# lfunc_search downloaded from the LMFDB on 30 April 2026.
# Search link: https://www.lmfdb.org/L/2/1152
# Query "{'degree': 2, 'conductor': 1152}" returned 1563 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.



"2-1152-24.5-c0-0-0"	0.7582367008746139	0.5749228945532188	2	1152	"24.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.22295663800765184	0	0.64291267251029234845886976374	["ModularForm/GL2/Q/holomorphic/1152/1/h/a/449/2"]
"2-1152-24.5-c0-0-1"	0.7582367008746139	0.5749228945532188	2	1152	"24.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.02704336199234818	0	1.47995591810136245514367711367	["ModularForm/GL2/Q/holomorphic/1152/1/h/a/449/4"]
"2-1152-24.5-c0-0-2"	0.7582367008746139	0.5749228945532188	2	1152	"24.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.22295663800765184	0	1.66556699678536343319573575223	["ModularForm/GL2/Q/holomorphic/1152/1/h/a/449/1"]
"2-1152-24.5-c0-0-3"	0.7582367008746139	0.5749228945532188	2	1152	"24.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.02704336199234818	0	1.69588644847303352507954150731	["ModularForm/GL2/Q/holomorphic/1152/1/h/a/449/3"]
"2-1152-72.29-c0-0-0"	0.7582367008746139	0.5749228945532188	2	1152	"72.29"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.3055555555555556	0	0.71063606592494478887874750811	["ModularForm/GL2/Q/holomorphic/1152/1/n/a/65/1"]
"2-1152-72.29-c0-0-1"	0.7582367008746139	0.5749228945532188	2	1152	"72.29"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.19444444444444448	0	1.89784221832519258796381481516	["ModularForm/GL2/Q/holomorphic/1152/1/n/b/65/1"]
"2-1152-72.43-c0-0-0"	0.7582367008746139	0.5749228945532188	2	1152	"72.43"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.05555555555555555	0	0.906721785050873677663317096060	["ModularForm/GL2/Q/holomorphic/1152/1/t/a/1087/1"]
"2-1152-72.43-c0-0-1"	0.7582367008746139	0.5749228945532188	2	1152	"72.43"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.05555555555555555	0	1.60322794885275983020278715933	["ModularForm/GL2/Q/holomorphic/1152/1/t/a/1087/2"]
"2-1152-72.5-c0-0-0"	0.7582367008746139	0.5749228945532188	2	1152	"72.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.19444444444444448	0	1.16313552105860819673581777060	["ModularForm/GL2/Q/holomorphic/1152/1/n/b/833/1"]
"2-1152-72.5-c0-0-1"	0.7582367008746139	0.5749228945532188	2	1152	"72.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.3055555555555556	0	1.82502763960839879152377636775	["ModularForm/GL2/Q/holomorphic/1152/1/n/a/833/1"]
"2-1152-72.67-c0-0-0"	0.7582367008746139	0.5749228945532188	2	1152	"72.67"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.05555555555555555	0	1.36436868098597528508970491646	["ModularForm/GL2/Q/holomorphic/1152/1/t/a/319/1"]
"2-1152-72.67-c0-0-1"	0.7582367008746139	0.5749228945532188	2	1152	"72.67"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.05555555555555555	0	1.63722745860050185923826561579	["ModularForm/GL2/Q/holomorphic/1152/1/t/a/319/2"]
"2-1152-8.3-c0-0-0"	0.7582367008746139	0.5749228945532188	2	1152	"8.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.25	0	0.918015980458153970151122476360	["ModularForm/GL2/Q/holomorphic/1152/1/b/b/703/2", "ArtinRepresentation/2.1152.8t11.b.a"]
"2-1152-8.3-c0-0-1"	0.7582367008746139	0.5749228945532188	2	1152	"8.3"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	1.34169372574896948271225308667	["ModularForm/GL2/Q/holomorphic/1152/1/b/a/703/1", "ModularForm/GL2/Q/holomorphic/1152/1/b/a", "ArtinRepresentation/2.1152.4t3.c.a", "ArtinRepresentation/2.1152.4t3.c"]
"2-1152-8.3-c0-0-2"	0.7582367008746139	0.5749228945532188	2	1152	"8.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.25	0	2.05433328193680623125449754459	["ModularForm/GL2/Q/holomorphic/1152/1/b/b/703/1", "ArtinRepresentation/2.1152.8t11.b.b"]
"2-1152-1.1-c1-0-0"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.65344977115887373240163738777	["EllipticCurve/Q/1152/a", "ModularForm/GL2/Q/holomorphic/1152/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/a"]
"2-1152-1.1-c1-0-1"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.795101455562395073664105794433	["EllipticCurve/Q/1152/c", "ModularForm/GL2/Q/holomorphic/1152/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/c"]
"2-1152-1.1-c1-0-10"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.36625703357770376353073884127	["EllipticCurve/Q/1152/t", "ModularForm/GL2/Q/holomorphic/1152/2/a/t/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/t"]
"2-1152-1.1-c1-0-11"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.70795903707382777058669654679	["EllipticCurve/Q/1152/b", "ModularForm/GL2/Q/holomorphic/1152/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/b"]
"2-1152-1.1-c1-0-12"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.74260187134927495442557965172	["EllipticCurve/Q/1152/e", "ModularForm/GL2/Q/holomorphic/1152/2/a/e/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/e"]
"2-1152-1.1-c1-0-13"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.82243002848641170832748081144	["EllipticCurve/Q/1152/f", "ModularForm/GL2/Q/holomorphic/1152/2/a/f/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/f"]
"2-1152-1.1-c1-0-14"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.82975631589070695133940004845	["EllipticCurve/Q/1152/g", "ModularForm/GL2/Q/holomorphic/1152/2/a/g/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/g"]
"2-1152-1.1-c1-0-15"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.86962407001750988737926530376	["EllipticCurve/Q/1152/i", "ModularForm/GL2/Q/holomorphic/1152/2/a/i/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/i"]
"2-1152-1.1-c1-0-16"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.89290593869789230240007927288	["EllipticCurve/Q/1152/j", "ModularForm/GL2/Q/holomorphic/1152/2/a/j/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/j"]
"2-1152-1.1-c1-0-17"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.98277685475006180754048515240	["EllipticCurve/Q/1152/m", "ModularForm/GL2/Q/holomorphic/1152/2/a/m/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/m"]
"2-1152-1.1-c1-0-18"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.02071693225675944817521065685	["EllipticCurve/Q/1152/k", "ModularForm/GL2/Q/holomorphic/1152/2/a/k/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/k"]
"2-1152-1.1-c1-0-19"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.07793680595226141750788729163	["EllipticCurve/Q/1152/n", "ModularForm/GL2/Q/holomorphic/1152/2/a/n/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/n"]
"2-1152-1.1-c1-0-2"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.861313696819797789656347648853	["EllipticCurve/Q/1152/d", "ModularForm/GL2/Q/holomorphic/1152/2/a/d/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/d"]
"2-1152-1.1-c1-0-3"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.02724387350145696940295704376	["EllipticCurve/Q/1152/h", "ModularForm/GL2/Q/holomorphic/1152/2/a/h/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/h"]
"2-1152-1.1-c1-0-4"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.06529864489425453121277159914	["EllipticCurve/Q/1152/o", "ModularForm/GL2/Q/holomorphic/1152/2/a/o/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/o"]
"2-1152-1.1-c1-0-5"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.16901968292393942798169217496	["EllipticCurve/Q/1152/l", "ModularForm/GL2/Q/holomorphic/1152/2/a/l/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/l"]
"2-1152-1.1-c1-0-6"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.27289759970492945430986166195	["EllipticCurve/Q/1152/p", "ModularForm/GL2/Q/holomorphic/1152/2/a/p/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/p"]
"2-1152-1.1-c1-0-7"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.28088417651653847704023663777	["EllipticCurve/Q/1152/s", "ModularForm/GL2/Q/holomorphic/1152/2/a/s/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/s"]
"2-1152-1.1-c1-0-8"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.31006766181093226223763545704	["EllipticCurve/Q/1152/q", "ModularForm/GL2/Q/holomorphic/1152/2/a/q/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/q"]
"2-1152-1.1-c1-0-9"	3.032946803498456	9.198766312851504	2	1152	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.34910975935301153966920068234	["EllipticCurve/Q/1152/r", "ModularForm/GL2/Q/holomorphic/1152/2/a/r/1/1", "ModularForm/GL2/Q/holomorphic/1152/2/a/r"]
"2-1152-12.11-c1-0-0"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4020433619923482	0	0.27176694672128188998320916940	["ModularForm/GL2/Q/holomorphic/1152/2/c/b/1151/4"]
"2-1152-12.11-c1-0-1"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3479566380076518	0	0.29286805446619933560333623045	["ModularForm/GL2/Q/holomorphic/1152/2/c/a/1151/2"]
"2-1152-12.11-c1-0-10"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1520433619923482	0	1.33243344650193482672169034751	["ModularForm/GL2/Q/holomorphic/1152/2/c/d/1151/2"]
"2-1152-12.11-c1-0-11"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1520433619923482	0	1.38847680784358031150558796350	["ModularForm/GL2/Q/holomorphic/1152/2/c/d/1151/4"]
"2-1152-12.11-c1-0-12"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3479566380076518	0	1.67208705540559493262913110002	["ModularForm/GL2/Q/holomorphic/1152/2/c/a/1151/3"]
"2-1152-12.11-c1-0-13"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4020433619923482	0	1.74409371386106661551645856375	["ModularForm/GL2/Q/holomorphic/1152/2/c/b/1151/1"]
"2-1152-12.11-c1-0-14"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3479566380076518	0	1.91805364102669268549813230830	["ModularForm/GL2/Q/holomorphic/1152/2/c/a/1151/1"]
"2-1152-12.11-c1-0-15"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4020433619923482	0	2.12154522017822879867372762996	["ModularForm/GL2/Q/holomorphic/1152/2/c/c/1151/1"]
"2-1152-12.11-c1-0-2"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4020433619923482	0	0.62423180138408618841870644975	["ModularForm/GL2/Q/holomorphic/1152/2/c/c/1151/4"]
"2-1152-12.11-c1-0-3"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1520433619923482	0	0.64734792517724004595993496822	["ModularForm/GL2/Q/holomorphic/1152/2/c/d/1151/1"]
"2-1152-12.11-c1-0-4"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3479566380076518	0	0.75882814927874498073317092590	["ModularForm/GL2/Q/holomorphic/1152/2/c/a/1151/4"]
"2-1152-12.11-c1-0-5"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1520433619923482	0	0.77942883312104095853371183816	["ModularForm/GL2/Q/holomorphic/1152/2/c/d/1151/3"]
"2-1152-12.11-c1-0-6"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.09795663800765181	0	0.830953813554536544138076068711	["ModularForm/GL2/Q/holomorphic/1152/2/c/c/1151/3"]
"2-1152-12.11-c1-0-7"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.09795663800765181	0	0.914404346678317626253285303243	["ModularForm/GL2/Q/holomorphic/1152/2/c/b/1151/3"]
"2-1152-12.11-c1-0-8"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.09795663800765181	0	1.19972866375679529908112501987	["ModularForm/GL2/Q/holomorphic/1152/2/c/c/1151/2"]
"2-1152-12.11-c1-0-9"	3.032946803498456	9.198766312851504	2	1152	"12.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.09795663800765181	0	1.24760914673966060729512368004	["ModularForm/GL2/Q/holomorphic/1152/2/c/b/1151/2"]
"2-1152-16.13-c1-0-0"	3.032946803498456	9.198766312851504	2	1152	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3866959140529853	0	0.07195221270101893830270542546	["ModularForm/GL2/Q/holomorphic/1152/2/k/f/289/1"]
"2-1152-16.13-c1-0-1"	3.032946803498456	9.198766312851504	2	1152	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.47124331797967306	0	0.084090252463627193104924800049	["ModularForm/GL2/Q/holomorphic/1152/2/k/d/289/3"]
"2-1152-16.13-c1-0-10"	3.032946803498456	9.198766312851504	2	1152	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.02875668202032699	0	1.10838198232179727568753270205	["ModularForm/GL2/Q/holomorphic/1152/2/k/d/289/2"]
"2-1152-16.13-c1-0-11"	3.032946803498456	9.198766312851504	2	1152	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1366959140529853	0	1.14346203360746750950481671300	["ModularForm/GL2/Q/holomorphic/1152/2/k/c/289/1"]
"2-1152-16.13-c1-0-12"	3.032946803498456	9.198766312851504	2	1152	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.043610715013776453	0	1.20334648314940526250947193952	["ModularForm/GL2/Q/holomorphic/1152/2/k/c/289/4"]
"2-1152-16.13-c1-0-13"	3.032946803498456	9.198766312851504	2	1152	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11330408594701469	0	1.38580784535627046025192429030	["ModularForm/GL2/Q/holomorphic/1152/2/k/f/289/3"]
"2-1152-16.13-c1-0-14"	3.032946803498456	9.198766312851504	2	1152	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.22124331797967303	0	1.68223547966626059777731504254	["ModularForm/GL2/Q/holomorphic/1152/2/k/d/289/4"]
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"2-1152-8.3-c4-0-41"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.125	0	0.72152106220129006920437117131	["ModularForm/GL2/Q/holomorphic/1152/5/b/l/703/3"]
"2-1152-8.3-c4-0-42"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.125	0	0.75596527776336247707957433022	["ModularForm/GL2/Q/holomorphic/1152/5/b/m/703/11"]
"2-1152-8.3-c4-0-43"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.125	0	0.76654670927743281215123544083	["ModularForm/GL2/Q/holomorphic/1152/5/b/n/703/14"]
"2-1152-8.3-c4-0-44"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.125	0	0.77060597983903006814827601465	["ModularForm/GL2/Q/holomorphic/1152/5/b/n/703/8"]
"2-1152-8.3-c4-0-45"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	true	0.0	0	0.77307437951315260817049598281	["ModularForm/GL2/Q/holomorphic/1152/5/b/a/703/2"]
"2-1152-8.3-c4-0-46"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.125	0	0.793294811691757624178113900700	["ModularForm/GL2/Q/holomorphic/1152/5/b/m/703/13"]
"2-1152-8.3-c4-0-47"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.0	0	0.801277789202179417450327163821	["ModularForm/GL2/Q/holomorphic/1152/5/b/j/703/3"]
"2-1152-8.3-c4-0-48"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.25	0	0.843389476105316871889506338259	["ModularForm/GL2/Q/holomorphic/1152/5/b/k/703/7"]
"2-1152-8.3-c4-0-49"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.0	0	0.862731231821676076865272957900	["ModularForm/GL2/Q/holomorphic/1152/5/b/j/703/4"]
"2-1152-8.3-c4-0-5"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.25	0	0.12113231724545790396343909530	["ModularForm/GL2/Q/holomorphic/1152/5/b/i/703/1"]
"2-1152-8.3-c4-0-50"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.125	0	0.863323227264423437561303321789	["ModularForm/GL2/Q/holomorphic/1152/5/b/m/703/7"]
"2-1152-8.3-c4-0-51"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.125	0	0.877090266435891891804507542477	["ModularForm/GL2/Q/holomorphic/1152/5/b/n/703/7"]
"2-1152-8.3-c4-0-52"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.25	0	0.891016625075144695346056372853	["ModularForm/GL2/Q/holomorphic/1152/5/b/b/703/1"]
"2-1152-8.3-c4-0-53"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.25	0	0.898456277846653474019292119659	["ModularForm/GL2/Q/holomorphic/1152/5/b/k/703/4"]
"2-1152-8.3-c4-0-54"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.25	0	0.899375656574012555344506807654	["ModularForm/GL2/Q/holomorphic/1152/5/b/i/703/4"]
"2-1152-8.3-c4-0-55"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.125	0	0.902390188880702187810529080641	["ModularForm/GL2/Q/holomorphic/1152/5/b/n/703/9"]
"2-1152-8.3-c4-0-56"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.125	0	0.976679094792394038109477265916	["ModularForm/GL2/Q/holomorphic/1152/5/b/m/703/4"]
"2-1152-8.3-c4-0-57"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.125	0	1.00085202324442886089364783042	["ModularForm/GL2/Q/holomorphic/1152/5/b/l/703/8"]
"2-1152-8.3-c4-0-58"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.25	0	1.00783873622038003180693953130	["ModularForm/GL2/Q/holomorphic/1152/5/b/k/703/3"]
"2-1152-8.3-c4-0-59"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.25	0	1.03122380763199872619876437937	["ModularForm/GL2/Q/holomorphic/1152/5/b/k/703/8"]
"2-1152-8.3-c4-0-6"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.375	0	0.14902721990414405963839343859	["ModularForm/GL2/Q/holomorphic/1152/5/b/l/703/4"]
"2-1152-8.3-c4-0-60"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.25	0	1.03391631352147966489412344065	["ModularForm/GL2/Q/holomorphic/1152/5/b/d/703/1"]
"2-1152-8.3-c4-0-61"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.0	0	1.06755717346053636301011323110	["ModularForm/GL2/Q/holomorphic/1152/5/b/h/703/4"]
"2-1152-8.3-c4-0-62"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.375	0	1.09924237826259834828727295800	["ModularForm/GL2/Q/holomorphic/1152/5/b/l/703/2"]
"2-1152-8.3-c4-0-63"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.375	0	1.11884657120821515458807065522	["ModularForm/GL2/Q/holomorphic/1152/5/b/n/703/6"]
"2-1152-8.3-c4-0-64"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.25	0	1.13533348100826526127121957511	["ModularForm/GL2/Q/holomorphic/1152/5/b/i/703/3"]
"2-1152-8.3-c4-0-65"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.375	0	1.17869355008245621737747352862	["ModularForm/GL2/Q/holomorphic/1152/5/b/l/703/5"]
"2-1152-8.3-c4-0-66"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.375	0	1.19062045565554262863144203323	["ModularForm/GL2/Q/holomorphic/1152/5/b/m/703/9"]
"2-1152-8.3-c4-0-67"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.25	0	1.19886194255219767465124236808	["ModularForm/GL2/Q/holomorphic/1152/5/b/g/703/3"]
"2-1152-8.3-c4-0-68"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.375	0	1.21970200866152641141479838817	["ModularForm/GL2/Q/holomorphic/1152/5/b/m/703/5"]
"2-1152-8.3-c4-0-69"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.5	0	1.23774209156394307270719871161	["ModularForm/GL2/Q/holomorphic/1152/5/b/f/703/2"]
"2-1152-8.3-c4-0-7"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.5	0	0.16340167187165227893247802036	["ModularForm/GL2/Q/holomorphic/1152/5/b/e/703/4"]
"2-1152-8.3-c4-0-70"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.375	0	1.27140808119334560964213246944	["ModularForm/GL2/Q/holomorphic/1152/5/b/n/703/1"]
"2-1152-8.3-c4-0-71"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.5	0	1.32479266077671511772195044568	["ModularForm/GL2/Q/holomorphic/1152/5/b/e/703/1"]
"2-1152-8.3-c4-0-72"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.5	0	1.45557761417758642427101661735	["ModularForm/GL2/Q/holomorphic/1152/5/b/c/703/1"]
"2-1152-8.3-c4-0-73"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.5	0	1.46911031922182331534834956634	["ModularForm/GL2/Q/holomorphic/1152/5/b/e/703/3"]
"2-1152-8.3-c4-0-74"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.5	0	1.50081814954096276108177439628	["ModularForm/GL2/Q/holomorphic/1152/5/b/f/703/1"]
"2-1152-8.3-c4-0-75"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.375	0	1.53544834848180481279135765387	["ModularForm/GL2/Q/holomorphic/1152/5/b/n/703/2"]
"2-1152-8.3-c4-0-76"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.375	0	1.64245500030644811178304524369	["ModularForm/GL2/Q/holomorphic/1152/5/b/n/703/5"]
"2-1152-8.3-c4-0-77"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.375	0	1.68545692157658499162633528658	["ModularForm/GL2/Q/holomorphic/1152/5/b/m/703/3"]
"2-1152-8.3-c4-0-78"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.375	0	1.76138677011686079896719702568	["ModularForm/GL2/Q/holomorphic/1152/5/b/m/703/1"]
"2-1152-8.3-c4-0-79"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.25	0	2.12343160604637611102546811650	["ModularForm/GL2/Q/holomorphic/1152/5/b/g/703/1"]
"2-1152-8.3-c4-0-8"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.5	0	0.16693581597358472653972015211	["ModularForm/GL2/Q/holomorphic/1152/5/b/e/703/2"]
"2-1152-8.3-c4-0-9"	10.912478979250714	119.0821974725887	2	1152	"8.3"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.125	0	0.21862105518154057825825327489	["ModularForm/GL2/Q/holomorphic/1152/5/b/n/703/3"]


# 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).