# lfunc_search downloaded from the LMFDB on 25 May 2026.
# Search link: https://www.lmfdb.org/L/2/1664/104.85
# Query "{'degree': 2, 'conductor': 1664}" returned 686 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.



"2-1664-104.21-c0-0-0"	0.9112871013140239	0.830444181021316	2	1664	"104.21"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2032082395472503	0	0.795084613688709256617665855902	["ModularForm/GL2/Q/holomorphic/1664/1/j/a/1217/1", "ArtinRepresentation/2.1664.8t17.b.b"]
"2-1664-104.21-c0-0-1"	0.9112871013140239	0.830444181021316	2	1664	"104.21"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2032082395472503	0	1.04894820454447513609737856557	["ModularForm/GL2/Q/holomorphic/1664/1/j/d/1217/2"]
"2-1664-104.21-c0-0-2"	0.9112871013140239	0.830444181021316	2	1664	"104.21"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2032082395472503	0	1.14921632071581298457794860717	["ModularForm/GL2/Q/holomorphic/1664/1/j/d/1217/1"]
"2-1664-104.21-c0-0-3"	0.9112871013140239	0.830444181021316	2	1664	"104.21"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.046791760452749714	0	1.47650125863509594565976935798	["ModularForm/GL2/Q/holomorphic/1664/1/j/b/1217/1", "ArtinRepresentation/2.1664.8t17.a.b"]
"2-1664-104.21-c0-0-4"	0.9112871013140239	0.830444181021316	2	1664	"104.21"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.29679176045274974	0	1.58274666754041462145847937560	["ModularForm/GL2/Q/holomorphic/1664/1/j/c/1217/1"]
"2-1664-104.21-c0-0-5"	0.9112871013140239	0.830444181021316	2	1664	"104.21"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.29679176045274974	0	2.14855686489585693498138425821	["ModularForm/GL2/Q/holomorphic/1664/1/j/c/1217/2"]
"2-1664-104.3-c0-0-0"	0.9112871013140239	0.830444181021316	2	1664	"104.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.20935380902961667	0	0.947507258943697932097113166545	["ModularForm/GL2/Q/holomorphic/1664/1/v/b/575/1"]
"2-1664-104.3-c0-0-1"	0.9112871013140239	0.830444181021316	2	1664	"104.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.3343538090296167	0	0.971566079071491586200456588183	["ModularForm/GL2/Q/holomorphic/1664/1/v/c/575/4"]
"2-1664-104.3-c0-0-2"	0.9112871013140239	0.830444181021316	2	1664	"104.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.16564619097038333	0	1.22278055363740273693253649068	["ModularForm/GL2/Q/holomorphic/1664/1/v/c/575/2"]
"2-1664-104.3-c0-0-3"	0.9112871013140239	0.830444181021316	2	1664	"104.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.08435380902961669	0	1.43414253410957338597672157298	["ModularForm/GL2/Q/holomorphic/1664/1/v/c/575/3"]
"2-1664-104.3-c0-0-4"	0.9112871013140239	0.830444181021316	2	1664	"104.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.41564619097038336	0	1.89896376261188422187572081805	["ModularForm/GL2/Q/holomorphic/1664/1/v/c/575/1"]
"2-1664-104.3-c0-0-5"	0.9112871013140239	0.830444181021316	2	1664	"104.3"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.29064619097038336	0	2.08573737184025460692560268882	["ModularForm/GL2/Q/holomorphic/1664/1/v/a/575/1"]
"2-1664-104.35-c0-0-0"	0.9112871013140239	0.830444181021316	2	1664	"104.35"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.41564619097038336	0	0.74449382581835817182630250279	["ModularForm/GL2/Q/holomorphic/1664/1/v/c/191/2"]
"2-1664-104.35-c0-0-1"	0.9112871013140239	0.830444181021316	2	1664	"104.35"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.29064619097038336	0	0.802366360950976542661856630263	["ModularForm/GL2/Q/holomorphic/1664/1/v/a/191/1"]
"2-1664-104.35-c0-0-2"	0.9112871013140239	0.830444181021316	2	1664	"104.35"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.16564619097038333	0	0.902424357008507505009242787324	["ModularForm/GL2/Q/holomorphic/1664/1/v/c/191/1"]
"2-1664-104.35-c0-0-3"	0.9112871013140239	0.830444181021316	2	1664	"104.35"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.08435380902961669	0	1.40221253724944380880096374806	["ModularForm/GL2/Q/holomorphic/1664/1/v/c/191/4"]
"2-1664-104.35-c0-0-4"	0.9112871013140239	0.830444181021316	2	1664	"104.35"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.20935380902961667	0	1.73489825323457938010636950553	["ModularForm/GL2/Q/holomorphic/1664/1/v/b/191/1"]
"2-1664-104.35-c0-0-5"	0.9112871013140239	0.830444181021316	2	1664	"104.35"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.3343538090296167	0	2.22871823289458226358217880647	["ModularForm/GL2/Q/holomorphic/1664/1/v/c/191/3"]
"2-1664-104.37-c0-0-0"	0.9112871013140239	0.830444181021316	2	1664	"104.37"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2561455694823664	0	0.63377323000300398363245130197	["ModularForm/GL2/Q/holomorphic/1664/1/bv/b/193/1"]
"2-1664-104.37-c0-0-1"	0.9112871013140239	0.830444181021316	2	1664	"104.37"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.006145569482366385	0	1.23165565578250541940892833199	["ModularForm/GL2/Q/holomorphic/1664/1/bv/a/193/1"]
"2-1664-104.43-c0-0-0"	0.9112871013140239	0.830444181021316	2	1664	"104.43"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.08537428472590003	0	0.942010971538081851395684486753	["ModularForm/GL2/Q/holomorphic/1664/1/x/a/1343/1"]
"2-1664-104.43-c0-0-1"	0.9112871013140239	0.830444181021316	2	1664	"104.43"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.08537428472590003	0	1.17912227529381637020140148377	["ModularForm/GL2/Q/holomorphic/1664/1/x/b/1343/1"]
"2-1664-104.45-c0-0-0"	0.9112871013140239	0.830444181021316	2	1664	"104.45"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.006145569482366385	0	1.31649520234461198368297876567	["ModularForm/GL2/Q/holomorphic/1664/1/bv/a/1345/1"]
"2-1664-104.45-c0-0-1"	0.9112871013140239	0.830444181021316	2	1664	"104.45"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2561455694823664	0	1.75555982644983007746764776447	["ModularForm/GL2/Q/holomorphic/1664/1/bv/b/1345/1"]
"2-1664-104.5-c0-0-0"	0.9112871013140239	0.830444181021316	2	1664	"104.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.29679176045274974	0	0.59389852830116037329931522557	["ModularForm/GL2/Q/holomorphic/1664/1/j/c/577/1"]
"2-1664-104.5-c0-0-1"	0.9112871013140239	0.830444181021316	2	1664	"104.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.29679176045274974	0	1.06619462788161135981329501116	["ModularForm/GL2/Q/holomorphic/1664/1/j/c/577/2"]
"2-1664-104.5-c0-0-2"	0.9112871013140239	0.830444181021316	2	1664	"104.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.046791760452749714	0	1.49032892334044718474348687978	["ModularForm/GL2/Q/holomorphic/1664/1/j/b/577/1", "ArtinRepresentation/2.1664.8t17.a.a"]
"2-1664-104.5-c0-0-3"	0.9112871013140239	0.830444181021316	2	1664	"104.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2032082395472503	0	1.51434127280716533811099605726	["ModularForm/GL2/Q/holomorphic/1664/1/j/d/577/1"]
"2-1664-104.5-c0-0-4"	0.9112871013140239	0.830444181021316	2	1664	"104.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2032082395472503	0	1.55089733187465623481227557059	["ModularForm/GL2/Q/holomorphic/1664/1/j/a/577/1", "ArtinRepresentation/2.1664.8t17.b.a"]
"2-1664-104.5-c0-0-5"	0.9112871013140239	0.830444181021316	2	1664	"104.5"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2032082395472503	0	1.68121218051828596162805361813	["ModularForm/GL2/Q/holomorphic/1664/1/j/d/577/2"]
"2-1664-104.51-c0-0-0"	0.9112871013140239	0.830444181021316	2	1664	"104.51"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.375	0	0.28253187131525117676412627523	["ModularForm/GL2/Q/holomorphic/1664/1/h/e/831/2"]
"2-1664-104.51-c0-0-1"	0.9112871013140239	0.830444181021316	2	1664	"104.51"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	0.51636305086772872947155622810	["ModularForm/GL2/Q/holomorphic/1664/1/h/c/831/1"]
"2-1664-104.51-c0-0-2"	0.9112871013140239	0.830444181021316	2	1664	"104.51"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	0.917290681975778831003821304406	["ModularForm/GL2/Q/holomorphic/1664/1/h/a/831/1", "ModularForm/GL2/Q/holomorphic/1664/1/h/a", "ArtinRepresentation/2.1664.4t3.e.a", "ArtinRepresentation/2.1664.4t3.e"]
"2-1664-104.51-c0-0-3"	0.9112871013140239	0.830444181021316	2	1664	"104.51"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.125	0	0.993342333303775654043931422512	["ModularForm/GL2/Q/holomorphic/1664/1/h/e/831/4"]
"2-1664-104.51-c0-0-4"	0.9112871013140239	0.830444181021316	2	1664	"104.51"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.25639394657444950735104589609	["ModularForm/GL2/Q/holomorphic/1664/1/h/d/831/1"]
"2-1664-104.51-c0-0-5"	0.9112871013140239	0.830444181021316	2	1664	"104.51"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	1.48509632923281712227798290294	["ModularForm/GL2/Q/holomorphic/1664/1/h/b/831/1", "ModularForm/GL2/Q/holomorphic/1664/1/h/b", "ArtinRepresentation/2.1664.4t3.f.a", "ArtinRepresentation/2.1664.4t3.f"]
"2-1664-104.51-c0-0-6"	0.9112871013140239	0.830444181021316	2	1664	"104.51"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.125	0	1.69582877733080275884475994879	["ModularForm/GL2/Q/holomorphic/1664/1/h/e/831/3"]
"2-1664-104.51-c0-0-7"	0.9112871013140239	0.830444181021316	2	1664	"104.51"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.71247571744736440363434726595	["ModularForm/GL2/Q/holomorphic/1664/1/h/c/831/2"]
"2-1664-104.51-c0-0-8"	0.9112871013140239	0.830444181021316	2	1664	"104.51"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.74418433642279049538799071040	["ModularForm/GL2/Q/holomorphic/1664/1/h/d/831/2"]
"2-1664-104.51-c0-0-9"	0.9112871013140239	0.830444181021316	2	1664	"104.51"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.375	0	1.90133902524943785099584134199	["ModularForm/GL2/Q/holomorphic/1664/1/h/e/831/1"]
"2-1664-104.75-c0-0-0"	0.9112871013140239	0.830444181021316	2	1664	"104.75"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.08537428472590003	0	1.29783840498086539447272391769	["ModularForm/GL2/Q/holomorphic/1664/1/x/a/959/1"]
"2-1664-104.75-c0-0-1"	0.9112871013140239	0.830444181021316	2	1664	"104.75"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.08537428472590003	0	1.72031026303898862251822839286	["ModularForm/GL2/Q/holomorphic/1664/1/x/b/959/1"]
"2-1664-104.85-c0-0-0"	0.9112871013140239	0.830444181021316	2	1664	"104.85"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.41256204857686696	0	1.74752263547627394428401010209	["ModularForm/GL2/Q/holomorphic/1664/1/bv/a/449/1"]
"2-1664-104.85-c0-0-1"	0.9112871013140239	0.830444181021316	2	1664	"104.85"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.16256204857686699	0	1.87171809884253102225877838598	["ModularForm/GL2/Q/holomorphic/1664/1/bv/b/449/1"]
"2-1664-104.93-c0-0-0"	0.9112871013140239	0.830444181021316	2	1664	"104.93"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.41256204857686696	0	0.02908911747078765163737097158	["ModularForm/GL2/Q/holomorphic/1664/1/bv/a/1601/1"]
"2-1664-104.93-c0-0-1"	0.9112871013140239	0.830444181021316	2	1664	"104.93"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.16256204857686699	0	1.16943198672185005380538512382	["ModularForm/GL2/Q/holomorphic/1664/1/bv/b/1601/1"]
"2-1664-1.1-c1-0-0"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.40430143103612874809424454455	["ModularForm/GL2/Q/holomorphic/1664/2/a/ba/1/2"]
"2-1664-1.1-c1-0-1"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.42386886155492492061098730422	["ModularForm/GL2/Q/holomorphic/1664/2/a/bb/1/3"]
"2-1664-1.1-c1-0-10"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.834205625393088810426308449046	["ModularForm/GL2/Q/holomorphic/1664/2/a/z/1/1"]
"2-1664-1.1-c1-0-11"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.848906116969302879647822827113	["ModularForm/GL2/Q/holomorphic/1664/2/a/v/1/2"]
"2-1664-1.1-c1-0-12"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.931572434021849514235398346995	["EllipticCurve/Q/1664/j", "ModularForm/GL2/Q/holomorphic/1664/2/a/j/1/1", "ModularForm/GL2/Q/holomorphic/1664/2/a/j"]
"2-1664-1.1-c1-0-13"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.944943587833217909844153323409	["ModularForm/GL2/Q/holomorphic/1664/2/a/v/1/1"]
"2-1664-1.1-c1-0-14"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.971637723601799818298973676418	["ModularForm/GL2/Q/holomorphic/1664/2/a/w/1/2"]
"2-1664-1.1-c1-0-15"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.977119081145605096066947230357	["ModularForm/GL2/Q/holomorphic/1664/2/a/ba/1/4"]
"2-1664-1.1-c1-0-16"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.06753820497528636424913397368	["ModularForm/GL2/Q/holomorphic/1664/2/a/bb/1/2"]
"2-1664-1.1-c1-0-17"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.13036424838435328795096380283	["ModularForm/GL2/Q/holomorphic/1664/2/a/w/1/1"]
"2-1664-1.1-c1-0-18"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.15688052336061152821135737218	["ModularForm/GL2/Q/holomorphic/1664/2/a/u/1/1"]
"2-1664-1.1-c1-0-19"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.18375222419322193539183848199	["ModularForm/GL2/Q/holomorphic/1664/2/a/y/1/1"]
"2-1664-1.1-c1-0-2"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.45207616146189499559120309103	["ModularForm/GL2/Q/holomorphic/1664/2/a/z/1/2"]
"2-1664-1.1-c1-0-20"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.19693558967587737588418810371	["EllipticCurve/Q/1664/s", "ModularForm/GL2/Q/holomorphic/1664/2/a/s/1/1", "ModularForm/GL2/Q/holomorphic/1664/2/a/s"]
"2-1664-1.1-c1-0-21"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.20469832482677991875827006353	["ModularForm/GL2/Q/holomorphic/1664/2/a/z/1/4"]
"2-1664-1.1-c1-0-22"	3.645148405256096	13.287106896341061	2	1664	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.29658404404318300490955748804	["ModularForm/GL2/Q/holomorphic/1664/2/a/bb/1/4"]
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"2-1664-1.1-c3-0-56"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.834870727391068843005983091205	["ModularForm/GL2/Q/holomorphic/1664/4/a/o/1/7"]
"2-1664-1.1-c3-0-57"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.836328911583285087316122730098	["ModularForm/GL2/Q/holomorphic/1664/4/a/t/1/11"]
"2-1664-1.1-c3-0-58"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.843902399545856271215660619695	["ModularForm/GL2/Q/holomorphic/1664/4/a/j/1/3"]
"2-1664-1.1-c3-0-59"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.857163471387743312004585477675	["ModularForm/GL2/Q/holomorphic/1664/4/a/o/1/6"]
"2-1664-1.1-c3-0-6"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.18931235316832567993248072894	["ModularForm/GL2/Q/holomorphic/1664/4/a/n/1/1"]
"2-1664-1.1-c3-0-60"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.865748446252073488217816196521	["ModularForm/GL2/Q/holomorphic/1664/4/a/q/1/5"]
"2-1664-1.1-c3-0-61"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.0	0	0.870293772560638494309750167666	["ModularForm/GL2/Q/holomorphic/1664/4/a/b/1/1", "ModularForm/GL2/Q/holomorphic/1664/4/a/b"]
"2-1664-1.1-c3-0-62"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.874371813088203009088782600113	["ModularForm/GL2/Q/holomorphic/1664/4/a/n/1/9"]
"2-1664-1.1-c3-0-63"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.888297866725944577183524804791	["ModularForm/GL2/Q/holomorphic/1664/4/a/o/1/9"]
"2-1664-1.1-c3-0-64"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.911236516348551338607789691500	["ModularForm/GL2/Q/holomorphic/1664/4/a/p/1/5"]
"2-1664-1.1-c3-0-65"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.924165912378720445530394318771	["ModularForm/GL2/Q/holomorphic/1664/4/a/h/1/2"]
"2-1664-1.1-c3-0-66"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.930602785843577409362361065762	["ModularForm/GL2/Q/holomorphic/1664/4/a/i/1/1"]
"2-1664-1.1-c3-0-67"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.945171365115494655405426570186	["ModularForm/GL2/Q/holomorphic/1664/4/a/s/1/2"]
"2-1664-1.1-c3-0-68"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.946287401268114069688839834747	["ModularForm/GL2/Q/holomorphic/1664/4/a/l/1/6"]
"2-1664-1.1-c3-0-69"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.946846049775354226629009709974	["ModularForm/GL2/Q/holomorphic/1664/4/a/r/1/9"]
"2-1664-1.1-c3-0-7"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.20432464163045747339396879196	["ModularForm/GL2/Q/holomorphic/1664/4/a/f/1/3"]
"2-1664-1.1-c3-0-70"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.979334715318907936876650967187	["ModularForm/GL2/Q/holomorphic/1664/4/a/t/1/1"]
"2-1664-1.1-c3-0-71"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.987310776044824666736456687130	["ModularForm/GL2/Q/holomorphic/1664/4/a/p/1/7"]
"2-1664-1.1-c3-0-72"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.988608245375070521430414586085	["ModularForm/GL2/Q/holomorphic/1664/4/a/j/1/5"]
"2-1664-1.1-c3-0-73"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.993558507943828022295864451635	["ModularForm/GL2/Q/holomorphic/1664/4/a/s/1/10"]
"2-1664-1.1-c3-0-74"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.993888984459610998073425741657	["ModularForm/GL2/Q/holomorphic/1664/4/a/l/1/5"]
"2-1664-1.1-c3-0-75"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	1.01898028861984335575820126358	["ModularForm/GL2/Q/holomorphic/1664/4/a/f/1/7"]
"2-1664-1.1-c3-0-76"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.02146925300914496586760153010	["ModularForm/GL2/Q/holomorphic/1664/4/a/g/1/3"]
"2-1664-1.1-c3-0-77"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.02263242706463326087303674310	["ModularForm/GL2/Q/holomorphic/1664/4/a/i/1/2"]
"2-1664-1.1-c3-0-78"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.02355901058795848665158743324	["ModularForm/GL2/Q/holomorphic/1664/4/a/j/1/1"]
"2-1664-1.1-c3-0-79"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.02600373576541642831360974174	["ModularForm/GL2/Q/holomorphic/1664/4/a/q/1/4"]
"2-1664-1.1-c3-0-8"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.27870188892013455633683553317	["ModularForm/GL2/Q/holomorphic/1664/4/a/t/1/3"]
"2-1664-1.1-c3-0-80"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.02657964849664619366361646429	["ModularForm/GL2/Q/holomorphic/1664/4/a/g/1/4"]
"2-1664-1.1-c3-0-81"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	1.05569748654699141992204357686	["ModularForm/GL2/Q/holomorphic/1664/4/a/f/1/5"]
"2-1664-1.1-c3-0-82"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.06199605424968391194621775193	["ModularForm/GL2/Q/holomorphic/1664/4/a/q/1/3"]
"2-1664-1.1-c3-0-83"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	1.06239807355690808028378405952	["ModularForm/GL2/Q/holomorphic/1664/4/a/r/1/10"]
"2-1664-1.1-c3-0-84"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.06941862829071518929812988413	["ModularForm/GL2/Q/holomorphic/1664/4/a/m/1/1"]
"2-1664-1.1-c3-0-85"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.07762579919557026659682940511	["ModularForm/GL2/Q/holomorphic/1664/4/a/m/1/2"]
"2-1664-1.1-c3-0-86"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	1.08235646228980059734456604549	["ModularForm/GL2/Q/holomorphic/1664/4/a/r/1/5"]
"2-1664-1.1-c3-0-87"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	1.09639783468183754079101659596	["ModularForm/GL2/Q/holomorphic/1664/4/a/t/1/8"]
"2-1664-1.1-c3-0-88"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	1.10435644119188532152123576426	["ModularForm/GL2/Q/holomorphic/1664/4/a/s/1/11"]
"2-1664-1.1-c3-0-89"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.10618085137538211521299431522	["ModularForm/GL2/Q/holomorphic/1664/4/a/e/1/5"]
"2-1664-1.1-c3-0-9"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.28368942336260516844694926259	["ModularForm/GL2/Q/holomorphic/1664/4/a/l/1/4"]
"2-1664-1.1-c3-0-90"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.12014841603645779898581833469	["ModularForm/GL2/Q/holomorphic/1664/4/a/m/1/5"]
"2-1664-1.1-c3-0-91"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.13325871394104124087851368058	["ModularForm/GL2/Q/holomorphic/1664/4/a/j/1/2"]
"2-1664-1.1-c3-0-92"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.13466099966790501025904537150	["ModularForm/GL2/Q/holomorphic/1664/4/a/e/1/3"]
"2-1664-1.1-c3-0-93"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.15566668054623693413682213472	["ModularForm/GL2/Q/holomorphic/1664/4/a/k/1/3"]
"2-1664-1.1-c3-0-94"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.16861916680466922679081378426	["ModularForm/GL2/Q/holomorphic/1664/4/a/e/1/1"]
"2-1664-1.1-c3-0-95"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.19481946301667594406353373779	["ModularForm/GL2/Q/holomorphic/1664/4/a/k/1/5"]
"2-1664-1.1-c3-0-96"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.22754390000816909958622749879	["ModularForm/GL2/Q/holomorphic/1664/4/a/k/1/1"]
"2-1664-1.1-c3-0-97"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.24629704453481264777244397912	["ModularForm/GL2/Q/holomorphic/1664/4/a/m/1/6"]
"2-1664-1.1-c3-0-98"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.24972901086451686119141924062	["ModularForm/GL2/Q/holomorphic/1664/4/a/h/1/3"]
"2-1664-1.1-c3-0-99"	9.908540672044113	98.17917824955242	2	1664	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	1.25267111397795249754947714521	["ModularForm/GL2/Q/holomorphic/1664/4/a/t/1/10"]


# 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).