
# lfunc_search downloaded from the LMFDB on 23 June 2026.
# Search link: https://www.lmfdb.org/L/2/273/7.4
# Query "{'degree': 2, 'conductor': 273}" returned 6859 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.



"2-273-273.107-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.107"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.13610695222325642	0	1.69426267454846610406584398035	["ModularForm/GL2/Q/holomorphic/273/1/s/a/107/1", "ArtinRepresentation/2.273.6t5.d.a"]
"2-273-273.107-c0-0-1"	0.3691134628387451	0.13624474844880965	2	273	"273.107"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.21944028555658976	0	2.09368771117900151686760285036	["ModularForm/GL2/Q/holomorphic/273/1/s/b/107/2"]
"2-273-273.107-c0-0-2"	0.3691134628387451	0.13624474844880965	2	273	"273.107"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.28055971444341027	0	2.52377090036080620067152435299	["ModularForm/GL2/Q/holomorphic/273/1/s/b/107/1"]
"2-273-273.110-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.110"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.14034814413035418	0	1.90838659093179909856543945911	["ModularForm/GL2/Q/holomorphic/273/1/ch/a/110/1"]
"2-273-273.125-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.125"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2032082395472503	0	1.56447021090035348653554707857	["ModularForm/GL2/Q/holomorphic/273/1/o/a/125/1", "ArtinRepresentation/2.273.8t17.c.a"]
"2-273-273.125-c0-0-1"	0.3691134628387451	0.13624474844880965	2	273	"273.125"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.046791760452749714	0	2.09530318620797307391385453868	["ModularForm/GL2/Q/holomorphic/273/1/o/b/125/1", "ArtinRepresentation/2.273.8t17.d.b"]
"2-273-273.179-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.179"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.1545392387471269	0	1.32217805949075965076820073204	["ModularForm/GL2/Q/holomorphic/273/1/x/a/179/1"]
"2-273-273.191-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.191"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.3007326674973564	0	1.46701386008400956752707974800	["ModularForm/GL2/Q/holomorphic/273/1/bm/b/191/1", "ArtinRepresentation/2.273.16t60.a.c"]
"2-273-273.191-c0-0-1"	0.3691134628387451	0.13624474844880965	2	273	"273.191"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.05073266749735639	0	2.08137434854167615783808386896	["ModularForm/GL2/Q/holomorphic/273/1/bm/a/191/1", "ArtinRepresentation/2.273.6t5.c.b"]
"2-273-273.191-c0-0-2"	0.3691134628387451	0.13624474844880965	2	273	"273.191"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.1992673325026436	0	3.09985039398409065577220373210	["ModularForm/GL2/Q/holomorphic/273/1/bm/b/191/2", "ArtinRepresentation/2.273.16t60.a.b"]
"2-273-273.206-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.206"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.14034814413035418	0	2.73138368709904615285565722032	["ModularForm/GL2/Q/holomorphic/273/1/ch/a/206/1"]
"2-273-273.212-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.212"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.1545392387471269	0	2.38374102043130098665145034659	["ModularForm/GL2/Q/holomorphic/273/1/x/a/212/1"]
"2-273-273.215-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.215"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.26606833496414645	0	3.06952599328811000904381042252	["ModularForm/GL2/Q/holomorphic/273/1/ch/a/215/1"]
"2-273-273.227-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.227"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.06930594976175361	0	2.07231612362859248253041835300	["ModularForm/GL2/Q/holomorphic/273/1/bs/a/227/1"]
"2-273-273.23-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.23"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.1586211415322603	0	2.63246840570324538629877096217	["ModularForm/GL2/Q/holomorphic/273/1/bp/a/23/1"]
"2-273-273.236-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.236"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.024277571143745815	0	2.59829944923730075654488430825	["ModularForm/GL2/Q/holomorphic/273/1/bs/a/236/1"]
"2-273-273.263-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.263"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.1992673325026436	0	1.91498777277529916463850108324	["ModularForm/GL2/Q/holomorphic/273/1/bm/b/263/2", "ArtinRepresentation/2.273.16t60.a.a"]
"2-273-273.263-c0-0-1"	0.3691134628387451	0.13624474844880965	2	273	"273.263"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.05073266749735639	0	2.46618336311894048396802786649	["ModularForm/GL2/Q/holomorphic/273/1/bm/a/263/1", "ArtinRepresentation/2.273.6t5.c.a"]
"2-273-273.263-c0-0-2"	0.3691134628387451	0.13624474844880965	2	273	"273.263"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.3007326674973564	0	2.55379765570476334429151299596	["ModularForm/GL2/Q/holomorphic/273/1/bm/b/263/1", "ArtinRepresentation/2.273.16t60.a.d"]
"2-273-273.59-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.59"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.024277571143745815	0	2.12255267909996772894638217098	["ModularForm/GL2/Q/holomorphic/273/1/bs/a/59/1"]
"2-273-273.74-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.74"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.28055971444341027	0	1.56870668635183199225822516103	["ModularForm/GL2/Q/holomorphic/273/1/s/b/74/2"]
"2-273-273.74-c0-0-1"	0.3691134628387451	0.13624474844880965	2	273	"273.74"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.13610695222325642	0	2.54094456523031923158939771246	["ModularForm/GL2/Q/holomorphic/273/1/s/a/74/1", "ArtinRepresentation/2.273.6t5.d.b"]
"2-273-273.74-c0-0-2"	0.3691134628387451	0.13624474844880965	2	273	"273.74"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.21944028555658976	0	2.75991142853910062421931303486	["ModularForm/GL2/Q/holomorphic/273/1/s/b/74/1"]
"2-273-273.80-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.80"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.26606833496414645	0	1.16752905340420434536210547571	["ModularForm/GL2/Q/holomorphic/273/1/ch/a/80/1"]
"2-273-273.83-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.83"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.046791760452749714	0	2.00358764672848900001252726229	["ModularForm/GL2/Q/holomorphic/273/1/o/b/83/1", "ArtinRepresentation/2.273.8t17.d.a"]
"2-273-273.83-c0-0-1"	0.3691134628387451	0.13624474844880965	2	273	"273.83"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2032082395472503	0	2.88086612501724707981685940959	["ModularForm/GL2/Q/holomorphic/273/1/o/a/83/1", "ArtinRepresentation/2.273.8t17.c.b"]
"2-273-273.89-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.89"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.06930594976175361	0	1.50214803518883393025586550229	["ModularForm/GL2/Q/holomorphic/273/1/bs/a/89/1"]
"2-273-273.95-c0-0-0"	0.3691134628387451	0.13624474844880965	2	273	"273.95"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.1586211415322603	0	1.55532597752984363062862192735	["ModularForm/GL2/Q/holomorphic/273/1/bp/a/95/1"]
"2-273-1.1-c1-0-0"	1.4764538513549808	2.1799159751809554	2	273	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.13463035130736646229008723762	["ModularForm/GL2/Q/holomorphic/273/2/a/e/1/1"]
"2-273-1.1-c1-0-1"	1.4764538513549808	2.1799159751809554	2	273	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.13885815283392249125382284398	["ModularForm/GL2/Q/holomorphic/273/2/a/c/1/1"]
"2-273-1.1-c1-0-10"	1.4764538513549808	2.1799159751809554	2	273	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	3.17105547427276418647900894383	["ModularForm/GL2/Q/holomorphic/273/2/a/d/1/3"]
"2-273-1.1-c1-0-2"	1.4764538513549808	2.1799159751809554	2	273	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.53473120245872328500297646797	["ModularForm/GL2/Q/holomorphic/273/2/a/e/1/2"]
"2-273-1.1-c1-0-3"	1.4764538513549808	2.1799159751809554	2	273	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.80095072107294184984518087908	["ModularForm/GL2/Q/holomorphic/273/2/a/d/1/1"]
"2-273-1.1-c1-0-4"	1.4764538513549808	2.1799159751809554	2	273	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.90263358533576758230802068213	["EllipticCurve/Q/273/a", "ModularForm/GL2/Q/holomorphic/273/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/273/2/a/a"]
"2-273-1.1-c1-0-5"	1.4764538513549808	2.1799159751809554	2	273	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.06303734463239796355681587821	["ModularForm/GL2/Q/holomorphic/273/2/a/e/1/3"]
"2-273-1.1-c1-0-6"	1.4764538513549808	2.1799159751809554	2	273	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.14157049850050474625482236726	["ModularForm/GL2/Q/holomorphic/273/2/a/c/1/2"]
"2-273-1.1-c1-0-7"	1.4764538513549808	2.1799159751809554	2	273	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.32837515651647384683207389232	["ModularForm/GL2/Q/holomorphic/273/2/a/d/1/2"]
"2-273-1.1-c1-0-8"	1.4764538513549808	2.1799159751809554	2	273	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	2.38895973908794646217186104367	["EllipticCurve/Q/273/b", "ModularForm/GL2/Q/holomorphic/273/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/273/2/a/b"]
"2-273-1.1-c1-0-9"	1.4764538513549808	2.1799159751809554	2	273	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.55677068828348872473276058447	["ModularForm/GL2/Q/holomorphic/273/2/a/e/1/4"]
"2-273-13.10-c1-0-0"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.40527383929264293	0	0.18461574104759830359332073419	["ModularForm/GL2/Q/holomorphic/273/2/bd/b/127/2"]
"2-273-13.10-c1-0-1"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.31248600444104585	0	0.54162034020040983132923793345	["ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/5"]
"2-273-13.10-c1-0-10"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1673422726081516	0	1.71586109997505953043835547531	["ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/4"]
"2-273-13.10-c1-0-11"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.37545365071087833	0	2.27668666330297373085927859866	["ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/3"]
"2-273-13.10-c1-0-12"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1326263939416967	0	2.44775914028182781655924382732	["ModularForm/GL2/Q/holomorphic/273/2/bd/b/127/7"]
"2-273-13.10-c1-0-13"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1460785050089644	0	2.67669109315649238727974834335	["ModularForm/GL2/Q/holomorphic/273/2/bd/b/127/8"]
"2-273-13.10-c1-0-14"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.26394824772285813	0	2.87088073098854890033205704952	["ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/8"]
"2-273-13.10-c1-0-15"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3078407372041368	0	3.05453953878134623888870215124	["ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/7"]
"2-273-13.10-c1-0-2"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.451277996988992	0	0.73181851413728863054185296625	["ModularForm/GL2/Q/holomorphic/273/2/bd/b/127/4"]
"2-273-13.10-c1-0-3"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.21104189179227245	0	0.841896706745642262145486861644	["ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/2"]
"2-273-13.10-c1-0-4"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4603260985436789	0	0.888676111604621731149161307124	["ModularForm/GL2/Q/holomorphic/273/2/bd/b/127/1"]
"2-273-13.10-c1-0-5"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.11348609705989612	0	1.10124861593729235968586562643	["ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/6"]
"2-273-13.10-c1-0-6"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.026510987832323	0	1.28555986199851768307966132343	["ModularForm/GL2/Q/holomorphic/273/2/bd/a/127/1"]
"2-273-13.10-c1-0-7"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.14115206017656806	0	1.30027106143439142890700495617	["ModularForm/GL2/Q/holomorphic/273/2/bd/b/127/5"]
"2-273-13.10-c1-0-8"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.09803339592004857	0	1.42153645387276627944332598064	["ModularForm/GL2/Q/holomorphic/273/2/bd/b/127/6"]
"2-273-13.10-c1-0-9"	1.4764538513549808	2.1799159751809554	2	273	"13.10"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.02910728382888315	0	1.56212433082419475863969869174	["ModularForm/GL2/Q/holomorphic/273/2/bd/b/127/3"]
"2-273-13.12-c1-0-0"	1.4764538513549808	2.1799159751809554	2	273	"13.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.002226748877492682	0	0.58587456943888545848658042567	["ModularForm/GL2/Q/holomorphic/273/2/c/c/64/1"]
"2-273-13.12-c1-0-1"	1.4764538513549808	2.1799159751809554	2	273	"13.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3206333332634313	0	0.61110081856408412835972233806	["ModularForm/GL2/Q/holomorphic/273/2/c/c/64/7"]
"2-273-13.12-c1-0-10"	1.4764538513549808	2.1799159751809554	2	273	"13.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.01374990700906781	0	1.97851998649247369470744504369	["ModularForm/GL2/Q/holomorphic/273/2/c/b/64/4"]
"2-273-13.12-c1-0-11"	1.4764538513549808	2.1799159751809554	2	273	"13.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.19443110971499797	0	2.12247920713668402735662001322	["ModularForm/GL2/Q/holomorphic/273/2/c/c/64/4"]
"2-273-13.12-c1-0-12"	1.4764538513549808	2.1799159751809554	2	273	"13.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.06737691467404182	0	2.14084616359296801334897363508	["ModularForm/GL2/Q/holomorphic/273/2/c/b/64/5"]
"2-273-13.12-c1-0-13"	1.4764538513549808	2.1799159751809554	2	273	"13.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.39721052857047345	0	2.40523797121673712154553993532	["ModularForm/GL2/Q/holomorphic/273/2/c/b/64/1"]
"2-273-13.12-c1-0-14"	1.4764538513549808	2.1799159751809554	2	273	"13.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4064164790945006	0	2.65376140931775816657558005927	["ModularForm/GL2/Q/holomorphic/273/2/c/a/64/1"]
"2-273-13.12-c1-0-15"	1.4764538513549808	2.1799159751809554	2	273	"13.12"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3206333332634313	0	3.21293486685804373081758743109	["ModularForm/GL2/Q/holomorphic/273/2/c/c/64/2"]
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"2-273-1.1-c11-0-45"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.68957815567530466681059461554	["ModularForm/GL2/Q/holomorphic/273/12/a/c/1/4"]
"2-273-1.1-c11-0-46"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.69159547949461129543697052363	["ModularForm/GL2/Q/holomorphic/273/12/a/f/1/10"]
"2-273-1.1-c11-0-47"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.70937048272279372725545318269	["ModularForm/GL2/Q/holomorphic/273/12/a/g/1/8"]
"2-273-1.1-c11-0-48"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.71795101894197198444647507905	["ModularForm/GL2/Q/holomorphic/273/12/a/g/1/11"]
"2-273-1.1-c11-0-49"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.73298537775691955260403971308	["ModularForm/GL2/Q/holomorphic/273/12/a/f/1/15"]
"2-273-1.1-c11-0-5"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.19189287893909676147308293164	["ModularForm/GL2/Q/holomorphic/273/12/a/h/1/9"]
"2-273-1.1-c11-0-50"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.74064887634526411711988578704	["ModularForm/GL2/Q/holomorphic/273/12/a/f/1/12"]
"2-273-1.1-c11-0-51"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.74118462759096183630361734406	["ModularForm/GL2/Q/holomorphic/273/12/a/e/1/2"]
"2-273-1.1-c11-0-52"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.74479967259017220814927949251	["ModularForm/GL2/Q/holomorphic/273/12/a/c/1/7"]
"2-273-1.1-c11-0-53"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.75718915904395943242013629168	["ModularForm/GL2/Q/holomorphic/273/12/a/f/1/5"]
"2-273-1.1-c11-0-54"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.75720425267183180441608037421	["ModularForm/GL2/Q/holomorphic/273/12/a/c/1/11"]
"2-273-1.1-c11-0-55"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.76413613479114461661253359413	["ModularForm/GL2/Q/holomorphic/273/12/a/g/1/4"]
"2-273-1.1-c11-0-56"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.76461410711648120168039007057	["ModularForm/GL2/Q/holomorphic/273/12/a/e/1/5"]
"2-273-1.1-c11-0-57"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.795376565750484546912950739255	["ModularForm/GL2/Q/holomorphic/273/12/a/c/1/1"]
"2-273-1.1-c11-0-58"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.796024854460543009207080111858	["ModularForm/GL2/Q/holomorphic/273/12/a/d/1/7"]
"2-273-1.1-c11-0-59"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.805566608209161363404181613537	["ModularForm/GL2/Q/holomorphic/273/12/a/g/1/1"]
"2-273-1.1-c11-0-6"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.20454212504644437537904377145	["ModularForm/GL2/Q/holomorphic/273/12/a/b/1/5"]
"2-273-1.1-c11-0-60"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.814342045068644457009225901288	["ModularForm/GL2/Q/holomorphic/273/12/a/e/1/17"]
"2-273-1.1-c11-0-61"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.843528896181341807989421086629	["ModularForm/GL2/Q/holomorphic/273/12/a/e/1/10"]
"2-273-1.1-c11-0-62"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.852935361431687585612412212390	["ModularForm/GL2/Q/holomorphic/273/12/a/f/1/13"]
"2-273-1.1-c11-0-63"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.853016380203428917914134948167	["ModularForm/GL2/Q/holomorphic/273/12/a/d/1/8"]
"2-273-1.1-c11-0-64"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.855552662882660601602544755775	["ModularForm/GL2/Q/holomorphic/273/12/a/d/1/1"]
"2-273-1.1-c11-0-65"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.868464964515303543501463300623	["ModularForm/GL2/Q/holomorphic/273/12/a/h/1/10"]
"2-273-1.1-c11-0-66"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.872807889515845925953456750795	["ModularForm/GL2/Q/holomorphic/273/12/a/c/1/9"]
"2-273-1.1-c11-0-67"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.882119619709009661842342462700	["ModularForm/GL2/Q/holomorphic/273/12/a/h/1/3"]
"2-273-1.1-c11-0-68"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.896543421024813254367088814593	["ModularForm/GL2/Q/holomorphic/273/12/a/b/1/14"]
"2-273-1.1-c11-0-69"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.901258631996339985708329465794	["ModularForm/GL2/Q/holomorphic/273/12/a/f/1/1"]
"2-273-1.1-c11-0-7"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.28020698937776541065849685501	["ModularForm/GL2/Q/holomorphic/273/12/a/f/1/4"]
"2-273-1.1-c11-0-70"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.904705683367168439746884086236	["ModularForm/GL2/Q/holomorphic/273/12/a/h/1/13"]
"2-273-1.1-c11-0-71"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.905511731543894317599664107178	["ModularForm/GL2/Q/holomorphic/273/12/a/g/1/12"]
"2-273-1.1-c11-0-72"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.915286894835724490841551986996	["ModularForm/GL2/Q/holomorphic/273/12/a/a/1/5"]
"2-273-1.1-c11-0-73"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.921712172108827491866747233593	["ModularForm/GL2/Q/holomorphic/273/12/a/f/1/8"]
"2-273-1.1-c11-0-74"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.926713782513340663230191470530	["ModularForm/GL2/Q/holomorphic/273/12/a/d/1/11"]
"2-273-1.1-c11-0-75"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.927386017637407700309289859839	["ModularForm/GL2/Q/holomorphic/273/12/a/g/1/3"]
"2-273-1.1-c11-0-76"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.929863401278693858495496339291	["ModularForm/GL2/Q/holomorphic/273/12/a/g/1/9"]
"2-273-1.1-c11-0-77"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.933884221076162771319191758558	["ModularForm/GL2/Q/holomorphic/273/12/a/c/1/6"]
"2-273-1.1-c11-0-78"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.945342638312064250656540050646	["ModularForm/GL2/Q/holomorphic/273/12/a/c/1/2"]
"2-273-1.1-c11-0-79"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.949065967146797810703919260956	["ModularForm/GL2/Q/holomorphic/273/12/a/c/1/5"]
"2-273-1.1-c11-0-8"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.28781378475020780189693888264	["ModularForm/GL2/Q/holomorphic/273/12/a/b/1/10"]
"2-273-1.1-c11-0-80"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.956131217881292619051879801057	["ModularForm/GL2/Q/holomorphic/273/12/a/d/1/4"]
"2-273-1.1-c11-0-81"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.969372516267062448259433340463	["ModularForm/GL2/Q/holomorphic/273/12/a/h/1/15"]
"2-273-1.1-c11-0-82"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.987225158667652923752220280200	["ModularForm/GL2/Q/holomorphic/273/12/a/a/1/9"]
"2-273-1.1-c11-0-83"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.991552252685637497132713805803	["ModularForm/GL2/Q/holomorphic/273/12/a/g/1/2"]
"2-273-1.1-c11-0-84"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.996682732690287624449270674774	["ModularForm/GL2/Q/holomorphic/273/12/a/g/1/5"]
"2-273-1.1-c11-0-85"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	0.996964415531094037690475223792	["ModularForm/GL2/Q/holomorphic/273/12/a/g/1/15"]
"2-273-1.1-c11-0-86"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	1.00924716326798379494140186656	["ModularForm/GL2/Q/holomorphic/273/12/a/f/1/16"]
"2-273-1.1-c11-0-87"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	1.01712165395852818063807569237	["ModularForm/GL2/Q/holomorphic/273/12/a/e/1/15"]
"2-273-1.1-c11-0-88"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	1.04107620639620857554249843954	["ModularForm/GL2/Q/holomorphic/273/12/a/g/1/10"]
"2-273-1.1-c11-0-89"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	1.04944235155310732884103275160	["ModularForm/GL2/Q/holomorphic/273/12/a/d/1/3"]
"2-273-1.1-c11-0-9"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	0.31701065075548840753615922087	["ModularForm/GL2/Q/holomorphic/273/12/a/f/1/11"]
"2-273-1.1-c11-0-90"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	1.06340309130723141463756837986	["ModularForm/GL2/Q/holomorphic/273/12/a/a/1/3"]
"2-273-1.1-c11-0-91"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	1.07128306377459021710067508715	["ModularForm/GL2/Q/holomorphic/273/12/a/a/1/1"]
"2-273-1.1-c11-0-92"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	1.07961153584622090385564780461	["ModularForm/GL2/Q/holomorphic/273/12/a/c/1/10"]
"2-273-1.1-c11-0-93"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	1.10699590734807624390120320581	["ModularForm/GL2/Q/holomorphic/273/12/a/g/1/13"]
"2-273-1.1-c11-0-94"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	1.10939622136731829573885331692	["ModularForm/GL2/Q/holomorphic/273/12/a/d/1/10"]
"2-273-1.1-c11-0-95"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	1.11336482591372665662260021118	["ModularForm/GL2/Q/holomorphic/273/12/a/e/1/16"]
"2-273-1.1-c11-0-96"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	1.11368883144490321849977467418	["ModularForm/GL2/Q/holomorphic/273/12/a/h/1/17"]
"2-273-1.1-c11-0-97"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	1.12064611471908608420367738852	["ModularForm/GL2/Q/holomorphic/273/12/a/a/1/6"]
"2-273-1.1-c11-0-98"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.0	0	1.14183910083794776243190226778	["ModularForm/GL2/Q/holomorphic/273/12/a/f/1/18"]
"2-273-1.1-c11-0-99"	14.483013784871153	209.75768829276782	2	273	"1.1"	[]	[[5.5, 0.0]]	11	true	true	false	true	0.5	1	1.15525680559478737048857222368	["ModularForm/GL2/Q/holomorphic/273/12/a/g/1/7"]


# 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).


