# lfunc_search downloaded from the LMFDB on 23 June 2026.
# Search link: https://www.lmfdb.org/L/2/2592/9.4/c1-0
# Query "{'degree': 2, 'conductor': 2592, 'spectral_label': 'c1-0'}" returned 560 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.



"2-2592-1.1-c1-0-0"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.32602178112493557679319365657	["ModularForm/GL2/Q/holomorphic/2592/2/a/u/1/1"]
"2-2592-1.1-c1-0-1"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.33447888971779307798694151993	["ModularForm/GL2/Q/holomorphic/2592/2/a/w/1/1"]
"2-2592-1.1-c1-0-10"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.870512331980832436414106425658	["ModularForm/GL2/Q/holomorphic/2592/2/a/t/1/1"]
"2-2592-1.1-c1-0-11"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.882515997143276502955034600173	["ModularForm/GL2/Q/holomorphic/2592/2/a/x/1/3"]
"2-2592-1.1-c1-0-12"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.900747617632598009084088353306	["ModularForm/GL2/Q/holomorphic/2592/2/a/s/1/1"]
"2-2592-1.1-c1-0-13"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.906323897796769393764080167284	["ModularForm/GL2/Q/holomorphic/2592/2/a/x/1/2"]
"2-2592-1.1-c1-0-14"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.04183626626039601496078575514	["ModularForm/GL2/Q/holomorphic/2592/2/a/u/1/4"]
"2-2592-1.1-c1-0-15"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.05452782238790190390759779110	["ModularForm/GL2/Q/holomorphic/2592/2/a/n/1/2"]
"2-2592-1.1-c1-0-16"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.06559269239501104444819619026	["ModularForm/GL2/Q/holomorphic/2592/2/a/w/1/4"]
"2-2592-1.1-c1-0-17"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.06837557476990618375946002698	["EllipticCurve/Q/2592/f", "ModularForm/GL2/Q/holomorphic/2592/2/a/f/1/1", "ModularForm/GL2/Q/holomorphic/2592/2/a/f"]
"2-2592-1.1-c1-0-18"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.09288727158030460235151020082	["ModularForm/GL2/Q/holomorphic/2592/2/a/u/1/3"]
"2-2592-1.1-c1-0-19"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.09291123114302028547127821993	["ModularForm/GL2/Q/holomorphic/2592/2/a/s/1/2"]
"2-2592-1.1-c1-0-2"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.55053076539044620349278114930	["ModularForm/GL2/Q/holomorphic/2592/2/a/x/1/1"]
"2-2592-1.1-c1-0-20"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.10257519052287726194513676147	["ModularForm/GL2/Q/holomorphic/2592/2/a/q/1/2"]
"2-2592-1.1-c1-0-21"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.20945780797206098361271470292	["ModularForm/GL2/Q/holomorphic/2592/2/a/t/1/2"]
"2-2592-1.1-c1-0-22"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.22926147462059190907207108373	["ModularForm/GL2/Q/holomorphic/2592/2/a/w/1/3"]
"2-2592-1.1-c1-0-23"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.27183880813480441140654468370	["EllipticCurve/Q/2592/h", "ModularForm/GL2/Q/holomorphic/2592/2/a/h/1/1", "ModularForm/GL2/Q/holomorphic/2592/2/a/h"]
"2-2592-1.1-c1-0-24"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.28142434047676578729566716608	["ModularForm/GL2/Q/holomorphic/2592/2/a/x/1/4"]
"2-2592-1.1-c1-0-25"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.28502141448365930031973361559	["EllipticCurve/Q/2592/a", "ModularForm/GL2/Q/holomorphic/2592/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/2592/2/a/a"]
"2-2592-1.1-c1-0-26"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.29162222912781718445665208888	["ModularForm/GL2/Q/holomorphic/2592/2/a/k/1/1"]
"2-2592-1.1-c1-0-27"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.34068784546076625184437100023	["ModularForm/GL2/Q/holomorphic/2592/2/a/r/1/2"]
"2-2592-1.1-c1-0-28"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.35113073394202297598788621155	["ModularForm/GL2/Q/holomorphic/2592/2/a/i/1/1"]
"2-2592-1.1-c1-0-29"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.40313273085513038178829937206	["ModularForm/GL2/Q/holomorphic/2592/2/a/v/1/1"]
"2-2592-1.1-c1-0-3"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.57381178061417432178908058149	["EllipticCurve/Q/2592/b", "ModularForm/GL2/Q/holomorphic/2592/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/2592/2/a/b"]
"2-2592-1.1-c1-0-30"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.40804108458245971944468667846	["ModularForm/GL2/Q/holomorphic/2592/2/a/m/1/1"]
"2-2592-1.1-c1-0-31"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.42073272012521395322399751058	["ModularForm/GL2/Q/holomorphic/2592/2/a/j/1/1"]
"2-2592-1.1-c1-0-32"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.47329622182797242636351288162	["ModularForm/GL2/Q/holomorphic/2592/2/a/l/1/1"]
"2-2592-1.1-c1-0-33"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.56974610630703964291935431360	["ModularForm/GL2/Q/holomorphic/2592/2/a/l/1/2"]
"2-2592-1.1-c1-0-34"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.57929474521379930906329591596	["ModularForm/GL2/Q/holomorphic/2592/2/a/v/1/2"]
"2-2592-1.1-c1-0-35"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.58663246186762614829046343021	["ModularForm/GL2/Q/holomorphic/2592/2/a/p/1/1"]
"2-2592-1.1-c1-0-36"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.58953134256885053149055926902	["ModularForm/GL2/Q/holomorphic/2592/2/a/i/1/2"]
"2-2592-1.1-c1-0-37"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.59855439628151168943818897603	["ModularForm/GL2/Q/holomorphic/2592/2/a/o/1/1"]
"2-2592-1.1-c1-0-38"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.60145796182948456188951188751	["EllipticCurve/Q/2592/d", "ModularForm/GL2/Q/holomorphic/2592/2/a/d/1/1", "ModularForm/GL2/Q/holomorphic/2592/2/a/d"]
"2-2592-1.1-c1-0-39"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.60192647411290427492429607549	["EllipticCurve/Q/2592/e", "ModularForm/GL2/Q/holomorphic/2592/2/a/e/1/1", "ModularForm/GL2/Q/holomorphic/2592/2/a/e"]
"2-2592-1.1-c1-0-4"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.62645019878666460909413764508	["ModularForm/GL2/Q/holomorphic/2592/2/a/n/1/1"]
"2-2592-1.1-c1-0-40"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.60347169177601591041401800268	["ModularForm/GL2/Q/holomorphic/2592/2/a/j/1/2"]
"2-2592-1.1-c1-0-41"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.66649992391956995295892711948	["ModularForm/GL2/Q/holomorphic/2592/2/a/v/1/3"]
"2-2592-1.1-c1-0-42"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.72925906536824499152018065956	["ModularForm/GL2/Q/holomorphic/2592/2/a/m/1/2"]
"2-2592-1.1-c1-0-43"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.73490294330663327596617513969	["ModularForm/GL2/Q/holomorphic/2592/2/a/o/1/2"]
"2-2592-1.1-c1-0-44"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.78599284719875021669502832306	["ModularForm/GL2/Q/holomorphic/2592/2/a/v/1/4"]
"2-2592-1.1-c1-0-45"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.85179095146423760832242357565	["ModularForm/GL2/Q/holomorphic/2592/2/a/k/1/2"]
"2-2592-1.1-c1-0-46"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.86485531322756247966908211949	["ModularForm/GL2/Q/holomorphic/2592/2/a/p/1/2"]
"2-2592-1.1-c1-0-47"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.86513620948226769101175426335	["EllipticCurve/Q/2592/g", "ModularForm/GL2/Q/holomorphic/2592/2/a/g/1/1", "ModularForm/GL2/Q/holomorphic/2592/2/a/g"]
"2-2592-1.1-c1-0-5"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.65084565961050136195540735714	["ModularForm/GL2/Q/holomorphic/2592/2/a/q/1/1"]
"2-2592-1.1-c1-0-6"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.70774184143114507895356192899	["ModularForm/GL2/Q/holomorphic/2592/2/a/r/1/1"]
"2-2592-1.1-c1-0-7"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.73714521852377401721058880406	["EllipticCurve/Q/2592/c", "ModularForm/GL2/Q/holomorphic/2592/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/2592/2/a/c"]
"2-2592-1.1-c1-0-8"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.74408152071536741952429232066	["ModularForm/GL2/Q/holomorphic/2592/2/a/w/1/2"]
"2-2592-1.1-c1-0-9"	4.549420205247685	20.697224203915887	2	2592	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.834980729851724420948109268771	["ModularForm/GL2/Q/holomorphic/2592/2/a/u/1/2"]
"2-2592-12.11-c1-0-0"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.375	0	0.02690514944651123807717560278	["ModularForm/GL2/Q/holomorphic/2592/2/c/b/2591/10"]
"2-2592-12.11-c1-0-1"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.375	0	0.03529180182747221178303250144	["ModularForm/GL2/Q/holomorphic/2592/2/c/c/2591/23"]
"2-2592-12.11-c1-0-10"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.125	0	0.55021113216939662643984859296	["ModularForm/GL2/Q/holomorphic/2592/2/c/c/2591/13"]
"2-2592-12.11-c1-0-11"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.125	0	0.55570998192254786953668420333	["ModularForm/GL2/Q/holomorphic/2592/2/c/c/2591/5"]
"2-2592-12.11-c1-0-12"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.125	0	0.58410380834040669658190158867	["ModularForm/GL2/Q/holomorphic/2592/2/c/b/2591/2"]
"2-2592-12.11-c1-0-13"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.125	0	0.58467053130933760889213066623	["ModularForm/GL2/Q/holomorphic/2592/2/c/a/2591/5"]
"2-2592-12.11-c1-0-14"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.125	0	0.60817917942490945894428681074	["ModularForm/GL2/Q/holomorphic/2592/2/c/c/2591/8"]
"2-2592-12.11-c1-0-15"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.375	0	0.62200018525869261892289536647	["ModularForm/GL2/Q/holomorphic/2592/2/c/c/2591/24"]
"2-2592-12.11-c1-0-16"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.125	0	0.64493630102439531410721613250	["ModularForm/GL2/Q/holomorphic/2592/2/c/b/2591/8"]
"2-2592-12.11-c1-0-17"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.125	0	0.64832338638082199580471221568	["ModularForm/GL2/Q/holomorphic/2592/2/c/c/2591/11"]
"2-2592-12.11-c1-0-18"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.125	0	0.67430395636676998203043728270	["ModularForm/GL2/Q/holomorphic/2592/2/c/b/2591/13"]
"2-2592-12.11-c1-0-19"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.375	0	0.72631396886592143574356536185	["ModularForm/GL2/Q/holomorphic/2592/2/c/b/2591/14"]
"2-2592-12.11-c1-0-2"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.375	0	0.16101950933217320771129919474	["ModularForm/GL2/Q/holomorphic/2592/2/c/c/2591/22"]
"2-2592-12.11-c1-0-20"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.125	0	0.810040687380502081316109747848	["ModularForm/GL2/Q/holomorphic/2592/2/c/b/2591/11"]
"2-2592-12.11-c1-0-21"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.125	0	0.836301245721500367004081310963	["ModularForm/GL2/Q/holomorphic/2592/2/c/c/2591/19"]
"2-2592-12.11-c1-0-22"	4.549420205247685	20.697224203915887	2	2592	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.125	0	0.930664122237625465759009081857	["ModularForm/GL2/Q/holomorphic/2592/2/c/a/2591/8"]
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"2-2592-9.4-c1-0-44"	4.549420205247685	20.697224203915887	2	2592	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3888888888888889	0	1.79786485739162219554929085746	["ModularForm/GL2/Q/holomorphic/2592/2/i/x/1729/1"]
"2-2592-9.4-c1-0-45"	4.549420205247685	20.697224203915887	2	2592	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.47222222222222227	0	1.80517923124658522389672591609	["ModularForm/GL2/Q/holomorphic/2592/2/i/bg/1729/3"]
"2-2592-9.4-c1-0-46"	4.549420205247685	20.697224203915887	2	2592	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4444444444444444	0	2.00870342631957920383614353262	["ModularForm/GL2/Q/holomorphic/2592/2/i/bc/1729/2"]
"2-2592-9.4-c1-0-47"	4.549420205247685	20.697224203915887	2	2592	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.47222222222222227	0	2.01260364942884000205549923310	["ModularForm/GL2/Q/holomorphic/2592/2/i/bh/1729/3"]
"2-2592-9.4-c1-0-5"	4.549420205247685	20.697224203915887	2	2592	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2777777777777778	0	0.28553088501887923982534574652	["ModularForm/GL2/Q/holomorphic/2592/2/i/s/1729/1"]
"2-2592-9.4-c1-0-6"	4.549420205247685	20.697224203915887	2	2592	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4444444444444444	0	0.30138793357138054951497464283	["ModularForm/GL2/Q/holomorphic/2592/2/i/l/1729/1"]
"2-2592-9.4-c1-0-7"	4.549420205247685	20.697224203915887	2	2592	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2777777777777778	0	0.38776380686161852716118348098	["ModularForm/GL2/Q/holomorphic/2592/2/i/o/1729/1"]
"2-2592-9.4-c1-0-8"	4.549420205247685	20.697224203915887	2	2592	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2777777777777778	0	0.47080440465157214461727120334	["ModularForm/GL2/Q/holomorphic/2592/2/i/bd/1729/2"]
"2-2592-9.4-c1-0-9"	4.549420205247685	20.697224203915887	2	2592	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2777777777777778	0	0.55197987167882812077438211262	["ModularForm/GL2/Q/holomorphic/2592/2/i/k/1729/1"]
"2-2592-9.7-c1-0-0"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.47222222222222227	0	0.02938150178928589719856032859	["ModularForm/GL2/Q/holomorphic/2592/2/i/bg/865/1"]
"2-2592-9.7-c1-0-1"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2222222222222222	0	0.13870858796283892039174895192	["ModularForm/GL2/Q/holomorphic/2592/2/i/ba/865/1"]
"2-2592-9.7-c1-0-10"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3888888888888889	0	0.50178148529365947104452759869	["ModularForm/GL2/Q/holomorphic/2592/2/i/x/865/1"]
"2-2592-9.7-c1-0-11"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3888888888888889	0	0.54623318411897654023694048051	["ModularForm/GL2/Q/holomorphic/2592/2/i/q/865/1"]
"2-2592-9.7-c1-0-12"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2222222222222222	0	0.56770777765987313015636651206	["ModularForm/GL2/Q/holomorphic/2592/2/i/n/865/1"]
"2-2592-9.7-c1-0-13"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2222222222222222	0	0.60258635956818946545576541919	["ModularForm/GL2/Q/holomorphic/2592/2/i/u/865/1"]
"2-2592-9.7-c1-0-14"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2222222222222222	0	0.63187051573737499434622558675	["ModularForm/GL2/Q/holomorphic/2592/2/i/v/865/1"]
"2-2592-9.7-c1-0-15"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2222222222222222	0	0.69331641873605864933057933350	["ModularForm/GL2/Q/holomorphic/2592/2/i/r/865/1"]
"2-2592-9.7-c1-0-16"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.027777777777777783	0	0.69409442198933225278803968401	["ModularForm/GL2/Q/holomorphic/2592/2/i/bg/865/2"]
"2-2592-9.7-c1-0-17"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2222222222222222	0	0.75564472798585506309834548674	["ModularForm/GL2/Q/holomorphic/2592/2/i/ba/865/2"]
"2-2592-9.7-c1-0-18"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.027777777777777783	0	0.795594916765003107919790976853	["ModularForm/GL2/Q/holomorphic/2592/2/i/bh/865/2"]
"2-2592-9.7-c1-0-19"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05555555555555555	0	0.820894858939716181770140725296	["ModularForm/GL2/Q/holomorphic/2592/2/i/p/865/1"]
"2-2592-9.7-c1-0-2"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4444444444444444	0	0.17816529173292805274193689836	["ModularForm/GL2/Q/holomorphic/2592/2/i/bc/865/2"]
"2-2592-9.7-c1-0-20"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11111111111111113	0	0.863385762978565064364809168957	["ModularForm/GL2/Q/holomorphic/2592/2/i/a/865/1"]
"2-2592-9.7-c1-0-21"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2222222222222222	0	0.867232148928527185356323545669	["ModularForm/GL2/Q/holomorphic/2592/2/i/be/865/2"]
"2-2592-9.7-c1-0-22"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11111111111111113	0	0.882638062411890367161897780691	["ModularForm/GL2/Q/holomorphic/2592/2/i/b/865/1"]
"2-2592-9.7-c1-0-23"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05555555555555555	0	0.889055183230549441424349587698	["ModularForm/GL2/Q/holomorphic/2592/2/i/m/865/1"]
"2-2592-9.7-c1-0-24"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.027777777777777783	0	0.892713042898072880487117797722	["ModularForm/GL2/Q/holomorphic/2592/2/i/y/865/2"]
"2-2592-9.7-c1-0-25"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.027777777777777783	0	0.911550917391254516397338482955	["ModularForm/GL2/Q/holomorphic/2592/2/i/bf/865/1"]
"2-2592-9.7-c1-0-26"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05555555555555555	0	1.01041727365449291567429926171	["ModularForm/GL2/Q/holomorphic/2592/2/i/bb/865/2"]
"2-2592-9.7-c1-0-27"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2777777777777778	0	1.01838773833009563796825520177	["ModularForm/GL2/Q/holomorphic/2592/2/i/c/865/1"]
"2-2592-9.7-c1-0-28"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2777777777777778	0	1.02721855768322341959256142173	["ModularForm/GL2/Q/holomorphic/2592/2/i/z/865/1"]
"2-2592-9.7-c1-0-29"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11111111111111113	0	1.16144321176864410002697463006	["ModularForm/GL2/Q/holomorphic/2592/2/i/t/865/1"]
"2-2592-9.7-c1-0-3"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.47222222222222227	0	0.21473210720472761115649899956	["ModularForm/GL2/Q/holomorphic/2592/2/i/bf/865/2"]
"2-2592-9.7-c1-0-30"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.027777777777777783	0	1.17104853430639920076666067478	["ModularForm/GL2/Q/holomorphic/2592/2/i/bh/865/4"]
"2-2592-9.7-c1-0-31"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.027777777777777783	0	1.19878492507477652118408339795	["ModularForm/GL2/Q/holomorphic/2592/2/i/bg/865/4"]
"2-2592-9.7-c1-0-32"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2777777777777778	0	1.22992936535524552514085026456	["ModularForm/GL2/Q/holomorphic/2592/2/i/bd/865/1"]
"2-2592-9.7-c1-0-33"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2777777777777778	0	1.30170355327052187319400668430	["ModularForm/GL2/Q/holomorphic/2592/2/i/f/865/1"]
"2-2592-9.7-c1-0-34"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4444444444444444	1	1.31603265489514064208339017567	["ModularForm/GL2/Q/holomorphic/2592/2/i/i/865/1"]
"2-2592-9.7-c1-0-35"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11111111111111113	0	1.32433605939148058526627400312	["ModularForm/GL2/Q/holomorphic/2592/2/i/w/865/1"]
"2-2592-9.7-c1-0-36"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2777777777777778	0	1.35091943175233921764231740144	["ModularForm/GL2/Q/holomorphic/2592/2/i/k/865/1"]
"2-2592-9.7-c1-0-37"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2777777777777778	0	1.37365606148837335769490840013	["ModularForm/GL2/Q/holomorphic/2592/2/i/o/865/1"]
"2-2592-9.7-c1-0-38"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2777777777777778	0	1.38136835743757724794755140731	["ModularForm/GL2/Q/holomorphic/2592/2/i/s/865/1"]
"2-2592-9.7-c1-0-39"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2777777777777778	0	1.38565204603463967075572696870	["ModularForm/GL2/Q/holomorphic/2592/2/i/g/865/1"]
"2-2592-9.7-c1-0-4"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.47222222222222227	0	0.21837843637915230441185237975	["ModularForm/GL2/Q/holomorphic/2592/2/i/bg/865/3"]
"2-2592-9.7-c1-0-40"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2777777777777778	0	1.43020052879659326360411529958	["ModularForm/GL2/Q/holomorphic/2592/2/i/bd/865/2"]
"2-2592-9.7-c1-0-41"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2777777777777778	0	1.53009503848404070202500526425	["ModularForm/GL2/Q/holomorphic/2592/2/i/z/865/2"]
"2-2592-9.7-c1-0-42"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4444444444444444	0	1.68318283003199357496676854302	["ModularForm/GL2/Q/holomorphic/2592/2/i/bc/865/1"]
"2-2592-9.7-c1-0-43"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.47222222222222227	0	1.69080113765547776762813704002	["ModularForm/GL2/Q/holomorphic/2592/2/i/y/865/1"]
"2-2592-9.7-c1-0-44"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4444444444444444	0	1.75698597975476198504091946700	["ModularForm/GL2/Q/holomorphic/2592/2/i/l/865/1"]
"2-2592-9.7-c1-0-45"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.47222222222222227	0	1.87024338168853367033371422859	["ModularForm/GL2/Q/holomorphic/2592/2/i/bh/865/1"]
"2-2592-9.7-c1-0-46"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3888888888888889	1	1.87434943159650414500715140578	["ModularForm/GL2/Q/holomorphic/2592/2/i/e/865/1"]
"2-2592-9.7-c1-0-47"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3888888888888889	1	1.92578464284909834771248956834	["ModularForm/GL2/Q/holomorphic/2592/2/i/h/865/1"]
"2-2592-9.7-c1-0-5"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2222222222222222	0	0.34699581546293214851588032655	["ModularForm/GL2/Q/holomorphic/2592/2/i/be/865/1"]
"2-2592-9.7-c1-0-6"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2222222222222222	0	0.36470484389903109025466912874	["ModularForm/GL2/Q/holomorphic/2592/2/i/d/865/1"]
"2-2592-9.7-c1-0-7"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2222222222222222	0	0.44604299955623282924723433910	["ModularForm/GL2/Q/holomorphic/2592/2/i/j/865/1"]
"2-2592-9.7-c1-0-8"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05555555555555555	0	0.47050646583233183624933664408	["ModularForm/GL2/Q/holomorphic/2592/2/i/bb/865/1"]
"2-2592-9.7-c1-0-9"	4.549420205247685	20.697224203915887	2	2592	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.47222222222222227	0	0.50053411384022147267961610989	["ModularForm/GL2/Q/holomorphic/2592/2/i/bh/865/3"]


# 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).