# lfunc_search downloaded from the LMFDB on 26 July 2026.
# Search link: https://www.lmfdb.org/L/2/1150/5.4
# Query "{'degree': 2, 'conductor': 1150}" returned 490 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.



"2-1150-1.1-c1-0-0"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.47417773513251705065752782599	["ModularForm/GL2/Q/holomorphic/1150/2/a/q/1/2"]
"2-1150-1.1-c1-0-1"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.52858867159432612116623557094	["ModularForm/GL2/Q/holomorphic/1150/2/a/r/1/1"]
"2-1150-1.1-c1-0-10"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.25111557919532713809209952606	["ModularForm/GL2/Q/holomorphic/1150/2/a/q/1/3"]
"2-1150-1.1-c1-0-11"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.27211587416571166300629431866	["ModularForm/GL2/Q/holomorphic/1150/2/a/s/1/2"]
"2-1150-1.1-c1-0-12"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.28646998934505136843688398432	["EllipticCurve/Q/1150/c", "ModularForm/GL2/Q/holomorphic/1150/2/a/c/1/1", "ModularForm/GL2/Q/holomorphic/1150/2/a/c"]
"2-1150-1.1-c1-0-13"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.35564478109443112808861515260	["EllipticCurve/Q/1150/h", "ModularForm/GL2/Q/holomorphic/1150/2/a/h/1/1", "ModularForm/GL2/Q/holomorphic/1150/2/a/h"]
"2-1150-1.1-c1-0-14"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.36787880357210621874848810705	["ModularForm/GL2/Q/holomorphic/1150/2/a/k/1/1"]
"2-1150-1.1-c1-0-15"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.38731647418095401445587881976	["EllipticCurve/Q/1150/a", "ModularForm/GL2/Q/holomorphic/1150/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/1150/2/a/a"]
"2-1150-1.1-c1-0-16"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.46896043750359807264804449626	["ModularForm/GL2/Q/holomorphic/1150/2/a/j/1/1"]
"2-1150-1.1-c1-0-17"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.52598777083604923783702801600	["EllipticCurve/Q/1150/d", "ModularForm/GL2/Q/holomorphic/1150/2/a/d/1/1", "ModularForm/GL2/Q/holomorphic/1150/2/a/d"]
"2-1150-1.1-c1-0-18"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.54300660971579174399171142752	["ModularForm/GL2/Q/holomorphic/1150/2/a/s/1/3"]
"2-1150-1.1-c1-0-19"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.57561527725012579569170153590	["ModularForm/GL2/Q/holomorphic/1150/2/a/p/1/2"]
"2-1150-1.1-c1-0-2"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.59523310370207552611287165788	["ModularForm/GL2/Q/holomorphic/1150/2/a/r/1/2"]
"2-1150-1.1-c1-0-20"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	1.59025346037222054836732618832	["EllipticCurve/Q/1150/i", "ModularForm/GL2/Q/holomorphic/1150/2/a/i/1/1", "ModularForm/GL2/Q/holomorphic/1150/2/a/i"]
"2-1150-1.1-c1-0-21"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.62634003225036130509439070344	["EllipticCurve/Q/1150/e", "ModularForm/GL2/Q/holomorphic/1150/2/a/e/1/1", "ModularForm/GL2/Q/holomorphic/1150/2/a/e"]
"2-1150-1.1-c1-0-22"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.65439286162488817182646439480	["ModularForm/GL2/Q/holomorphic/1150/2/a/m/1/1"]
"2-1150-1.1-c1-0-23"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.73086645546949651249292237371	["ModularForm/GL2/Q/holomorphic/1150/2/a/o/1/2"]
"2-1150-1.1-c1-0-24"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.76221570872595072155969042059	["ModularForm/GL2/Q/holomorphic/1150/2/a/l/1/1"]
"2-1150-1.1-c1-0-25"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.78059550635149144342141258246	["ModularForm/GL2/Q/holomorphic/1150/2/a/j/1/2"]
"2-1150-1.1-c1-0-26"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	1.85622918971842028675810874009	["EllipticCurve/Q/1150/f", "ModularForm/GL2/Q/holomorphic/1150/2/a/f/1/1", "ModularForm/GL2/Q/holomorphic/1150/2/a/f"]
"2-1150-1.1-c1-0-27"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.91124882116910577009098346391	["ModularForm/GL2/Q/holomorphic/1150/2/a/s/1/4"]
"2-1150-1.1-c1-0-28"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.94037600691710858111368295286	["ModularForm/GL2/Q/holomorphic/1150/2/a/k/1/2"]
"2-1150-1.1-c1-0-29"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.95836919282468872674729701641	["ModularForm/GL2/Q/holomorphic/1150/2/a/l/1/2"]
"2-1150-1.1-c1-0-3"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.891204744434295621705736593891	["EllipticCurve/Q/1150/b", "ModularForm/GL2/Q/holomorphic/1150/2/a/b/1/1", "ModularForm/GL2/Q/holomorphic/1150/2/a/b"]
"2-1150-1.1-c1-0-30"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	1.98607894827714731779788254404	["ModularForm/GL2/Q/holomorphic/1150/2/a/n/1/1"]
"2-1150-1.1-c1-0-31"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.32756097422350121058519862216	["ModularForm/GL2/Q/holomorphic/1150/2/a/m/1/2"]
"2-1150-1.1-c1-0-32"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.34660090484329951311745814004	["ModularForm/GL2/Q/holomorphic/1150/2/a/n/1/2"]
"2-1150-1.1-c1-0-33"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.38465115805353625308496539318	["EllipticCurve/Q/1150/g", "ModularForm/GL2/Q/holomorphic/1150/2/a/g/1/1", "ModularForm/GL2/Q/holomorphic/1150/2/a/g"]
"2-1150-1.1-c1-0-4"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.921654928992955515374758864058	["ModularForm/GL2/Q/holomorphic/1150/2/a/r/1/3"]
"2-1150-1.1-c1-0-5"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.926352951191884097594504054965	["ModularForm/GL2/Q/holomorphic/1150/2/a/o/1/1"]
"2-1150-1.1-c1-0-6"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.962055933637588161213534009753	["ModularForm/GL2/Q/holomorphic/1150/2/a/s/1/1"]
"2-1150-1.1-c1-0-7"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.988449079867128240513664410925	["ModularForm/GL2/Q/holomorphic/1150/2/a/q/1/1"]
"2-1150-1.1-c1-0-8"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.08862002845527615608999315659	["ModularForm/GL2/Q/holomorphic/1150/2/a/p/1/1"]
"2-1150-1.1-c1-0-9"	3.03031289348926	9.182796232447249	2	1150	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.19072978266894994161330839974	["ModularForm/GL2/Q/holomorphic/1150/2/a/r/1/4"]
"2-1150-115.22-c1-0-0"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4409752625358031	0	0.03430109588745761739466833721	["ModularForm/GL2/Q/holomorphic/1150/2/e/c/1057/1"]
"2-1150-115.22-c1-0-1"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.33302674238490554	0	0.03800909347313345600066192224	["ModularForm/GL2/Q/holomorphic/1150/2/e/f/1057/3"]
"2-1150-115.22-c1-0-10"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4741496361404376	0	0.40485668785958006269189348062	["ModularForm/GL2/Q/holomorphic/1150/2/e/b/1057/3"]
"2-1150-115.22-c1-0-11"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.047691286113858054	0	0.59917987331130324971714845611	["ModularForm/GL2/Q/holomorphic/1150/2/e/d/1057/3"]
"2-1150-115.22-c1-0-12"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3204841639569977	0	0.63196118610792884909149371762	["ModularForm/GL2/Q/holomorphic/1150/2/e/e/1057/7"]
"2-1150-115.22-c1-0-13"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.059024737464196904	0	0.65510549360242059568550023036	["ModularForm/GL2/Q/holomorphic/1150/2/e/b/1057/2"]
"2-1150-115.22-c1-0-14"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.17565918493288685	0	0.65881067148119718298267406416	["ModularForm/GL2/Q/holomorphic/1150/2/e/a/1057/1"]
"2-1150-115.22-c1-0-15"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.34964217268477904	0	0.68875702258215341444403455925	["ModularForm/GL2/Q/holomorphic/1150/2/e/c/1057/3"]
"2-1150-115.22-c1-0-16"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2720136703511156	0	0.70452498653383754493034288117	["ModularForm/GL2/Q/holomorphic/1150/2/e/f/1057/7"]
"2-1150-115.22-c1-0-17"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.0033076448682189323	0	0.804805920804619978619137419554	["ModularForm/GL2/Q/holomorphic/1150/2/e/e/1057/1"]
"2-1150-115.22-c1-0-18"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3297383945383456	0	0.859823007528611115377045408899	["ModularForm/GL2/Q/holomorphic/1150/2/e/d/1057/6"]
"2-1150-115.22-c1-0-19"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.01003343807337185	0	0.919239604298989622892903143740	["ModularForm/GL2/Q/holomorphic/1150/2/e/f/1057/2"]
"2-1150-115.22-c1-0-2"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3830868985802543	0	0.17445733770296326029142663286	["ModularForm/GL2/Q/holomorphic/1150/2/e/e/1057/6"]
"2-1150-115.22-c1-0-20"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.16854541532764	0	1.02387638948887752971806428294	["ModularForm/GL2/Q/holomorphic/1150/2/e/d/1057/8"]
"2-1150-115.22-c1-0-21"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.12477144278563473	0	1.06604561344271333853877089250	["ModularForm/GL2/Q/holomorphic/1150/2/e/f/1057/4"]
"2-1150-115.22-c1-0-22"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3458054791763323	0	1.07797198455628186385186724583	["ModularForm/GL2/Q/holomorphic/1150/2/e/f/1057/1"]
"2-1150-115.22-c1-0-23"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1214830949390747	0	1.22221007665860524294360924889	["ModularForm/GL2/Q/holomorphic/1150/2/e/d/1057/5"]
"2-1150-115.22-c1-0-24"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.07793732856590546	0	1.27279920865189364957743694216	["ModularForm/GL2/Q/holomorphic/1150/2/e/a/1057/4"]
"2-1150-115.22-c1-0-25"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.23523292863898027	0	1.33262057621065509256559078151	["ModularForm/GL2/Q/holomorphic/1150/2/e/c/1057/2"]
"2-1150-115.22-c1-0-26"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05097963396041808	0	1.36964871302101826652147261881	["ModularForm/GL2/Q/holomorphic/1150/2/e/f/1057/6"]
"2-1150-115.22-c1-0-27"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.24233722415285663	0	1.37666516485162184250528577807	["ModularForm/GL2/Q/holomorphic/1150/2/e/d/1057/2"]
"2-1150-115.22-c1-0-28"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.0033076448682189323	0	1.39790039835585083222957733075	["ModularForm/GL2/Q/holomorphic/1150/2/e/e/1057/8"]
"2-1150-115.22-c1-0-29"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3518673761076702	0	1.44755742330506947529198856065	["ModularForm/GL2/Q/holomorphic/1150/2/e/a/1057/2"]
"2-1150-115.22-c1-0-3"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.25414551974068883	0	0.18844998978468210225886696380	["ModularForm/GL2/Q/holomorphic/1150/2/e/a/1057/3"]
"2-1150-115.22-c1-0-30"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.025850363859562436	0	1.47362690077764815662349646143	["ModularForm/GL2/Q/holomorphic/1150/2/e/c/1057/4"]
"2-1150-115.22-c1-0-31"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3830868985802543	0	1.55768087306258218572501767400	["ModularForm/GL2/Q/holomorphic/1150/2/e/e/1057/3"]
"2-1150-115.22-c1-0-32"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2931212925945291	0	1.58934429434920166787314380576	["ModularForm/GL2/Q/holomorphic/1150/2/e/e/1057/4"]
"2-1150-115.22-c1-0-33"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.0637583707518448	0	1.67870080256529324008335900654	["ModularForm/GL2/Q/holomorphic/1150/2/e/f/1057/8"]
"2-1150-115.22-c1-0-34"	3.03031289348926	9.182796232447249	2	1150	"115.22"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.15035782731522096	0	1.95008719699737186397160142424	["ModularForm/GL2/Q/holomorphic/1150/2/e/b/1057/4"]
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"2-1150-5.4-c3-0-56"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.42620819117478337	0	0.835254387052923671624045068930	["ModularForm/GL2/Q/holomorphic/1150/4/b/s/599/1"]
"2-1150-5.4-c3-0-57"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.07379180882521663	0	0.848989906706030922468774433118	["ModularForm/GL2/Q/holomorphic/1150/4/b/p/599/6"]
"2-1150-5.4-c3-0-58"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.07379180882521663	0	0.854894285522365722715373442220	["ModularForm/GL2/Q/holomorphic/1150/4/b/p/599/10"]
"2-1150-5.4-c3-0-59"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.17620819117478337	0	0.876654422280860193196099420729	["ModularForm/GL2/Q/holomorphic/1150/4/b/l/599/4"]
"2-1150-5.4-c3-0-6"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.17620819117478337	0	0.12034394608747334737632088644	["ModularForm/GL2/Q/holomorphic/1150/4/b/c/599/1"]
"2-1150-5.4-c3-0-60"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.17620819117478337	0	0.878206225962369372861895647440	["ModularForm/GL2/Q/holomorphic/1150/4/b/o/599/4"]
"2-1150-5.4-c3-0-61"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.17620819117478337	0	0.882113993166037752937518040873	["ModularForm/GL2/Q/holomorphic/1150/4/b/o/599/3"]
"2-1150-5.4-c3-0-62"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.32379180882521663	0	0.897248456880566907557979659947	["ModularForm/GL2/Q/holomorphic/1150/4/b/k/599/1"]
"2-1150-5.4-c3-0-63"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.07379180882521663	0	0.903953447924548595143975502573	["ModularForm/GL2/Q/holomorphic/1150/4/b/r/599/5"]
"2-1150-5.4-c3-0-64"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.32379180882521663	0	0.906459372450286294349796373993	["ModularForm/GL2/Q/holomorphic/1150/4/b/i/599/4"]
"2-1150-5.4-c3-0-65"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.07379180882521663	0	0.941624383233353930270901723271	["ModularForm/GL2/Q/holomorphic/1150/4/b/r/599/9"]
"2-1150-5.4-c3-0-66"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.07379180882521663	0	0.972895003448224875065122154906	["ModularForm/GL2/Q/holomorphic/1150/4/b/p/599/8"]
"2-1150-5.4-c3-0-67"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.32379180882521663	0	0.978073184713639528164462533027	["ModularForm/GL2/Q/holomorphic/1150/4/b/n/599/3"]
"2-1150-5.4-c3-0-68"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.07379180882521663	0	0.991412859247281376712393853845	["ModularForm/GL2/Q/holomorphic/1150/4/b/p/599/9"]
"2-1150-5.4-c3-0-69"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.32379180882521663	0	1.00386904827594000664747202837	["ModularForm/GL2/Q/holomorphic/1150/4/b/m/599/5"]
"2-1150-5.4-c3-0-7"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.32379180882521663	0	0.13110793077978796814127002882	["ModularForm/GL2/Q/holomorphic/1150/4/b/m/599/8"]
"2-1150-5.4-c3-0-70"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.42620819117478337	0	1.03562842730791786220130780942	["ModularForm/GL2/Q/holomorphic/1150/4/b/s/599/2"]
"2-1150-5.4-c3-0-71"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.17620819117478337	0	1.05808425363997772378796888485	["ModularForm/GL2/Q/holomorphic/1150/4/b/o/599/2"]
"2-1150-5.4-c3-0-72"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.17620819117478337	0	1.05999657720044858822879493193	["ModularForm/GL2/Q/holomorphic/1150/4/b/e/599/2"]
"2-1150-5.4-c3-0-73"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.42620819117478337	0	1.07097172665865397480658694150	["ModularForm/GL2/Q/holomorphic/1150/4/b/s/599/3"]
"2-1150-5.4-c3-0-74"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.17620819117478337	0	1.09271194208669265942416787122	["ModularForm/GL2/Q/holomorphic/1150/4/b/h/599/2"]
"2-1150-5.4-c3-0-75"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.32379180882521663	0	1.11306784095856652707275930997	["ModularForm/GL2/Q/holomorphic/1150/4/b/n/599/4"]
"2-1150-5.4-c3-0-76"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.32379180882521663	0	1.11412862230001541476485473563	["ModularForm/GL2/Q/holomorphic/1150/4/b/n/599/2"]
"2-1150-5.4-c3-0-77"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.07379180882521663	0	1.12224493871462529914776851255	["ModularForm/GL2/Q/holomorphic/1150/4/b/r/599/8"]
"2-1150-5.4-c3-0-78"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.07379180882521663	0	1.15927084695269911018827039854	["ModularForm/GL2/Q/holomorphic/1150/4/b/g/599/2"]
"2-1150-5.4-c3-0-79"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.42620819117478337	0	1.23141058573424199767128400408	["ModularForm/GL2/Q/holomorphic/1150/4/b/q/599/2"]
"2-1150-5.4-c3-0-8"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.07379180882521663	0	0.13583000218548890710904027847	["ModularForm/GL2/Q/holomorphic/1150/4/b/r/599/10"]
"2-1150-5.4-c3-0-80"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.42620819117478337	0	1.23162587101440826475761795410	["ModularForm/GL2/Q/holomorphic/1150/4/b/s/599/5"]
"2-1150-5.4-c3-0-81"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.17620819117478337	0	1.26849416123214427271909840127	["ModularForm/GL2/Q/holomorphic/1150/4/b/c/599/2"]
"2-1150-5.4-c3-0-82"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.32379180882521663	0	1.27571558097792040737598978161	["ModularForm/GL2/Q/holomorphic/1150/4/b/j/599/3"]
"2-1150-5.4-c3-0-83"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.32379180882521663	0	1.27815635221946347534161152726	["ModularForm/GL2/Q/holomorphic/1150/4/b/k/599/2"]
"2-1150-5.4-c3-0-84"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.42620819117478337	0	1.30858669601261720639310279419	["ModularForm/GL2/Q/holomorphic/1150/4/b/s/599/4"]
"2-1150-5.4-c3-0-85"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.42620819117478337	0	1.31814206919265547499885288367	["ModularForm/GL2/Q/holomorphic/1150/4/b/q/599/6"]
"2-1150-5.4-c3-0-86"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.32379180882521663	0	1.33589800648295368466652250812	["ModularForm/GL2/Q/holomorphic/1150/4/b/m/599/6"]
"2-1150-5.4-c3-0-87"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.17620819117478337	0	1.35476392304137573098790371354	["ModularForm/GL2/Q/holomorphic/1150/4/b/l/599/5"]
"2-1150-5.4-c3-0-88"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.42620819117478337	0	1.35914385341698879122594529817	["ModularForm/GL2/Q/holomorphic/1150/4/b/q/599/1"]
"2-1150-5.4-c3-0-89"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.32379180882521663	0	1.37052687062700917711489631880	["ModularForm/GL2/Q/holomorphic/1150/4/b/m/599/1"]
"2-1150-5.4-c3-0-9"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.32379180882521663	0	0.17658715307711696440638220173	["ModularForm/GL2/Q/holomorphic/1150/4/b/i/599/2"]
"2-1150-5.4-c3-0-90"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.32379180882521663	0	1.50878242894335972480673174145	["ModularForm/GL2/Q/holomorphic/1150/4/b/d/599/2"]
"2-1150-5.4-c3-0-91"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.42620819117478337	0	1.60439504191156680228169048207	["ModularForm/GL2/Q/holomorphic/1150/4/b/q/599/4"]
"2-1150-5.4-c3-0-92"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.32379180882521663	0	1.62541387133119907854911041620	["ModularForm/GL2/Q/holomorphic/1150/4/b/m/599/2"]
"2-1150-5.4-c3-0-93"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.32379180882521663	0	1.65684409707550611319220977305	["ModularForm/GL2/Q/holomorphic/1150/4/b/j/599/1"]
"2-1150-5.4-c3-0-94"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.17620819117478337	0	1.72163002908638853191889191173	["ModularForm/GL2/Q/holomorphic/1150/4/b/b/599/1"]
"2-1150-5.4-c3-0-95"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.42620819117478337	0	1.76643162912234817159620643549	["ModularForm/GL2/Q/holomorphic/1150/4/b/q/599/8"]
"2-1150-5.4-c3-0-96"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.42620819117478337	0	1.83987885092670672762528274596	["ModularForm/GL2/Q/holomorphic/1150/4/b/s/599/7"]
"2-1150-5.4-c3-0-97"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.32379180882521663	0	1.90588488483409420668612895043	["ModularForm/GL2/Q/holomorphic/1150/4/b/i/599/3"]
"2-1150-5.4-c3-0-98"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.17620819117478337	0	1.93513853607854464517670590945	["ModularForm/GL2/Q/holomorphic/1150/4/b/l/599/1"]
"2-1150-5.4-c3-0-99"	8.237244472917006	67.85219650660174	2	1150	"5.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.07379180882521663	0	2.15281469697496483046126643579	["ModularForm/GL2/Q/holomorphic/1150/4/b/r/599/1"]


# 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).