378200948172776763938066	["ModularForm/GL2/Q/holomorphic/230/2/j/a/219/3"]
"2-230-115.104-c1-0-11"	1.355197124587213	1.8365592464894498	2	230	"115.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3953552292860085	0	2.69582686761624989354899681381	["ModularForm/GL2/Q/holomorphic/230/2/j/a/219/8"]
"2-230-115.104-c1-0-2"	1.355197124587213	1.8365592464894498	2	230	"115.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2524005274449185	0	1.52903905307078829828229951206	["ModularForm/GL2/Q/holomorphic/230/2/j/a/219/1"]
"2-230-115.104-c1-0-3"	1.355197124587213	1.8365592464894498	2	230	"115.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.041135307003221336	0	1.54211775409847842789496895428	["ModularForm/GL2/Q/holomorphic/230/2/j/a/219/7"]
"2-230-115.104-c1-0-4"	1.355197124587213	1.8365592464894498	2	230	"115.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.018953929166171907	0	1.58240121479891051909584764313	["ModularForm/GL2/Q/holomorphic/230/2/j/a/219/5"]
"2-230-115.104-c1-0-5"	1.355197124587213	1.8365592464894498	2	230	"115.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.21549121842387087	0	1.59666000192414349408473048414	["ModularForm/GL2/Q/holomorphic/230/2/j/a/219/11"]
"2-230-115.104-c1-0-6"	1.355197124587213	1.8365592464894498	2	230	"115.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.04775747712930168	0	1.91231656730616068047949782799	["ModularForm/GL2/Q/holomorphic/230/2/j/a/219/6"]
"2-230-115.104-c1-0-7"	1.355197124587213	1.8365592464894498	2	230	"115.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.15807870769537052	0	2.01677731271154320299033765550	["ModularForm/GL2/Q/holomorphic/230/2/j/a/219/10"]
"2-230-115.104-c1-0-8"	1.355197124587213	1.8365592464894498	2	230	"115.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.12456150111126842	0	2.15353692045450461323992492623	["ModularForm/GL2/Q/holomorphic/230/2/j/a/219/12"]
"2-230-115.104-c1-0-9"	1.355197124587213	1.8365592464894498	2	230	"115.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.25862398616404714	0	2.20800868978405972867055828281	["ModularForm/GL2/Q/holomorphic/230/2/j/a/219/4"]
"2-230-115.107-c1-0-0"	1.355197124587213	1.8365592464894498	2	230	"115.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.35097454124906874	0	0.16990004659376939617852954153	["ModularForm/GL2/Q/holomorphic/230/2/l/a/107/1"]
"2-230-115.107-c1-0-1"	1.355197124587213	1.8365592464894498	2	230	"115.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4895425026282534	0	0.20130751450998712522374884626	["ModularForm/GL2/Q/holomorphic/230/2/l/a/107/3"]
"2-230-115.107-c1-0-10"	1.355197124587213	1.8365592464894498	2	230	"115.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.06787954726257464	0	2.74074648020749611654462935948	["ModularForm/GL2/Q/holomorphic/230/2/l/a/107/12"]
"2-230-115.107-c1-0-11"	1.355197124587213	1.8365592464894498	2	230	"115.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.42648836256015965	0	3.14811512949486847703030957772	["ModularForm/GL2/Q/holomorphic/230/2/l/a/107/8"]
"2-230-115.107-c1-0-2"	1.355197124587213	1.8365592464894498	2	230	"115.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.004069601688380532	0	1.60080432458950548837993333137	["ModularForm/GL2/Q/holomorphic/230/2/l/a/107/2"]
"2-230-115.107-c1-0-3"	1.355197124587213	1.8365592464894498	2	230	"115.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.19964226454983883	0	1.63193607662966851948253136587	["ModularForm/GL2/Q/holomorphic/230/2/l/a/107/6"]
"2-230-115.107-c1-0-4"	1.355197124587213	1.8365592464894498	2	230	"115.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1003199021182886	0	1.75588956227101151867646256350	["ModularForm/GL2/Q/holomorphic/230/2/l/a/107/5"]
"2-230-115.107-c1-0-5"	1.355197124587213	1.8365592464894498	2	230	"115.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.016165621044509897	0	2.03075227437301681880970173609	["ModularForm/GL2/Q/holomorphic/230/2/l/a/107/11"]
"2-230-115.107-c1-0-6"	1.355197124587213	1.8365592464894498	2	230	"115.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.20145171073886578	0	2.16427147867789928796633228247	["ModularForm/GL2/Q/holomorphic/230/2/l/a/107/4"]
"2-230-115.107-c1-0-7"	1.355197124587213	1.8365592464894498	2	230	"115.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.06545842814800333	0	2.26695507139995154032368517533	["ModularForm/GL2/Q/holomorphic/230/2/l/a/107/10"]
"2-230-115.107-c1-0-8"	1.355197124587213	1.8365592464894498	2	230	"115.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.17647783103209694	0	2.27828827807884745504051909790	["ModularForm/GL2/Q/holomorphic/230/2/l/a/107/9"]
"2-230-115.107-c1-0-9"	1.355197124587213	1.8365592464894498	2	230	"115.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2703981487966747	0	2.39312421810747674340938610171	["ModularForm/GL2/Q/holomorphic/230/2/l/a/107/7"]
"2-230-115.112-c1-0-0"	1.355197124587213	1.8365592464894498	2	230	"115.112"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4942881051186596	0	0.06277972182918096919072109762	["ModularForm/GL2/Q/holomorphic/230/2/l/a/227/2"]
"2-230-115.112-c1-0-1"	1.355197124587213	1.8365592464894498	2	230	"115.112"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3514435895248457	0	1.17969197607111677785866130496	["ModularForm/GL2/Q/holomorphic/230/2/l/a/227/6"]
"2-230-115.112-c1-0-10"	1.355197124587213	1.8365592464894498	2	230	"115.112"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.409596698417857	0	3.13796266592131990522111996351	["ModularForm/GL2/Q/holomorphic/230/2/l/a/227/8"]
"2-230-115.112-c1-0-11"	1.355197124587213	1.8365592464894498	2	230	"115.112"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.48649685055370767	0	3.33036818435355229011922900934	["ModularForm/GL2/Q/holomorphic/230/2/l/a/227/7"]
"2-230-115.112-c1-0-2"	1.355197124587213	1.8365592464894498	2	230	"115.112"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07806505933447239	0	1.42422371499378164924005155299	["ModularForm/GL2/Q/holomorphic/230/2/l/a/227/4"]
"2-230-115.112-c1-0-3"	1.355197124587213	1.8365592464894498	2	230	"115.112"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.016319812662764856	0	1.57829267150163496034549564046	["ModularForm/GL2/Q/holomorphic/230/2/l/a/227/3"]
"2-230-115.112-c1-0-4"	1.355197124587213	1.8365592464894498	2	230	"115.112"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.04351872392606453	0	1.74840737251890112527265629782	["ModularForm/GL2/Q/holomorphic/230/2/l/a/227/11"]
"2-230-115.112-c1-0-5"	1.355197124587213	1.8365592464894498	2	230	"115.112"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.057658463172508966	0	1.91185724924424943718160662748	["ModularForm/GL2/Q/holomorphic/230/2/l/a/227/12"]
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"2-230-23.22-c12-0-60"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.1076889200225427	0	0.71508229962914782098370729675	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/23"]
"2-230-23.22-c12-0-61"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3474884706212692	0	0.72742827277235072199500006708	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/42"]
"2-230-23.22-c12-0-62"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3284930893448066	0	0.75487442747450553142860183708	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/16"]
"2-230-23.22-c12-0-63"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.23239006784924424	0	0.814845767478504013639804626488	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/83"]
"2-230-23.22-c12-0-64"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.09227976564971131	0	0.848500212325058371397022817151	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/63"]
"2-230-23.22-c12-0-65"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.47540997157963527	0	0.864730948822882047611268093563	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/1"]
"2-230-23.22-c12-0-66"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.16520446735661293	0	0.916190831877466979532290756346	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/20"]
"2-230-23.22-c12-0-67"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.31366001033895635	0	0.924701232324383472120311328514	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/30"]
"2-230-23.22-c12-0-68"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.24784352309395719	0	0.947132874612005411716928304715	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/80"]
"2-230-23.22-c12-0-69"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.08455532130909627	0	0.971798917654986726800377965087	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/81"]
"2-230-23.22-c12-0-7"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.1833112853239845	0	0.084557936395020897223216521928	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/2"]
"2-230-23.22-c12-0-70"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.08168391163084206	0	0.982557948836521341174706183421	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/43"]
"2-230-23.22-c12-0-71"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.2841517385343376	0	1.00692057704518519541573915900	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/55"]
"2-230-23.22-c12-0-72"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.45508263420641315	0	1.01926455779640383566759128808	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/11"]
"2-230-23.22-c12-0-73"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.09227976564971131	0	1.03554328259964767587519098585	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/82"]
"2-230-23.22-c12-0-74"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3065959916213995	0	1.03705222141653386141188217876	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/96"]
"2-230-23.22-c12-0-75"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.26848883609769764	0	1.06365298354478097543071472912	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/10"]
"2-230-23.22-c12-0-76"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.38252346122628905	0	1.08706065330047500589398323199	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/79"]
"2-230-23.22-c12-0-77"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.33661323304037316	0	1.10910225544948367164676738466	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/78"]
"2-230-23.22-c12-0-78"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.1938636343051003	0	1.14045586929711257890001739349	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/46"]
"2-230-23.22-c12-0-79"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.44012919845931114	0	1.15790579549031128955842392991	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/41"]
"2-230-23.22-c12-0-8"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.47016157938037323	0	0.10838636339630991435437080020	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/60"]
"2-230-23.22-c12-0-80"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.47016157938037323	0	1.16974810415006692968552858580	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/85"]
"2-230-23.22-c12-0-81"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3036226190812045	0	1.18922235945184547469340459865	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/73"]
"2-230-23.22-c12-0-82"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.48719522607005245	0	1.20748730932542382912141723558	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/70"]
"2-230-23.22-c12-0-83"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.2796752643484197	0	1.21237983395776261372368382709	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/94"]
"2-230-23.22-c12-0-84"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.28895429122604366	0	1.23143400485660818700356936862	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/27"]
"2-230-23.22-c12-0-85"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.3270649939960549	0	1.29007091038852190840214355828	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/44"]
"2-230-23.22-c12-0-86"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.08455532130909627	0	1.29644523878140617230746576178	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/64"]
"2-230-23.22-c12-0-87"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.44635120925473715	0	1.31012147277194164955436385153	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/36"]
"2-230-23.22-c12-0-88"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.31028511072922116	0	1.46182619753299601387929248052	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/57"]
"2-230-23.22-c12-0-89"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.3106912456077789	0	1.48333892056203975458199488692	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/74"]
"2-230-23.22-c12-0-9"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.28895429122604366	0	0.10976893681944554893937629118	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/22"]
"2-230-23.22-c12-0-90"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.28535590532790794	0	1.61116902951612309124466123546	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/52"]
"2-230-23.22-c12-0-91"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.4189164428691458	0	1.61361768239096702463766233179	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/89"]
"2-230-23.22-c12-0-92"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.4169116119818799	0	1.62717714090156325261447408776	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/15"]
"2-230-23.22-c12-0-93"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.4028687447696137	0	1.66210505810696860885913872215	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/12"]
"2-230-23.22-c12-0-94"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.35784935050099026	0	1.72744118202471212459759611747	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/53"]
"2-230-23.22-c12-0-95"	14.49891644136022	210.2185779735457	2	230	"23.22"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.42658450835132733	0	1.84174055837996027832730366540	["ModularForm/GL2/Q/holomorphic/230/13/d/a/91/61"]


# 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).