# lfunc_search downloaded from the LMFDB on 03 June 2026.
# Search link: https://www.lmfdb.org/L/2/790/395.372
# Query "{'degree': 2, 'conductor': 790}" returned 6065 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.



"2-790-1.1-c1-0-0"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.66129211271111095658333882162	["ModularForm/GL2/Q/holomorphic/790/2/a/f/1/2"]
"2-790-1.1-c1-0-1"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.69243670782824985625721312085	["ModularForm/GL2/Q/holomorphic/790/2/a/c/1/1"]
"2-790-1.1-c1-0-10"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.37536416052055293128492931521	["ModularForm/GL2/Q/holomorphic/790/2/a/c/1/2"]
"2-790-1.1-c1-0-11"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.47062258284317295421951399690	["ModularForm/GL2/Q/holomorphic/790/2/a/h/1/3"]
"2-790-1.1-c1-0-12"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.51874453325172991173697743269	["ModularForm/GL2/Q/holomorphic/790/2/a/e/1/2"]
"2-790-1.1-c1-0-13"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.67438115828764461137580562770	["ModularForm/GL2/Q/holomorphic/790/2/a/g/1/3"]
"2-790-1.1-c1-0-14"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.70400809706984473942335709920	["ModularForm/GL2/Q/holomorphic/790/2/a/h/1/4"]
"2-790-1.1-c1-0-15"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.74222804820396302723543971858	["ModularForm/GL2/Q/holomorphic/790/2/a/g/1/4"]
"2-790-1.1-c1-0-16"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.75898602917307334345150167851	["ModularForm/GL2/Q/holomorphic/790/2/a/b/1/1"]
"2-790-1.1-c1-0-17"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.78665878549507984698666690840	["ModularForm/GL2/Q/holomorphic/790/2/a/h/1/5"]
"2-790-1.1-c1-0-18"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.95661039475284721784000332261	["ModularForm/GL2/Q/holomorphic/790/2/a/e/1/3"]
"2-790-1.1-c1-0-19"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.07758147102690413945886444983	["ModularForm/GL2/Q/holomorphic/790/2/a/h/1/6"]
"2-790-1.1-c1-0-2"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.72862133246549127135939975865	["ModularForm/GL2/Q/holomorphic/790/2/a/f/1/1"]
"2-790-1.1-c1-0-20"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.10647338123247741126184570477	["EllipticCurve/Q/790/a", "ModularForm/GL2/Q/holomorphic/790/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/790/2/a/a"]
"2-790-1.1-c1-0-21"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.22532262958073072172114897302	["ModularForm/GL2/Q/holomorphic/790/2/a/e/1/4"]
"2-790-1.1-c1-0-22"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.27862932156548711223897159638	["ModularForm/GL2/Q/holomorphic/790/2/a/b/1/2"]
"2-790-1.1-c1-0-23"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.38525811849792422574914057814	["ModularForm/GL2/Q/holomorphic/790/2/a/d/1/1"]
"2-790-1.1-c1-0-24"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.56099566757501977939466754210	["ModularForm/GL2/Q/holomorphic/790/2/a/d/1/2"]
"2-790-1.1-c1-0-3"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.02117828576769090198602687098	["ModularForm/GL2/Q/holomorphic/790/2/a/g/1/1"]
"2-790-1.1-c1-0-4"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.07240902513105387875593623343	["ModularForm/GL2/Q/holomorphic/790/2/a/h/1/2"]
"2-790-1.1-c1-0-5"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.16860723122617811826774427794	["ModularForm/GL2/Q/holomorphic/790/2/a/h/1/1"]
"2-790-1.1-c1-0-6"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.18187350412669819998460779621	["ModularForm/GL2/Q/holomorphic/790/2/a/f/1/3"]
"2-790-1.1-c1-0-7"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.24936507076355904783845995846	["ModularForm/GL2/Q/holomorphic/790/2/a/g/1/2"]
"2-790-1.1-c1-0-8"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.35039763546811584636279591493	["ModularForm/GL2/Q/holomorphic/790/2/a/e/1/1"]
"2-790-1.1-c1-0-9"	2.5116093963196495	6.308181759681154	2	790	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.36286724370304758495087797159	["ModularForm/GL2/Q/holomorphic/790/2/a/f/1/4"]
"2-790-395.103-c1-0-0"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.012954694502498499	0	0.21867464534628506104127827680	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/1"]
"2-790-395.103-c1-0-1"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05405512205505466	0	0.31149797741856622344648265414	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/3"]
"2-790-395.103-c1-0-10"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3061074959742896	0	0.804233095011578522616170868754	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/20"]
"2-790-395.103-c1-0-11"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4836924472246809	0	0.814051593963899189404738082799	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/35"]
"2-790-395.103-c1-0-12"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.26736616331498453	0	0.920936166061380674881175826373	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/34"]
"2-790-395.103-c1-0-13"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.461420362153977	0	0.929611369948560993000596616219	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/38"]
"2-790-395.103-c1-0-14"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.38174863065733455	0	0.947046261837932272101504458789	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/40"]
"2-790-395.103-c1-0-15"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05021153559980081	0	0.975379636461282929026308178354	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/13"]
"2-790-395.103-c1-0-16"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.03907130888078836	0	0.978981918302586043215792852013	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/19"]
"2-790-395.103-c1-0-17"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.21854376233773884	0	1.07231070431878100196964539256	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/2"]
"2-790-395.103-c1-0-18"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.24041861997940508	0	1.10868625728788771918379748160	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/5"]
"2-790-395.103-c1-0-19"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.08647650796316086	0	1.14041637857710321210289576362	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/16"]
"2-790-395.103-c1-0-2"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.32185433844686057	0	0.32271409236410258012311712977	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/37"]
"2-790-395.103-c1-0-20"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2655567189687325	0	1.19120172020972659310310153057	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/33"]
"2-790-395.103-c1-0-21"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.037440512088729554	0	1.23623329103278827192009753466	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/31"]
"2-790-395.103-c1-0-22"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.10366170149852277	0	1.37549857203130764455722587720	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/26"]
"2-790-395.103-c1-0-23"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.03612204401859196	0	1.40877619455578170602538328118	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/28"]
"2-790-395.103-c1-0-24"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.21094011595691467	0	1.47576741188717033493564672574	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/14"]
"2-790-395.103-c1-0-25"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3597696765473246	0	1.50085857465224864057979322467	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/11"]
"2-790-395.103-c1-0-26"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.19274086679217406	0	1.52938900555105578452251768736	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/27"]
"2-790-395.103-c1-0-27"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.46633146043733464	0	1.56307193015341956110455971305	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/6"]
"2-790-395.103-c1-0-28"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3091019235995109	0	1.59328927331637074886336682441	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/9"]
"2-790-395.103-c1-0-29"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2516883665377216	0	1.63856468006921973135884081910	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/12"]
"2-790-395.103-c1-0-3"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4893537543648538	0	0.35753778289627873229500117832	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/18"]
"2-790-395.103-c1-0-30"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.03753725803390787	0	1.66005147207636395903401699475	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/32"]
"2-790-395.103-c1-0-31"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.0035315149452271846	0	1.66536669172953032057437463113	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/36"]
"2-790-395.103-c1-0-32"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.15292607214906187	0	1.69994091786652338021383317453	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/24"]
"2-790-395.103-c1-0-33"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.46689983531017637	0	1.94218865762231215702662668227	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/8"]
"2-790-395.103-c1-0-34"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2691013545959052	0	1.95459953109118837580361302049	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/29"]
"2-790-395.103-c1-0-35"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.34460861544410665	0	2.04585325869953121260239583691	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/17"]
"2-790-395.103-c1-0-36"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4176292186566677	0	2.11802413222833753911565325418	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/4"]
"2-790-395.103-c1-0-37"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4869449543091671	0	2.15994580264833829289696964630	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/21"]
"2-790-395.103-c1-0-38"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3224678862502031	0	2.26926432910124371254785349009	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/7"]
"2-790-395.103-c1-0-39"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4264573377721935	0	2.38091430851478730509142155058	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/23"]
"2-790-395.103-c1-0-4"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.33415346855974276	0	0.37018123376581883054113561479	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/39"]
"2-790-395.103-c1-0-5"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.48275311960680545	0	0.49328854501364141634436032202	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/30"]
"2-790-395.103-c1-0-6"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.14337978452694536	0	0.55242490242548363632859804054	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/22"]
"2-790-395.103-c1-0-7"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2896729321068555	0	0.56611719193097052882630810931	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/25"]
"2-790-395.103-c1-0-8"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.18266025037053643	0	0.58616709151684291477916554838	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/10"]
"2-790-395.103-c1-0-9"	2.5116093963196495	6.308181759681154	2	790	"395.103"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.12313031073153044	0	0.66343776073989394269257391544	["ModularForm/GL2/Q/holomorphic/790/2/k/a/103/15"]
"2-790-395.104-c1-0-0"	2.5116093963196495	6.308181759681154	2	790	"395.104"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3146982456178393	0	0.02140787969186270542282958608	["ModularForm/GL2/Q/holomorphic/790/2/t/a/499/24"]
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"2-790-1.1-c5-0-64"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.02242240541934264466866982079	["ModularForm/GL2/Q/holomorphic/790/6/a/f/1/8"]
"2-790-1.1-c5-0-65"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.02840497142468950752136375196	["ModularForm/GL2/Q/holomorphic/790/6/a/h/1/11"]
"2-790-1.1-c5-0-66"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.03068416689636013058707275868	["ModularForm/GL2/Q/holomorphic/790/6/a/g/1/14"]
"2-790-1.1-c5-0-67"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.03155641827396051787945887059	["ModularForm/GL2/Q/holomorphic/790/6/a/b/1/3"]
"2-790-1.1-c5-0-68"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.03482323396312763996682568975	["ModularForm/GL2/Q/holomorphic/790/6/a/h/1/3"]
"2-790-1.1-c5-0-69"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.03997593148071992252382407817	["ModularForm/GL2/Q/holomorphic/790/6/a/f/1/9"]
"2-790-1.1-c5-0-7"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.33314199416243991919696589779	["ModularForm/GL2/Q/holomorphic/790/6/a/e/1/11"]
"2-790-1.1-c5-0-70"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.04423526890740922991066472563	["ModularForm/GL2/Q/holomorphic/790/6/a/b/1/7"]
"2-790-1.1-c5-0-71"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.04467055617876859095480086537	["ModularForm/GL2/Q/holomorphic/790/6/a/e/1/17"]
"2-790-1.1-c5-0-72"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.04597347456486610523929579110	["ModularForm/GL2/Q/holomorphic/790/6/a/f/1/2"]
"2-790-1.1-c5-0-73"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.05582324387883408363056894200	["ModularForm/GL2/Q/holomorphic/790/6/a/g/1/13"]
"2-790-1.1-c5-0-74"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.07839776819374547481570719675	["ModularForm/GL2/Q/holomorphic/790/6/a/g/1/17"]
"2-790-1.1-c5-0-75"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.11013875694960423832881718356	["ModularForm/GL2/Q/holomorphic/790/6/a/h/1/14"]
"2-790-1.1-c5-0-76"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.11122459041185525884765120667	["ModularForm/GL2/Q/holomorphic/790/6/a/d/1/3"]
"2-790-1.1-c5-0-77"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.11590129433449996506165049445	["ModularForm/GL2/Q/holomorphic/790/6/a/a/1/3"]
"2-790-1.1-c5-0-78"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.11694334847768782896755684969	["ModularForm/GL2/Q/holomorphic/790/6/a/a/1/1"]
"2-790-1.1-c5-0-79"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.13057801453371644926556796554	["ModularForm/GL2/Q/holomorphic/790/6/a/b/1/4"]
"2-790-1.1-c5-0-8"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.33535331609545858149222004272	["ModularForm/GL2/Q/holomorphic/790/6/a/h/1/6"]
"2-790-1.1-c5-0-80"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.13082683597757687977434850470	["ModularForm/GL2/Q/holomorphic/790/6/a/d/1/6"]
"2-790-1.1-c5-0-81"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.14164536500628220314353815081	["ModularForm/GL2/Q/holomorphic/790/6/a/f/1/3"]
"2-790-1.1-c5-0-82"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.15667582652988155754001649099	["ModularForm/GL2/Q/holomorphic/790/6/a/e/1/16"]
"2-790-1.1-c5-0-83"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.16699687165626490563879865649	["ModularForm/GL2/Q/holomorphic/790/6/a/f/1/11"]
"2-790-1.1-c5-0-84"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.17299027539198147376770374443	["ModularForm/GL2/Q/holomorphic/790/6/a/b/1/1"]
"2-790-1.1-c5-0-85"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.17671973140591857774262571010	["ModularForm/GL2/Q/holomorphic/790/6/a/g/1/16"]
"2-790-1.1-c5-0-86"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.18244532490507455701561010263	["ModularForm/GL2/Q/holomorphic/790/6/a/h/1/18"]
"2-790-1.1-c5-0-87"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.21113009431394665404444845774	["ModularForm/GL2/Q/holomorphic/790/6/a/d/1/7"]
"2-790-1.1-c5-0-88"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.22512646172753631112100189116	["ModularForm/GL2/Q/holomorphic/790/6/a/g/1/15"]
"2-790-1.1-c5-0-89"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.22729094037323851795516932256	["ModularForm/GL2/Q/holomorphic/790/6/a/h/1/20"]
"2-790-1.1-c5-0-9"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	0.35763789467045814571750670307	["ModularForm/GL2/Q/holomorphic/790/6/a/e/1/12"]
"2-790-1.1-c5-0-90"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.23056720806277165832567083338	["ModularForm/GL2/Q/holomorphic/790/6/a/c/1/15"]
"2-790-1.1-c5-0-91"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.24353881258865253155706886608	["ModularForm/GL2/Q/holomorphic/790/6/a/d/1/5"]
"2-790-1.1-c5-0-92"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.24572605275535814820034104373	["ModularForm/GL2/Q/holomorphic/790/6/a/a/1/5"]
"2-790-1.1-c5-0-93"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.0	0	1.27464475728057395009391815596	["ModularForm/GL2/Q/holomorphic/790/6/a/h/1/15"]
"2-790-1.1-c5-0-94"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.28968763233052199069307539957	["ModularForm/GL2/Q/holomorphic/790/6/a/b/1/10"]
"2-790-1.1-c5-0-95"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.29182473476823037159045331196	["ModularForm/GL2/Q/holomorphic/790/6/a/d/1/4"]
"2-790-1.1-c5-0-96"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.30001419012896611227832646199	["ModularForm/GL2/Q/holomorphic/790/6/a/d/1/8"]
"2-790-1.1-c5-0-97"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.30358328647848181157547356055	["ModularForm/GL2/Q/holomorphic/790/6/a/f/1/15"]
"2-790-1.1-c5-0-98"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.30453534195255180692732155947	["ModularForm/GL2/Q/holomorphic/790/6/a/a/1/4"]
"2-790-1.1-c5-0-99"	11.256252380444156	126.70321765225472	2	790	"1.1"	[]	[[2.5, 0.0]]	5	true	true	false	true	0.5	1	1.30687218909251861001460186008	["ModularForm/GL2/Q/holomorphic/790/6/a/f/1/12"]


# Label --
#    Each L-function $L$ has a label of the form d-N-q.k-x-y-i, where

#     * $d$ is the degree of $L$.
#     * $N$ is the conductor of $L$.  When $N$ is a perfect power $m^n$ we write $N$ as $m$e$n$, since $N$ can be very large for some imprimitive L-functions.
#     * q.k is the label of the primitive Dirichlet character from which the central character is induced.
#     * x-y is the spectral label encoding the $\mu_j$ and $\nu_j$ in the analytically normalized functional equation.
#     * i is a non-negative integer disambiguating between L-functions that would otherwise have the same label.


#$\alpha$ (root_analytic_conductor) --
#    If $d$ is the degree of the L-function $L(s)$, the **root analytic conductor** $\alpha$ of $L$ is the $d$th root of the analytic conductor of $L$.  It plays a role analogous to the root discriminant for number fields.


#$A$ (analytic_conductor) --
#    The **analytic conductor** of an L-function $L(s)$ with infinity factor $L_{\infty}(s)$ and conductor $N$ is the real number
#    \[
#    A := \mathrm{exp}\left(2\mathrm{Re}\left(\frac{L_{\infty}'(1/2)}{L_{\infty}(1/2)}\right)\right)N.
#    \]



#$d$ (degree) --
#    The **degree** of an L-function is the number $J + 2K$ of Gamma factors occurring in its functional equation

#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s).
#    \]

#    The degree appears as the first component of the Selberg data of $L(s).$ In all known cases it is the degree of the polynomial of the inverse of the Euler factor at any prime not dividing the conductor.



#$N$ (conductor) --
#    The **conductor** of an L-function is the integer $N$  occurring in its functional equation

#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s).
#    \]


#    The conductor of an analytic L-function is the second component in the Selberg data. For a Dirichlet L-function
#     associated with a primitive Dirichlet character, the conductor of the L-function is the same as the conductor of the character. For a primitive L-function associated with a cusp form $\phi$ on $GL(2)/\mathbb Q$, the conductor of the L-function is the same as the level of $\phi$.

#    In the literature, the word _level_ is sometimes used instead of _conductor_.


#$\chi$ (central_character) --
#    An L-function has an Euler product of the form
#    $L(s) = \prod_p L_p(p^{-s})^{-1}$
#    where $L_p(x) = 1 + a_p x + \ldots + (-1)^d \chi(p) x^d$. The character $\chi$ is a Dirichlet character mod $N$ and is called **central character** of the L-function.
#    Here, $N$ is the conductor of $L$.


#$\mu$ (mus) --
#    All known analytic L-functions have a **functional equation** that can be written in the form
#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s),
#    \]
#    where $N$ is an integer, $\Gamma_{\mathbb R}$ and $\Gamma_{\mathbb C}$ are defined in terms of the $\Gamma$-function, $\mathrm{Re}(\mu_j) = 0 \ \mathrm{or} \ 1$ (assuming Selberg's eigenvalue conjecture), and $\mathrm{Re}(\nu_k)$ is a positive integer
#    or half-integer,
#    \[
#    \sum \mu_j + 2 \sum \nu_k \ \ \ \ \text{is real},
#    \]
#    and $\varepsilon$ is the sign of the functional equation.
#    With those restrictions on the spectral parameters, the
#    data in the functional equation is specified uniquely.  The integer $d = J + 2 K$
#    is the degree of the L-function. The integer $N$ is  the conductor (or level)
#    of the L-function.  The pair $[J,K]$ is the signature of the L-function.  The parameters
#    in the functional equation can be used to make up the 4-tuple called the Selberg data.


#    The axioms of the Selberg class are less restrictive than
#    given above.

#    Note that the functional equation above has the central point at $s=1/2$, and relates $s\leftrightarrow 1-s$.

#    For many L-functions there is another normalization which is natural. The corresponding functional equation relates $s\leftrightarrow w+1-s$ for some positive integer $w$,
#    called the motivic weight of the L-function. The central point is at $s=(w+1)/2$, and the arithmetically normalized Dirichlet coefficients $a_n n^{w/2}$ are algebraic integers.



#$\nu$ (nus) --
#    All known analytic L-functions have a **functional equation** that can be written in the form
#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s),
#    \]
#    where $N$ is an integer, $\Gamma_{\mathbb R}$ and $\Gamma_{\mathbb C}$ are defined in terms of the $\Gamma$-function, $\mathrm{Re}(\mu_j) = 0 \ \mathrm{or} \ 1$ (assuming Selberg's eigenvalue conjecture), and $\mathrm{Re}(\nu_k)$ is a positive integer
#    or half-integer,
#    \[
#    \sum \mu_j + 2 \sum \nu_k \ \ \ \ \text{is real},
#    \]
#    and $\varepsilon$ is the sign of the functional equation.
#    With those restrictions on the spectral parameters, the
#    data in the functional equation is specified uniquely.  The integer $d = J + 2 K$
#    is the degree of the L-function. The integer $N$ is  the conductor (or level)
#    of the L-function.  The pair $[J,K]$ is the signature of the L-function.  The parameters
#    in the functional equation can be used to make up the 4-tuple called the Selberg data.


#    The axioms of the Selberg class are less restrictive than
#    given above.

#    Note that the functional equation above has the central point at $s=1/2$, and relates $s\leftrightarrow 1-s$.

#    For many L-functions there is another normalization which is natural. The corresponding functional equation relates $s\leftrightarrow w+1-s$ for some positive integer $w$,
#    called the motivic weight of the L-function. The central point is at $s=(w+1)/2$, and the arithmetically normalized Dirichlet coefficients $a_n n^{w/2}$ are algebraic integers.



#$w$ (motivic_weight) --
#    The **motivic weight** (or **arithmetic weight**) of an arithmetic L-function with analytic normalization $L_{an}(s)=\sum_{n=1}^\infty a_nn^{-s}$ is the least nonnegative integer $w$ for which $a_nn^{w/2}$ is an algebraic integer for all $n\ge 1$.

#    If the L-function arises from a motive, then the weight of the motive has the
#    same parity as the motivic weight of the L-function, but the weight of the motive
#    could be larger.  This apparent discrepancy comes from the fact that a Tate twist
#    increases the weight of the motive.  This corresponds to the change of variables
#    $s \mapsto s + j$ in the L-function of the motive.


#prim (primitive) --
#    An L-function is <b>primitive</b> if it cannot be written as a product of nontrivial L-functions.  The "trivial L-function" is the constant function $1$.


#arith (algebraic) --
#    An L-function $L(s) = \sum_{n=1}^{\infty} a_n n^{-s}$  is called **arithmetic** if its Dirichlet coefficients $a_n$ are algebraic numbers.


#$\mathbb{Q}$ (rational) --
#    A **rational** L-function $L(s)$ is an arithmetic L-function with coefficient field $\Q$; equivalently, its Euler product in the arithmetic normalization can be written as a product over rational primes
#    \[
#    L(s)=\prod_pL_p(p^{-s})^{-1}
#    \]
#    with $L_p\in \Z[T]$.


#self-dual (self_dual) --
#    An L-function $L(s) = \sum_{n=1}^{\infty} \frac{a_n}{n^s}$ is called **self-dual** if its Dirichlet coefficients $a_n$ are real.


#$\operatorname{Arg}(\epsilon)$ (root_angle) --
#    The **root angle** of an L-function is the argument of its root number, as a real number $\alpha$ with $-0.5 < \alpha \le 0.5$.


#$r$ (order_of_vanishing) --
#    The **analytic rank** of an L-function $L(s)$ is its order of vanishing at its central point.

#    When the analytic rank $r$ is positive, the value listed in the LMFDB is typically an upper bound that is believed to be tight (in the sense that there are known to be $r$ zeroes located very near to the central point).


#First zero (z1) --
#    The **zeros** of an L-function $L(s)$ are the complex numbers $\rho$ for which $L(\rho)=0$.

#    Under the Riemann Hypothesis, every non-trivial zero $\rho$ lies on the critical line $\Re(s)=1/2$ (in the analytic normalization).

#    The **lowest zero** of an L-function $L(s)$ is the least $\gamma>0$ for which $L(1/2+i\gamma)=0$. Note that even when $L(1/2)=0$, the lowest zero is by definition a positive real number.


#Origin (instance_urls) --
#    L-functions arise from many different sources. Already in degree 2 we have examples of
#    L-functions associated with holomorphic cusp forms, with Maass forms, with elliptic curves, with characters of number fields (Hecke characters), and with 2-dimensional representations of the Galois group of a number field (Artin L-functions).

#    Sometimes an L-function may arise from more than one source. For example, the L-functions associated with elliptic curves are also associated with weight 2 cusp forms. A goal of the Langlands program ostensibly is to prove that any degree $d$ L-function is associated with an automorphic form on $\mathrm{GL}(d)$. Because of this representation theoretic genesis, one can associate an L-function not only to an automorphic representation but also to symmetric powers, or exterior powers of that representation, or to the tensor product of two representations (the Rankin-Selberg product of two L-functions).