# lfunc_search downloaded from the LMFDB on 14 April 2026.
# Search link: https://www.lmfdb.org/L/2/140/7.4
# Query "{'degree': 2, 'conductor': 140}" returned 5582 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.



"2-140-140.39-c0-0-0"	0.2643276409470268	0.06986910176862034	2	140	"140.39"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.23991352347302694	0	2.07304643702320871970159871316	["ModularForm/GL2/Q/holomorphic/140/1/p/b/39/1", "ArtinRepresentation/2.140.12t18.a.b"]
"2-140-140.39-c0-0-1"	0.2643276409470268	0.06986910176862034	2	140	"140.39"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.26008647652697303	0	3.43782950479146480647989201129	["ModularForm/GL2/Q/holomorphic/140/1/p/a/39/1", "ArtinRepresentation/2.140.6t5.a.b"]
"2-140-140.79-c0-0-0"	0.2643276409470268	0.06986910176862034	2	140	"140.79"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.26008647652697303	0	1.84798733176887999444039248112	["ModularForm/GL2/Q/holomorphic/140/1/p/a/79/1", "ArtinRepresentation/2.140.6t5.a.a"]
"2-140-140.79-c0-0-1"	0.2643276409470268	0.06986910176862034	2	140	"140.79"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.23991352347302694	0	3.98412937626303021390155283110	["ModularForm/GL2/Q/holomorphic/140/1/p/b/79/1", "ArtinRepresentation/2.140.12t18.a.a"]
"2-140-35.34-c0-0-0"	0.2643276409470268	0.06986910176862034	2	140	"35.34"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	2.27790387327828597147359808295	["ModularForm/GL2/Q/holomorphic/140/1/h/a/69/1", "ModularForm/GL2/Q/holomorphic/140/1/h/a", "ArtinRepresentation/2.140.3t2.a.a", "ArtinRepresentation/2.140.3t2.a"]
"2-140-35.34-c0-0-1"	0.2643276409470268	0.06986910176862034	2	140	"35.34"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	2.94378740484957857899261155773	["ModularForm/GL2/Q/holomorphic/140/1/h/b/69/1", "ModularForm/GL2/Q/holomorphic/140/1/h/b", "ArtinRepresentation/2.140.6t3.b.a", "ArtinRepresentation/2.140.6t3.b"]
"2-140-1.1-c1-0-0"	1.0573105637881075	1.1179056282979258	2	140	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	2.14587146010097196258543648767	["EllipticCurve/Q/140/a", "ModularForm/GL2/Q/holomorphic/140/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/140/2/a/a"]
"2-140-1.1-c1-0-1"	1.0573105637881075	1.1179056282979258	2	140	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	2.51163217316890307126702952381	["EllipticCurve/Q/140/b", "ModularForm/GL2/Q/holomorphic/140/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/140/2/a/b"]
"2-140-140.107-c1-0-0"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.40368334741317113	0	0.43716217427513491148188221340	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/5"]
"2-140-140.107-c1-0-1"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3365885547678245	0	0.60071247949818989118635114694	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/1"]
"2-140-140.107-c1-0-10"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1500738797564373	0	1.84338477840446813923839826609	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/18"]
"2-140-140.107-c1-0-11"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.005372859140170569	0	2.19986676452856643319575936019	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/7"]
"2-140-140.107-c1-0-12"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.20301761906041862	0	2.52599602846283328643248464874	["ModularForm/GL2/Q/holomorphic/140/2/w/a/107/2"]
"2-140-140.107-c1-0-13"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.012332300471936735	0	2.56445638530701183312832970649	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/15"]
"2-140-140.107-c1-0-14"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1627643648394402	0	2.64732285800970374544578323199	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/14"]
"2-140-140.107-c1-0-15"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.031683238603502	0	2.91626448318781514947800572574	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/17"]
"2-140-140.107-c1-0-16"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3868188926586767	0	2.92873295805024079938535832826	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/2"]
"2-140-140.107-c1-0-17"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.35073529666600545	0	3.31108299589409512519999036216	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/9"]
"2-140-140.107-c1-0-18"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.20356038870648713	0	3.38699846775626402746226689821	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/16"]
"2-140-140.107-c1-0-19"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4205708675230891	0	3.69744815068364833388565949659	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/10"]
"2-140-140.107-c1-0-2"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.14940016172094128	0	1.14385388712366063806434872252	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/11"]
"2-140-140.107-c1-0-3"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2969823809395814	0	1.23768073943128594321233979278	["ModularForm/GL2/Q/holomorphic/140/2/w/a/107/1"]
"2-140-140.107-c1-0-4"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2879055637910582	0	1.34826230270172419826486134523	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/8"]
"2-140-140.107-c1-0-5"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3170909236419926	0	1.38752120652624158726527407363	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/13"]
"2-140-140.107-c1-0-6"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.09942591380403389	0	1.49040401736910101681167573581	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/4"]
"2-140-140.107-c1-0-7"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3461839837222913	0	1.58560624449428496782729827499	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/12"]
"2-140-140.107-c1-0-8"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.061936420584840994	0	1.59376519658918880339279193464	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/6"]
"2-140-140.107-c1-0-9"	1.0573105637881075	1.1179056282979258	2	140	"140.107"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.05991769868344926	0	1.62735153914142671557160614790	["ModularForm/GL2/Q/holomorphic/140/2/w/b/107/3"]
"2-140-140.123-c1-0-0"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4205708675230891	0	1.02184339697857863559871320338	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/10"]
"2-140-140.123-c1-0-1"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3868188926586767	0	1.03470017744885340154249762695	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/2"]
"2-140-140.123-c1-0-10"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.031683238603502	0	2.23800330495145838765323398138	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/17"]
"2-140-140.123-c1-0-11"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.012332300471936735	0	2.34414087006765527717485909203	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/15"]
"2-140-140.123-c1-0-12"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2969823809395814	0	2.39170931242141706673947769068	["ModularForm/GL2/Q/holomorphic/140/2/w/a/123/1"]
"2-140-140.123-c1-0-13"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3365885547678245	0	2.63969082676195790057150123532	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/1"]
"2-140-140.123-c1-0-14"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2879055637910582	0	2.72104953339073150533551713316	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/8"]
"2-140-140.123-c1-0-15"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.14940016172094128	0	2.94114444187696286511911107527	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/11"]
"2-140-140.123-c1-0-16"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1500738797564373	0	3.17895571492141533924426507501	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/18"]
"2-140-140.123-c1-0-17"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3170909236419926	0	3.34609269282438897258670000837	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/13"]
"2-140-140.123-c1-0-18"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3461839837222913	0	3.63626148797905064348225983888	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/12"]
"2-140-140.123-c1-0-19"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.40368334741317113	0	3.85514707231834011944279388509	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/5"]
"2-140-140.123-c1-0-2"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.20301761906041862	0	1.36060225857218438043513669614	["ModularForm/GL2/Q/holomorphic/140/2/w/a/123/2"]
"2-140-140.123-c1-0-3"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.005372859140170569	0	1.40957235883127094120216417481	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/7"]
"2-140-140.123-c1-0-4"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05991769868344926	0	1.64053576479233959535615754039	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/3"]
"2-140-140.123-c1-0-5"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.09942591380403389	0	1.75140685284424110077742034208	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/4"]
"2-140-140.123-c1-0-6"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.35073529666600545	0	1.75766320941467999695530518432	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/9"]
"2-140-140.123-c1-0-7"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1627643648394402	0	1.77763940322548329785701910621	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/14"]
"2-140-140.123-c1-0-8"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.061936420584840994	0	1.86326379968310992905558198682	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/6"]
"2-140-140.123-c1-0-9"	1.0573105637881075	1.1179056282979258	2	140	"140.123"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.20356038870648713	0	2.06187929405194383416754488374	["ModularForm/GL2/Q/holomorphic/140/2/w/b/123/16"]
"2-140-140.139-c1-0-0"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.23229285697432167	0	0.72683490191407248632891211873	["ModularForm/GL2/Q/holomorphic/140/2/c/b/139/6"]
"2-140-140.139-c1-0-1"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.351942292223583	0	1.11334332249999428311661756511	["ModularForm/GL2/Q/holomorphic/140/2/c/a/139/2"]
"2-140-140.139-c1-0-10"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.06789801830316045	0	2.08474065639691169435157347492	["ModularForm/GL2/Q/holomorphic/140/2/c/b/139/11"]
"2-140-140.139-c1-0-11"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.148057707776417	0	2.18875343104242022248358488470	["ModularForm/GL2/Q/holomorphic/140/2/c/a/139/4"]
"2-140-140.139-c1-0-12"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.09781430431378342	0	2.21142003745176111209483557497	["ModularForm/GL2/Q/holomorphic/140/2/c/b/139/15"]
"2-140-140.139-c1-0-13"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.09781430431378342	0	2.48131089780307161443287760164	["ModularForm/GL2/Q/holomorphic/140/2/c/b/139/14"]
"2-140-140.139-c1-0-14"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.351942292223583	0	2.89485568630563151867614750405	["ModularForm/GL2/Q/holomorphic/140/2/c/a/139/1"]
"2-140-140.139-c1-0-15"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.23229285697432167	0	2.98181506426816068131242571592	["ModularForm/GL2/Q/holomorphic/140/2/c/b/139/7"]
"2-140-140.139-c1-0-16"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.148057707776417	0	3.25283978547436296107913775342	["ModularForm/GL2/Q/holomorphic/140/2/c/a/139/3"]
"2-140-140.139-c1-0-17"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4174650678430916	0	3.28411836707665735112511349210	["ModularForm/GL2/Q/holomorphic/140/2/c/b/139/5"]
"2-140-140.139-c1-0-18"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.24757222913119661	0	3.45910536814225071726263898508	["ModularForm/GL2/Q/holomorphic/140/2/c/b/139/13"]
"2-140-140.139-c1-0-19"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.41814009348574727	0	3.74402375277462123785425278531	["ModularForm/GL2/Q/holomorphic/140/2/c/b/139/9"]
"2-140-140.139-c1-0-2"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2027371707495442	0	1.17360308605400830749127709577	["ModularForm/GL2/Q/holomorphic/140/2/c/b/139/3"]
"2-140-140.139-c1-0-3"	1.0573105637881075	1.1179056282979258	2	140	"140.139"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.41814009348574727	0	1.18660354279074811794868915584	["ModularForm/GL2/Q/holomorphic/140/2/c/b/139/12"]
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"2-140-7.4-c15-0-29"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	0.1780168501316161	0	0.848694451828775303432919629568	["ModularForm/GL2/Q/holomorphic/140/16/i/b/81/8"]
"2-140-7.4-c15-0-3"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	-0.1358573269251092	0	0.14044462949094711735584487843	["ModularForm/GL2/Q/holomorphic/140/16/i/a/81/19"]
"2-140-7.4-c15-0-30"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	0.16399155708389554	0	0.946762430011097658765406345307	["ModularForm/GL2/Q/holomorphic/140/16/i/a/81/2"]
"2-140-7.4-c15-0-31"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	0.4466340467820133	0	0.984020424985039033184581513016	["ModularForm/GL2/Q/holomorphic/140/16/i/b/81/11"]
"2-140-7.4-c15-0-32"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	0.32180392236729105	0	1.01639111862489427341837871394	["ModularForm/GL2/Q/holomorphic/140/16/i/b/81/7"]
"2-140-7.4-c15-0-33"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	0.30863174388916775	0	1.02869873667215586886926213831	["ModularForm/GL2/Q/holomorphic/140/16/i/a/81/17"]
"2-140-7.4-c15-0-34"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	0.2592668303263683	0	1.17301288845198364693499496815	["ModularForm/GL2/Q/holomorphic/140/16/i/a/81/8"]
"2-140-7.4-c15-0-35"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	0.28428209060573345	0	1.24943311050386751831239164406	["ModularForm/GL2/Q/holomorphic/140/16/i/a/81/14"]
"2-140-7.4-c15-0-36"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	-0.4983719322338143	0	1.25700104221502496509601398514	["ModularForm/GL2/Q/holomorphic/140/16/i/b/81/17"]
"2-140-7.4-c15-0-37"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	0.49370795085118063	0	1.46001726347501658287979964472	["ModularForm/GL2/Q/holomorphic/140/16/i/a/81/16"]
"2-140-7.4-c15-0-38"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	-0.2956723803245831	0	1.64790643267751182116021491174	["ModularForm/GL2/Q/holomorphic/140/16/i/b/81/15"]
"2-140-7.4-c15-0-39"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	-0.29719249571150047	0	1.90193629277053298313908411873	["ModularForm/GL2/Q/holomorphic/140/16/i/b/81/21"]
"2-140-7.4-c15-0-4"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	-0.4016427442934824	0	0.15269216531359763092903756734	["ModularForm/GL2/Q/holomorphic/140/16/i/a/81/15"]
"2-140-7.4-c15-0-5"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	0.3841669212939634	0	0.17383148982344114892040611684	["ModularForm/GL2/Q/holomorphic/140/16/i/b/81/12"]
"2-140-7.4-c15-0-6"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	-0.4532483107005181	0	0.17909105782774157256532663153	["ModularForm/GL2/Q/holomorphic/140/16/i/b/81/4"]
"2-140-7.4-c15-0-7"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	0.4748160008596651	0	0.20846281729441024219383717518	["ModularForm/GL2/Q/holomorphic/140/16/i/a/81/7"]
"2-140-7.4-c15-0-8"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	0.4714653384452144	0	0.23240858772374827875582725718	["ModularForm/GL2/Q/holomorphic/140/16/i/a/81/9"]
"2-140-7.4-c15-0-9"	14.134033647189634	199.77090713988872	2	140	"7.4"	[]	[[7.5, 0.0]]	15	true	true	false	false	-0.3220152591808338	0	0.23881059209298094225625469631	["ModularForm/GL2/Q/holomorphic/140/16/i/b/81/13"]


# 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).