# lfunc_search downloaded from the LMFDB on 24 October 2026.
# Search link: https://www.lmfdb.org/L/2/272
# Query "{'degree': 2, 'conductor': 272}" returned 5010 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.



"2-272-68.15-c0-0-0"	0.36843681064217326	0.13574568343617666	2	272	"68.15"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.012089257049555817	0	2.14609788915881474491639592003	["ModularForm/GL2/Q/holomorphic/272/1/u/a/15/1"]
"2-272-68.19-c0-0-0"	0.36843681064217326	0.13574568343617666	2	272	"68.19"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.13240552554478652	0	2.61360036432131000754634776807	["ModularForm/GL2/Q/holomorphic/272/1/u/a/223/1"]
"2-272-68.43-c0-0-0"	0.36843681064217326	0.13574568343617666	2	272	"68.43"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.13240552554478652	0	1.47703458376679677731471711938	["ModularForm/GL2/Q/holomorphic/272/1/u/a/111/1"]
"2-272-68.59-c0-0-0"	0.36843681064217326	0.13574568343617666	2	272	"68.59"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.012089257049555817	0	2.04911209781765483770770257482	["ModularForm/GL2/Q/holomorphic/272/1/u/a/127/1"]
"2-272-68.67-c0-0-0"	0.36843681064217326	0.13574568343617666	2	272	"68.67"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.63165721366859624258729802914	["ModularForm/GL2/Q/holomorphic/272/1/g/a/271/1", "ArtinRepresentation/2.272.8t6.b.b"]
"2-272-68.67-c0-0-1"	0.36843681064217326	0.13574568343617666	2	272	"68.67"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	2.62230025663909593241240640806	["ModularForm/GL2/Q/holomorphic/272/1/g/a/271/2", "ArtinRepresentation/2.272.8t6.b.a"]
"2-272-1.1-c1-0-0"	1.4737472425686935	2.1719309349788274	2	272	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.989417793767317894634255709039	["ModularForm/GL2/Q/holomorphic/272/2/a/e/1/1"]
"2-272-1.1-c1-0-1"	1.4737472425686935	2.1719309349788274	2	272	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.45395524885242083018695564650	["ModularForm/GL2/Q/holomorphic/272/2/a/f/1/1"]
"2-272-1.1-c1-0-2"	1.4737472425686935	2.1719309349788274	2	272	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.78722102085145557690346531679	["EllipticCurve/Q/272/c", "ModularForm/GL2/Q/holomorphic/272/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/272/2/a/c"]
"2-272-1.1-c1-0-3"	1.4737472425686935	2.1719309349788274	2	272	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.84590143985780086612851937706	["ModularForm/GL2/Q/holomorphic/272/2/a/e/1/2"]
"2-272-1.1-c1-0-4"	1.4737472425686935	2.1719309349788274	2	272	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.95520344137895444953340586126	["EllipticCurve/Q/272/d", "ModularForm/GL2/Q/holomorphic/272/2/a/d/1/1", "ModularForm/GL2/Q/holomorphic/272/2/a/d"]
"2-272-1.1-c1-0-5"	1.4737472425686935	2.1719309349788274	2	272	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.29602170294392146313536467747	["ModularForm/GL2/Q/holomorphic/272/2/a/f/1/2"]
"2-272-1.1-c1-0-6"	1.4737472425686935	2.1719309349788274	2	272	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.43872790837340716861606160980	["EllipticCurve/Q/272/a", "ModularForm/GL2/Q/holomorphic/272/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/272/2/a/a"]
"2-272-1.1-c1-0-7"	1.4737472425686935	2.1719309349788274	2	272	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.88331668043848910381979864823	["EllipticCurve/Q/272/b", "ModularForm/GL2/Q/holomorphic/272/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/272/2/a/b"]
"2-272-16.13-c1-0-0"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.14999077524476453	0	0.27283725662468322713463354199	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/7"]
"2-272-16.13-c1-0-1"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3775303445828389	0	0.29444852107876938519326045074	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/6"]
"2-272-16.13-c1-0-10"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1878575215559777	0	1.53646010190554525274276561367	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/2"]
"2-272-16.13-c1-0-11"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.11472246789330826	0	1.56357470790665733619689675545	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/16"]
"2-272-16.13-c1-0-12"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2580881122205046	0	1.66195098943844402564649367215	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/13"]
"2-272-16.13-c1-0-13"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.31763028816518973	0	1.69416877098699805265037914149	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/10"]
"2-272-16.13-c1-0-14"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.0964254549771341	0	1.70892370879982073194435846885	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/3"]
"2-272-16.13-c1-0-15"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.06250000000000001	0	1.81780544749252090678688973333	["ModularForm/GL2/Q/holomorphic/272/2/l/a/205/1"]
"2-272-16.13-c1-0-16"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1717452235692313	0	1.84806215412237140302724944629	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/12"]
"2-272-16.13-c1-0-17"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.08795537270151338	0	1.99796645114113912522585858895	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/5"]
"2-272-16.13-c1-0-18"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4366584619989016	0	2.01849518020895850763191125338	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/1"]
"2-272-16.13-c1-0-19"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.19449851544447805	0	2.06178847307017437334734632662	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/10"]
"2-272-16.13-c1-0-2"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4398605589019118	0	0.68095503102625686533830358159	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/12"]
"2-272-16.13-c1-0-20"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.0004741186789299185	0	2.08420301877690105677820831532	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/11"]
"2-272-16.13-c1-0-21"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.262424978214236	0	2.12129791580671121439795040761	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/2"]
"2-272-16.13-c1-0-22"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4535902137559199	0	2.17067015118340914930815862870	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/5"]
"2-272-16.13-c1-0-23"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.10566006103396239	0	2.23564029367511535541512907619	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/15"]
"2-272-16.13-c1-0-24"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.04660230748935626	0	2.32175543664549658077434513330	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/6"]
"2-272-16.13-c1-0-25"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2122315522773133	0	2.41642604888447670163514799311	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/11"]
"2-272-16.13-c1-0-26"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1527797898328604	0	2.42192268666097228866083214299	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/14"]
"2-272-16.13-c1-0-27"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.32513711618888486	0	2.51024989462559078659853048116	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/13"]
"2-272-16.13-c1-0-28"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.25114138717408646	0	2.55522360621446574125572147798	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/15"]
"2-272-16.13-c1-0-29"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4767681242074312	0	2.61458635296188546981993159255	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/8"]
"2-272-16.13-c1-0-3"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.01087696836016147	0	0.73738151330611810530213321505	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/1"]
"2-272-16.13-c1-0-30"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.41658534100290007	0	3.17383907648099418112129262623	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/9"]
"2-272-16.13-c1-0-31"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.42087488122577793	0	3.56566727994137034974294817862	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/14"]
"2-272-16.13-c1-0-4"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.047705257920122625	0	0.78473953631294649242790483065	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/4"]
"2-272-16.13-c1-0-5"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4143795003335736	0	0.816185675969577792486047795100	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/4"]
"2-272-16.13-c1-0-6"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.469717024005936	0	0.935022316026765515711472153870	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/7"]
"2-272-16.13-c1-0-7"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1532917234332889	0	0.952191651848680683715234603067	["ModularForm/GL2/Q/holomorphic/272/2/l/b/205/3"]
"2-272-16.13-c1-0-8"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.08855920832355635	0	1.11810697344179333845668716053	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/8"]
"2-272-16.13-c1-0-9"	1.4737472425686935	2.1719309349788274	2	272	"16.13"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.11664847243867241	0	1.46783037158735659521941721154	["ModularForm/GL2/Q/holomorphic/272/2/l/c/205/9"]
"2-272-16.5-c1-0-0"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4366584619989016	0	0.07742693805914477655838073514	["ModularForm/GL2/Q/holomorphic/272/2/l/b/69/1"]
"2-272-16.5-c1-0-1"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.42087488122577793	0	0.35999275391869874303199059594	["ModularForm/GL2/Q/holomorphic/272/2/l/c/69/14"]
"2-272-16.5-c1-0-10"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.01087696836016147	0	1.19560223424588963463725986330	["ModularForm/GL2/Q/holomorphic/272/2/l/c/69/1"]
"2-272-16.5-c1-0-11"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.047705257920122625	0	1.20175424886667575150993863925	["ModularForm/GL2/Q/holomorphic/272/2/l/b/69/4"]
"2-272-16.5-c1-0-12"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.06250000000000001	0	1.32955340829206491408254256595	["ModularForm/GL2/Q/holomorphic/272/2/l/a/69/1"]
"2-272-16.5-c1-0-13"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.25114138717408646	0	1.41296079080723127411766346548	["ModularForm/GL2/Q/holomorphic/272/2/l/b/69/15"]
"2-272-16.5-c1-0-14"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.10566006103396239	0	1.42779175723293637277051247557	["ModularForm/GL2/Q/holomorphic/272/2/l/c/69/15"]
"2-272-16.5-c1-0-15"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11664847243867241	0	1.46038683723954600649722046076	["ModularForm/GL2/Q/holomorphic/272/2/l/c/69/9"]
"2-272-16.5-c1-0-16"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1527797898328604	0	1.61956845784685530218536168802	["ModularForm/GL2/Q/holomorphic/272/2/l/b/69/14"]
"2-272-16.5-c1-0-17"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.08795537270151338	0	1.64649810370625197410417190112	["ModularForm/GL2/Q/holomorphic/272/2/l/b/69/5"]
"2-272-16.5-c1-0-18"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2122315522773133	0	1.64906091974799633536123633413	["ModularForm/GL2/Q/holomorphic/272/2/l/c/69/11"]
"2-272-16.5-c1-0-19"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3775303445828389	0	1.65118585947750151152872057230	["ModularForm/GL2/Q/holomorphic/272/2/l/b/69/6"]
"2-272-16.5-c1-0-2"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.19449851544447805	0	0.56416300230860313259391114280	["ModularForm/GL2/Q/holomorphic/272/2/l/b/69/10"]
"2-272-16.5-c1-0-20"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.14999077524476453	0	1.89414539173344614152418539276	["ModularForm/GL2/Q/holomorphic/272/2/l/c/69/7"]
"2-272-16.5-c1-0-21"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1532917234332889	0	2.11973883993109244704310768409	["ModularForm/GL2/Q/holomorphic/272/2/l/b/69/3"]
"2-272-16.5-c1-0-22"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1878575215559777	0	2.12441198971600611910409891161	["ModularForm/GL2/Q/holomorphic/272/2/l/c/69/2"]
"2-272-16.5-c1-0-23"	1.4737472425686935	2.1719309349788274	2	272	"16.5"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.08855920832355635	0	2.29299955747137335345605821529	["ModularForm/GL2/Q/holomorphic/272/2/l/c/69/8"]
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"2-272-17.16-c11-0-64"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.023409872899043824	0	0.866664498629908364937390285495	["ModularForm/GL2/Q/holomorphic/272/12/b/f/33/23"]
"2-272-17.16-c11-0-65"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.10118720103013752	0	0.876094439952634600815582899637	["ModularForm/GL2/Q/holomorphic/272/12/b/c/33/13"]
"2-272-17.16-c11-0-66"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.04750434502268342	0	0.876148227016227760208701394706	["ModularForm/GL2/Q/holomorphic/272/12/b/e/33/12"]
"2-272-17.16-c11-0-67"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.036196157547645706	0	0.884793558750199595127422225215	["ModularForm/GL2/Q/holomorphic/272/12/b/d/33/16"]
"2-272-17.16-c11-0-68"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.45257419971111373	0	0.899347077915212842643779655067	["ModularForm/GL2/Q/holomorphic/272/12/b/c/33/1"]
"2-272-17.16-c11-0-69"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.23784131180304904	0	0.908796767109781432966421245186	["ModularForm/GL2/Q/holomorphic/272/12/b/a/33/4"]
"2-272-17.16-c11-0-7"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.013188444924491692	0	0.12738856901330954297226107156	["ModularForm/GL2/Q/holomorphic/272/12/b/f/33/25"]
"2-272-17.16-c11-0-70"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.04358963741781061	0	0.913816729812842301822642837533	["ModularForm/GL2/Q/holomorphic/272/12/b/f/33/11"]
"2-272-17.16-c11-0-71"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.2971453231635718	0	0.957301142224212040971549231004	["ModularForm/GL2/Q/holomorphic/272/12/b/f/33/10"]
"2-272-17.16-c11-0-72"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.2806530564717502	0	0.960954528584356284130181567579	["ModularForm/GL2/Q/holomorphic/272/12/b/b/33/5"]
"2-272-17.16-c11-0-73"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.26737657720066266	0	1.01438189198051501726047744695	["ModularForm/GL2/Q/holomorphic/272/12/b/e/33/22"]
"2-272-17.16-c11-0-74"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.3615627496046409	0	1.01531562942354249945202382388	["ModularForm/GL2/Q/holomorphic/272/12/b/d/33/6"]
"2-272-17.16-c11-0-75"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.37319659769680574	0	1.02521232313088360661698199192	["ModularForm/GL2/Q/holomorphic/272/12/b/e/33/9"]
"2-272-17.16-c11-0-76"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.15345123829746726	0	1.05301089574061879594782787131	["ModularForm/GL2/Q/holomorphic/272/12/b/d/33/8"]
"2-272-17.16-c11-0-77"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.4739804719214675	0	1.08301479754725665056364944717	["ModularForm/GL2/Q/holomorphic/272/12/b/b/33/1"]
"2-272-17.16-c11-0-78"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.16347632012708788	0	1.08517716555340999566649358587	["ModularForm/GL2/Q/holomorphic/272/12/b/f/33/19"]
"2-272-17.16-c11-0-79"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.33545836403312873	0	1.12307561128217123728404579638	["ModularForm/GL2/Q/holomorphic/272/12/b/d/33/14"]
"2-272-17.16-c11-0-8"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.4739804719214675	0	0.13032751531660706060956622308	["ModularForm/GL2/Q/holomorphic/272/12/b/b/33/8"]
"2-272-17.16-c11-0-80"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.45255068874214915	0	1.13099100326987384112352765706	["ModularForm/GL2/Q/holomorphic/272/12/b/e/33/8"]
"2-272-17.16-c11-0-81"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.47215757772696715	0	1.20394690306412550359377233250	["ModularForm/GL2/Q/holomorphic/272/12/b/c/33/5"]
"2-272-17.16-c11-0-82"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.2789125689943108	0	1.23606219172634458188273323511	["ModularForm/GL2/Q/holomorphic/272/12/b/d/33/13"]
"2-272-17.16-c11-0-83"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.30088752489661336	0	1.25688841829393142881401220020	["ModularForm/GL2/Q/holomorphic/272/12/b/c/33/8"]
"2-272-17.16-c11-0-84"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.3769137945243588	0	1.25991557186636087737269526231	["ModularForm/GL2/Q/holomorphic/272/12/b/a/33/6"]
"2-272-17.16-c11-0-85"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.43167162985643565	0	1.26843099393118819073929084353	["ModularForm/GL2/Q/holomorphic/272/12/b/f/33/13"]
"2-272-17.16-c11-0-86"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.4308055510467315	0	1.30872020533153627207265287574	["ModularForm/GL2/Q/holomorphic/272/12/b/e/33/14"]
"2-272-17.16-c11-0-87"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.38743092061431844	0	1.31235565909137509625247149126	["ModularForm/GL2/Q/holomorphic/272/12/b/f/33/3"]
"2-272-17.16-c11-0-88"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.4831558498510741	0	1.31251021593983978452652860408	["ModularForm/GL2/Q/holomorphic/272/12/b/d/33/5"]
"2-272-17.16-c11-0-89"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.3562820437470889	0	1.37121980883170970542773725736	["ModularForm/GL2/Q/holomorphic/272/12/b/f/33/6"]
"2-272-17.16-c11-0-9"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	0.16348887477921423	0	0.13152068358758314764146447437	["ModularForm/GL2/Q/holomorphic/272/12/b/a/33/8"]
"2-272-17.16-c11-0-90"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.2893572309156207	0	1.63143620976445521631169630193	["ModularForm/GL2/Q/holomorphic/272/12/b/b/33/2"]
"2-272-17.16-c11-0-91"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.16348887477921423	0	1.67711173901027915620296562020	["ModularForm/GL2/Q/holomorphic/272/12/b/a/33/1"]
"2-272-17.16-c11-0-92"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.3365419236136385	0	1.68759674534987550587988345939	["ModularForm/GL2/Q/holomorphic/272/12/b/c/33/10"]
"2-272-17.16-c11-0-93"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.2909036533498276	0	1.70017363076561999982497097701	["ModularForm/GL2/Q/holomorphic/272/12/b/f/33/12"]
"2-272-17.16-c11-0-94"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.22155232479740933	0	1.70684373825203699741746227974	["ModularForm/GL2/Q/holomorphic/272/12/b/e/33/5"]
"2-272-17.16-c11-0-95"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.4008324166689819	0	1.79110655581047293112999027139	["ModularForm/GL2/Q/holomorphic/272/12/b/f/33/26"]
"2-272-17.16-c11-0-96"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.2572507111880854	0	1.87407174307389300043090915270	["ModularForm/GL2/Q/holomorphic/272/12/b/e/33/6"]
"2-272-17.16-c11-0-97"	14.456463783104367	208.9893451122082	2	272	"17.16"	[]	[[5.5, 0.0]]	11	true	true	false	false	-0.013188444924491692	0	2.24174326992198306030778089907	["ModularForm/GL2/Q/holomorphic/272/12/b/f/33/2"]


# 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).