# lfunc_search downloaded from the LMFDB on 20 April 2026.
# Search link: https://www.lmfdb.org/L/2/405/135.113
# Query "{'degree': 2, 'conductor': 405}" returned 12996 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.



"2-405-45.14-c0-0-0"	0.44957905880541854	0.202121330116366	2	405	"45.14"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.19444444444444448	0	1.72241182277389574123742867895	["ModularForm/GL2/Q/holomorphic/405/1/h/b/134/1", "ArtinRepresentation/2.405.6t5.a.b"]
"2-405-45.14-c0-0-1"	0.44957905880541854	0.202121330116366	2	405	"45.14"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.3055555555555556	0	2.41658163365104649263169340771	["ModularForm/GL2/Q/holomorphic/405/1/h/a/134/1", "ArtinRepresentation/2.405.12t18.a.a"]
"2-405-45.29-c0-0-0"	0.44957905880541854	0.202121330116366	2	405	"45.29"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.3055555555555556	0	1.30758115796568570267697600701	["ModularForm/GL2/Q/holomorphic/405/1/h/a/269/1", "ArtinRepresentation/2.405.12t18.a.b"]
"2-405-45.29-c0-0-1"	0.44957905880541854	0.202121330116366	2	405	"45.29"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.19444444444444448	0	2.36470940730744213209832599340	["ModularForm/GL2/Q/holomorphic/405/1/h/b/269/1", "ArtinRepresentation/2.405.6t5.a.a"]
"2-405-1.1-c1-0-0"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.923154092891884846354495886643	["ModularForm/GL2/Q/holomorphic/405/2/a/h/1/1"]
"2-405-1.1-c1-0-1"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.954570366014384757362295281472	["ModularForm/GL2/Q/holomorphic/405/2/a/i/1/1"]
"2-405-1.1-c1-0-10"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.06014522909482997436709887093	["EllipticCurve/Q/405/b", "ModularForm/GL2/Q/holomorphic/405/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/405/2/a/b"]
"2-405-1.1-c1-0-11"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.22456788844258673958989510895	["ModularForm/GL2/Q/holomorphic/405/2/a/h/1/2"]
"2-405-1.1-c1-0-12"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.23768245130265216385360926189	["ModularForm/GL2/Q/holomorphic/405/2/a/j/1/3"]
"2-405-1.1-c1-0-13"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.30189805881882976209364768483	["EllipticCurve/Q/405/c", "ModularForm/GL2/Q/holomorphic/405/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/405/2/a/c"]
"2-405-1.1-c1-0-14"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.75549156342552231674726398882	["ModularForm/GL2/Q/holomorphic/405/2/a/g/1/2"]
"2-405-1.1-c1-0-15"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.80534791056945823123328757931	["EllipticCurve/Q/405/e", "ModularForm/GL2/Q/holomorphic/405/2/a/e/1/1", "ModularForm/GL2/Q/holomorphic/405/2/a/e"]
"2-405-1.1-c1-0-2"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.05768489668298083823781522462	["ModularForm/GL2/Q/holomorphic/405/2/a/i/1/2"]
"2-405-1.1-c1-0-3"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.21556430091835107025965573141	["ModularForm/GL2/Q/holomorphic/405/2/a/j/1/1"]
"2-405-1.1-c1-0-4"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.27645214139714047950709921081	["EllipticCurve/Q/405/d", "ModularForm/GL2/Q/holomorphic/405/2/a/d/1/1", "ModularForm/GL2/Q/holomorphic/405/2/a/d"]
"2-405-1.1-c1-0-5"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.38882093900943339040678353578	["ModularForm/GL2/Q/holomorphic/405/2/a/j/1/2"]
"2-405-1.1-c1-0-6"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.84657171814318698813806363337	["EllipticCurve/Q/405/a", "ModularForm/GL2/Q/holomorphic/405/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/405/2/a/a"]
"2-405-1.1-c1-0-7"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.89342420448833102084428967755	["ModularForm/GL2/Q/holomorphic/405/2/a/i/1/3"]
"2-405-1.1-c1-0-8"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.89799498723585767421033230965	["EllipticCurve/Q/405/f", "ModularForm/GL2/Q/holomorphic/405/2/a/f/1/1", "ModularForm/GL2/Q/holomorphic/405/2/a/f"]
"2-405-1.1-c1-0-9"	1.7983162352216746	3.233941281861857	2	405	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.94056688123354518976348832487	["ModularForm/GL2/Q/holomorphic/405/2/a/g/1/1"]
"2-405-135.113-c1-0-0"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.27947243166392616	0	0.14002109513411742260699057692	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/1"]
"2-405-135.113-c1-0-1"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.29489930089292715	0	0.50920318828066062126285147583	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/9"]
"2-405-135.113-c1-0-10"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.10285922912259342	0	1.73480675889668266889741055682	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/15"]
"2-405-135.113-c1-0-11"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4783074370296376	0	1.98393283198562795238463464506	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/5"]
"2-405-135.113-c1-0-12"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.013785481137915029	0	2.13785361222183083549442324322	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/14"]
"2-405-135.113-c1-0-13"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.008812407339491384	0	2.41454747057818454791051454506	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/16"]
"2-405-135.113-c1-0-14"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.25503923136437	0	2.55913681700033657167755101910	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/12"]
"2-405-135.113-c1-0-15"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4566332614295178	0	2.62230441185709511574535922784	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/11"]
"2-405-135.113-c1-0-2"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.28417348277028603	0	0.53542751125153900756630352204	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/3"]
"2-405-135.113-c1-0-3"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.013603148255351562	0	0.836648713086775467802123676355	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/6"]
"2-405-135.113-c1-0-4"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.18806104439814897	0	0.836872879079531810798887576801	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/8"]
"2-405-135.113-c1-0-5"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.16686700381500866	0	0.923658218986730734117082146200	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/2"]
"2-405-135.113-c1-0-6"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.13488375106567455	0	1.39771573173073518143430264979	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/13"]
"2-405-135.113-c1-0-7"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.20915339439516623	0	1.50440156933454808036514484149	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/4"]
"2-405-135.113-c1-0-8"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.21470977535359848	0	1.61813760210631701019077345371	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/7"]
"2-405-135.113-c1-0-9"	1.7983162352216746	3.233941281861857	2	405	"135.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.08799537818924638	0	1.69946867104208499804346607872	["ModularForm/GL2/Q/holomorphic/405/2/r/a/368/10"]
"2-405-135.122-c1-0-0"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.30802432041171934	0	0.00489317427004339501535876248	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/5"]
"2-405-135.122-c1-0-1"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.30153216597629434	0	0.16057895545516383469301059701	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/2"]
"2-405-135.122-c1-0-10"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05004661599587816	0	1.89983781530157592517414644996	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/13"]
"2-405-135.122-c1-0-11"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4768226554168539	0	1.99177792850579375813037325540	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/3"]
"2-405-135.122-c1-0-12"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.10862841824149178	0	2.20024352431318745740436581391	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/10"]
"2-405-135.122-c1-0-13"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.29040567382294763	0	2.21943262317393436463784996337	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/9"]
"2-405-135.122-c1-0-14"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.38903189791102444	0	2.35930057351484156081364663766	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/8"]
"2-405-135.122-c1-0-15"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1866877750997147	0	2.43844860885888964601096415526	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/12"]
"2-405-135.122-c1-0-2"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.14468394563940276	0	0.71254551061077797961176970918	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/7"]
"2-405-135.122-c1-0-3"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.011623775291157254	0	0.997468405866986239595126058438	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/4"]
"2-405-135.122-c1-0-4"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.0022690586644755445	0	1.14124257505695039024895091163	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/6"]
"2-405-135.122-c1-0-5"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.21301380592006733	0	1.14202336889060938911935856744	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/11"]
"2-405-135.122-c1-0-6"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3038193556465284	0	1.43163658792941009953552947446	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/16"]
"2-405-135.122-c1-0-7"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3244973832067339	0	1.49171922871098973201352554945	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/1"]
"2-405-135.122-c1-0-8"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.23479495789766164	0	1.56582141398329910624058420975	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/14"]
"2-405-135.122-c1-0-9"	1.7983162352216746	3.233941281861857	2	405	"135.122"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.25319291205307654	0	1.83059841490269804121193592483	["ModularForm/GL2/Q/holomorphic/405/2/r/a/152/15"]
"2-405-135.124-c1-0-0"	1.7983162352216746	3.233941281861857	2	405	"135.124"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.48229070447135153	0	0.35425249709978298709618950835	["ModularForm/GL2/Q/holomorphic/405/2/p/a/289/8"]
"2-405-135.124-c1-0-1"	1.7983162352216746	3.233941281861857	2	405	"135.124"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4226294157204033	0	0.38243046484647628005294603000	["ModularForm/GL2/Q/holomorphic/405/2/p/a/289/4"]
"2-405-135.124-c1-0-10"	1.7983162352216746	3.233941281861857	2	405	"135.124"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11120517800520009	0	1.50896187539183308010712110662	["ModularForm/GL2/Q/holomorphic/405/2/p/a/289/6"]
"2-405-135.124-c1-0-11"	1.7983162352216746	3.233941281861857	2	405	"135.124"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.18986715724205205	0	1.84529731621976267767424286668	["ModularForm/GL2/Q/holomorphic/405/2/p/a/289/14"]
"2-405-135.124-c1-0-12"	1.7983162352216746	3.233941281861857	2	405	"135.124"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1669682464875584	0	1.89432542931033838476106485130	["ModularForm/GL2/Q/holomorphic/405/2/p/a/289/13"]
"2-405-135.124-c1-0-13"	1.7983162352216746	3.233941281861857	2	405	"135.124"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.331042695307295	0	2.21561870827049004407906165104	["ModularForm/GL2/Q/holomorphic/405/2/p/a/289/5"]
"2-405-135.124-c1-0-14"	1.7983162352216746	3.233941281861857	2	405	"135.124"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.34963337142818274	0	2.53659032410437891988825140942	["ModularForm/GL2/Q/holomorphic/405/2/p/a/289/15"]
"2-405-135.124-c1-0-15"	1.7983162352216746	3.233941281861857	2	405	"135.124"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4797306990911692	0	3.01414094076431959719880203269	["ModularForm/GL2/Q/holomorphic/405/2/p/a/289/16"]
"2-405-135.124-c1-0-2"	1.7983162352216746	3.233941281861857	2	405	"135.124"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.428595297778405	0	0.46202693375141026443975120237	["ModularForm/GL2/Q/holomorphic/405/2/p/a/289/1"]
"2-405-135.124-c1-0-3"	1.7983162352216746	3.233941281861857	2	405	"135.124"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07532576968546842	0	1.06969652407124384301688881359	["ModularForm/GL2/Q/holomorphic/405/2/p/a/289/12"]
"2-405-135.124-c1-0-4"	1.7983162352216746	3.233941281861857	2	405	"135.124"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.33862316322248925	0	1.10163763475206201899055631869	["ModularForm/GL2/Q/holomorphic/405/2/p/a/289/2"]
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"2-405-1.1-c7-0-48"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.888825875270673308228522156340	["ModularForm/GL2/Q/holomorphic/405/8/a/i/1/11"]
"2-405-1.1-c7-0-49"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.895848201220803239952117081814	["ModularForm/GL2/Q/holomorphic/405/8/a/g/1/4"]
"2-405-1.1-c7-0-5"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.23811623292763848321201992218	["ModularForm/GL2/Q/holomorphic/405/8/a/i/1/5"]
"2-405-1.1-c7-0-50"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.913876561116197273867310692664	["ModularForm/GL2/Q/holomorphic/405/8/a/i/1/6"]
"2-405-1.1-c7-0-51"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.917347724372784628982244558654	["ModularForm/GL2/Q/holomorphic/405/8/a/i/1/15"]
"2-405-1.1-c7-0-52"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.930949255316611112386852530612	["ModularForm/GL2/Q/holomorphic/405/8/a/a/1/3"]
"2-405-1.1-c7-0-53"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.932567123726349268678299140746	["ModularForm/GL2/Q/holomorphic/405/8/a/h/1/12"]
"2-405-1.1-c7-0-54"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.947978805332731922251051130734	["ModularForm/GL2/Q/holomorphic/405/8/a/g/1/9"]
"2-405-1.1-c7-0-55"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.958638135031946039010580433262	["ModularForm/GL2/Q/holomorphic/405/8/a/j/1/2"]
"2-405-1.1-c7-0-56"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.965908185006393123133629307177	["ModularForm/GL2/Q/holomorphic/405/8/a/g/1/1"]
"2-405-1.1-c7-0-57"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.971824625380709742566743668300	["ModularForm/GL2/Q/holomorphic/405/8/a/j/1/8"]
"2-405-1.1-c7-0-58"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	0.974975547607478631125239828973	["ModularForm/GL2/Q/holomorphic/405/8/a/e/1/3"]
"2-405-1.1-c7-0-59"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.00260555987357758741192900116	["ModularForm/GL2/Q/holomorphic/405/8/a/f/1/4"]
"2-405-1.1-c7-0-6"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.26659542494703166097924859849	["ModularForm/GL2/Q/holomorphic/405/8/a/i/1/7"]
"2-405-1.1-c7-0-60"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	1.01711786880509286542335386756	["ModularForm/GL2/Q/holomorphic/405/8/a/c/1/6"]
"2-405-1.1-c7-0-61"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.01746906501624435534552451436	["ModularForm/GL2/Q/holomorphic/405/8/a/f/1/8"]
"2-405-1.1-c7-0-62"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.01758957285509956472976444955	["ModularForm/GL2/Q/holomorphic/405/8/a/g/1/7"]
"2-405-1.1-c7-0-63"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.02986281357309989871957863138	["ModularForm/GL2/Q/holomorphic/405/8/a/g/1/8"]
"2-405-1.1-c7-0-64"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.03338572539623845178062084417	["ModularForm/GL2/Q/holomorphic/405/8/a/e/1/6"]
"2-405-1.1-c7-0-65"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.03407577278149507891420228122	["ModularForm/GL2/Q/holomorphic/405/8/a/f/1/3"]
"2-405-1.1-c7-0-66"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.03834751445802315317389076078	["ModularForm/GL2/Q/holomorphic/405/8/a/e/1/7"]
"2-405-1.1-c7-0-67"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.04628669120468334062737874784	["ModularForm/GL2/Q/holomorphic/405/8/a/f/1/7"]
"2-405-1.1-c7-0-68"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.05773166923830580183671758790	["ModularForm/GL2/Q/holomorphic/405/8/a/g/1/2"]
"2-405-1.1-c7-0-69"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.05926018210227866714917109137	["ModularForm/GL2/Q/holomorphic/405/8/a/g/1/6"]
"2-405-1.1-c7-0-7"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.29918997178942273878155569071	["ModularForm/GL2/Q/holomorphic/405/8/a/j/1/1"]
"2-405-1.1-c7-0-70"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	1.06711815091591323858244493277	["ModularForm/GL2/Q/holomorphic/405/8/a/j/1/13"]
"2-405-1.1-c7-0-71"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	1.07538898173637275813542211138	["ModularForm/GL2/Q/holomorphic/405/8/a/i/1/14"]
"2-405-1.1-c7-0-72"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.08487554151021884223976956862	["ModularForm/GL2/Q/holomorphic/405/8/a/b/1/3"]
"2-405-1.1-c7-0-73"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.08733919463827654545357785429	["ModularForm/GL2/Q/holomorphic/405/8/a/f/1/1"]
"2-405-1.1-c7-0-74"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	1.09300099721070514964533237170	["ModularForm/GL2/Q/holomorphic/405/8/a/j/1/15"]
"2-405-1.1-c7-0-75"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.13048035630896707330649601437	["ModularForm/GL2/Q/holomorphic/405/8/a/e/1/1"]
"2-405-1.1-c7-0-76"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.15099930511876438679850787325	["ModularForm/GL2/Q/holomorphic/405/8/a/f/1/6"]
"2-405-1.1-c7-0-77"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.16406384351093866718936512530	["ModularForm/GL2/Q/holomorphic/405/8/a/e/1/9"]
"2-405-1.1-c7-0-78"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.16563207919320192136349482779	["ModularForm/GL2/Q/holomorphic/405/8/a/e/1/2"]
"2-405-1.1-c7-0-79"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	1.17617580370320362483642500849	["ModularForm/GL2/Q/holomorphic/405/8/a/h/1/14"]
"2-405-1.1-c7-0-8"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.30748367525252382294234016150	["ModularForm/GL2/Q/holomorphic/405/8/a/c/1/5"]
"2-405-1.1-c7-0-80"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.18068850073097591523641377338	["ModularForm/GL2/Q/holomorphic/405/8/a/a/1/2"]
"2-405-1.1-c7-0-81"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.18465095362668843528697136796	["ModularForm/GL2/Q/holomorphic/405/8/a/a/1/1"]
"2-405-1.1-c7-0-82"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	1.20760846760758316173625725418	["ModularForm/GL2/Q/holomorphic/405/8/a/h/1/13"]
"2-405-1.1-c7-0-83"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.21451146627267237623801847860	["ModularForm/GL2/Q/holomorphic/405/8/a/b/1/4"]
"2-405-1.1-c7-0-84"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.21766144967610558719918737916	["ModularForm/GL2/Q/holomorphic/405/8/a/f/1/9"]
"2-405-1.1-c7-0-85"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.23897647533502487628326556774	["ModularForm/GL2/Q/holomorphic/405/8/a/e/1/5"]
"2-405-1.1-c7-0-86"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.24527476540038212415092087992	["ModularForm/GL2/Q/holomorphic/405/8/a/g/1/11"]
"2-405-1.1-c7-0-87"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.24638563046988659917156688204	["ModularForm/GL2/Q/holomorphic/405/8/a/e/1/4"]
"2-405-1.1-c7-0-88"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.25295186726701100582569406416	["ModularForm/GL2/Q/holomorphic/405/8/a/g/1/10"]
"2-405-1.1-c7-0-89"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.26378046377684800964451693993	["ModularForm/GL2/Q/holomorphic/405/8/a/a/1/5"]
"2-405-1.1-c7-0-9"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	0.34673398460309329125313792026	["ModularForm/GL2/Q/holomorphic/405/8/a/i/1/9"]
"2-405-1.1-c7-0-90"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.27157911936182131254548612184	["ModularForm/GL2/Q/holomorphic/405/8/a/b/1/5"]
"2-405-1.1-c7-0-91"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	1.28048388654146858831747661856	["ModularForm/GL2/Q/holomorphic/405/8/a/d/1/7"]
"2-405-1.1-c7-0-92"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.29742441655707932090850563057	["ModularForm/GL2/Q/holomorphic/405/8/a/a/1/4"]
"2-405-1.1-c7-0-93"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.34999259826472278971457756453	["ModularForm/GL2/Q/holomorphic/405/8/a/b/1/2"]
"2-405-1.1-c7-0-94"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.35941573253481412359076258884	["ModularForm/GL2/Q/holomorphic/405/8/a/f/1/10"]
"2-405-1.1-c7-0-95"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.39795271935176594808224811835	["ModularForm/GL2/Q/holomorphic/405/8/a/e/1/8"]
"2-405-1.1-c7-0-96"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.39802167359637749354240870672	["ModularForm/GL2/Q/holomorphic/405/8/a/e/1/10"]
"2-405-1.1-c7-0-97"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.42019979234611593692544952603	["ModularForm/GL2/Q/holomorphic/405/8/a/g/1/3"]
"2-405-1.1-c7-0-98"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.0	0	1.43001363571810140790876151527	["ModularForm/GL2/Q/holomorphic/405/8/a/j/1/14"]
"2-405-1.1-c7-0-99"	11.247930268323563	126.51593532106936	2	405	"1.1"	[]	[[3.5, 0.0]]	7	true	true	false	true	0.5	1	1.58446251381559777771106513640	["ModularForm/GL2/Q/holomorphic/405/8/a/f/1/11"]


# 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).