
# lfunc_search downloaded from the LMFDB on 15 June 2026.
# Search link: https://www.lmfdb.org/L/2/1700/17.4
# Query "{'degree': 2, 'conductor': 1700}" returned 797 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.



"2-1700-1700.1023-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1023"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.19964058231842613	0	1.50373503166047338106851101531	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1023/1"]
"2-1700-1700.1027-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1027"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.008687053240977682	0	1.43592559376222063469285254023	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1027/1"]
"2-1700-1700.1039-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1039"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.33759447445521346	0	0.900272728950032762836475207389	["ModularForm/GL2/Q/holomorphic/1700/1/cf/a/1039/1"]
"2-1700-1700.1039-c0-0-1"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1039"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.21240552554478653	0	1.17841441402173499584502073447	["ModularForm/GL2/Q/holomorphic/1700/1/cf/b/1039/1"]
"2-1700-1700.1047-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1047"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.33922368970946654	0	0.931973995585883260744862846271	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1047/1"]
"2-1700-1700.1079-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1079"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.04791074295044418	0	1.49514057908659586193389073207	["ModularForm/GL2/Q/holomorphic/1700/1/cf/b/1079/1"]
"2-1700-1700.1079-c0-0-1"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1079"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.1979107429504442	0	1.59517129940446703033594456416	["ModularForm/GL2/Q/holomorphic/1700/1/cf/a/1079/1"]
"2-1700-1700.1083-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1083"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.33922368970946654	0	1.75263699796479246589887659605	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1083/1"]
"2-1700-1700.1127-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1127"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2436870532409777	0	1.16578491827162009154312579226	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1127/1"]
"2-1700-1700.1163-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1163"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2436870532409777	0	0.76847801472527419422316198589	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1163/1"]
"2-1700-1700.1167-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1167"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.29276494322636043	0	1.98934041005452220279049376748	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1167/1"]
"2-1700-1700.1183-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1183"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.23422368970946653	0	0.838097898000839788912044359396	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1183/1"]
"2-1700-1700.1187-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1187"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.007764943226360405	0	1.67231088486710008786715254713	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1187/1"]
"2-1700-1700.1211-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1211"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.4244947825943423	0	0.32901043354308044261183015996	["ModularForm/GL2/Q/holomorphic/1700/1/bw/a/1211/1"]
"2-1700-1700.1211-c0-0-1"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1211"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2755052174056577	0	0.943650228019319695501273725805	["ModularForm/GL2/Q/holomorphic/1700/1/bw/b/1211/1"]
"2-1700-1700.1227-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1227"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.12464058231842612	0	0.72892549318298143564676637011	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1227/1"]
"2-1700-1700.1239-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1239"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.09208925704955581	0	1.36702451386486016297676511654	["ModularForm/GL2/Q/holomorphic/1700/1/cf/b/1239/1"]
"2-1700-1700.1239-c0-0-1"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1239"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.45791074295044415	0	2.23028156091514542771601116508	["ModularForm/GL2/Q/holomorphic/1700/1/cf/a/1239/1"]
"2-1700-1700.1247-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1247"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.08964058231842612	0	1.70430892814240646979456928530	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1247/1"]
"2-1700-1700.1263-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1263"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.008687053240977682	0	1.03359593864792033218995930699	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1263/1"]
"2-1700-1700.1271-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1271"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.18449478259434232	0	1.33965835950133370764036930544	["ModularForm/GL2/Q/holomorphic/1700/1/bw/a/1271/1"]
"2-1700-1700.1271-c0-0-1"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1271"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.08449478259434233	0	1.54229158408636676130282228954	["ModularForm/GL2/Q/holomorphic/1700/1/bw/b/1271/1"]
"2-1700-1700.1287-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1287"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2557763102905335	0	0.62459905141775432112484928239	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1287/1"]
"2-1700-1700.1291-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1291"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.28	0	1.16331426320585817344454030506	["ModularForm/GL2/Q/holomorphic/1700/1/bd/b/1291/1"]
"2-1700-1700.1291-c0-0-1"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1291"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.08	0	1.63038382719944708214375346258	["ModularForm/GL2/Q/holomorphic/1700/1/bd/a/1291/1"]
"2-1700-1700.1303-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1303"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.062235056773639594	0	1.30426642679347490495718284585	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1303/1"]
"2-1700-1700.1323-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1323"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.022764943226360405	0	0.818768757327887588178236263065	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1323/1"]
"2-1700-1700.1363-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1363"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.1403594176815739	0	1.40552086273439776635201547181	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1363/1"]
"2-1700-1700.1367-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1367"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.3986870532409777	0	0.922534409068122103518394460587	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1367/1"]
"2-1700-1700.1379-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1379"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.1575944744552135	0	0.32905139289381597737333822044	["ModularForm/GL2/Q/holomorphic/1700/1/cf/a/1379/1"]
"2-1700-1700.1379-c0-0-1"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1379"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.19240552554478654	0	1.95989484806982909799248937729	["ModularForm/GL2/Q/holomorphic/1700/1/cf/b/1379/1"]
"2-1700-1700.1383-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1383"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.3053594176815739	0	1.22599155912068048702481135131	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1383/1"]
"2-1700-1700.1387-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1387"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2292236897094665	0	0.998529324778889567835004346577	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1387/1"]
"2-1700-1700.1419-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1419"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.07208925704955582	0	1.28690329399683093214661558761	["ModularForm/GL2/Q/holomorphic/1700/1/cf/b/1419/1"]
"2-1700-1700.1419-c0-0-1"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1419"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2779107429504442	0	1.79103417969873406581896297135	["ModularForm/GL2/Q/holomorphic/1700/1/cf/a/1419/1"]
"2-1700-1700.1423-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1423"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2292236897094665	0	2.05884733041094397746155640327	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1423/1"]
"2-1700-1700.1467-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1467"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2536870532409777	0	1.72991124010168544348519011316	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1467/1"]
"2-1700-1700.147-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.147"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.08723505677363959	0	0.76218979166036468935683884055	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/147/1"]
"2-1700-1700.1503-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1503"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2536870532409777	0	0.790077141867558966896586057069	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1503/1"]
"2-1700-1700.1523-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1523"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2557763102905335	0	1.31367620885069629729739853348	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1523/1"]
"2-1700-1700.1527-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1527"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.0522350567736396	0	1.87664796417784778846242500168	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1527/1"]
"2-1700-1700.1539-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1539"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.1024055255447865	0	1.00483640184300363379274600265	["ModularForm/GL2/Q/holomorphic/1700/1/cf/a/1539/1"]
"2-1700-1700.1539-c0-0-1"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1539"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.052405525544786516	0	1.68544135996880037208631605018	["ModularForm/GL2/Q/holomorphic/1700/1/cf/b/1539/1"]
"2-1700-1700.1567-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1567"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.11464058231842612	0	1.42181011535008910160315535246	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1567/1"]
"2-1700-1700.1579-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1579"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.07208925704955582	0	0.870669723590842858217500510004	["ModularForm/GL2/Q/holomorphic/1700/1/cf/b/1579/1"]
"2-1700-1700.1579-c0-0-1"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1579"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2779107429504442	0	1.22551918619632178116218428808	["ModularForm/GL2/Q/holomorphic/1700/1/cf/a/1579/1"]
"2-1700-1700.1587-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1587"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.19964058231842613	0	1.39715659910480077504907747716	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1587/1"]
"2-1700-1700.1603-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1603"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.3986870532409777	0	2.32215769317125269549179789577	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1603/1"]
"2-1700-1700.1611-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1611"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.13550521740565769	0	1.30685690056780472807340383870	["ModularForm/GL2/Q/holomorphic/1700/1/bw/a/1611/1"]
"2-1700-1700.1611-c0-0-1"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1611"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.43550521740565773	0	1.75758179055812805942877392270	["ModularForm/GL2/Q/holomorphic/1700/1/bw/b/1611/1"]
"2-1700-1700.1627-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1627"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.1957763102905335	0	1.26454910472499034384127604804	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/1627/1"]
"2-1700-1700.163-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.163"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.1957763102905335	0	1.40713241605534348415337768628	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/163/1"]
"2-1700-1700.1631-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1631"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.04	0	1.00899321686997688347326664900	["ModularForm/GL2/Q/holomorphic/1700/1/bd/b/1631/1"]
"2-1700-1700.1631-c0-0-1"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1631"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.44	0	1.55692707384562825795468341266	["ModularForm/GL2/Q/holomorphic/1700/1/bd/a/1631/1"]
"2-1700-1700.1663-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.1663"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.3172350567736396	0	2.14879936610179577248701995306	["ModularForm/GL2/Q/holomorphic/1700/1/ct/a/1663/1"]
"2-1700-1700.167-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.167"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.062235056773639594	0	0.789949436765481920070612921978	["ModularForm/GL2/Q/holomorphic/1700/1/cm/a/167/1"]
"2-1700-1700.179-c0-0-0"	0.9210920266054332	0.8484105214761041	2	1700	"1700.179"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.07240552554478652	0	1.26885553823216649194396075232	["ModularForm/GL2/Q/holomorphic/1700/1/cf/b/179/1"]
"2-1700-1700.179-c0-0-1"	0.9210920266054332	0.8484105214761041	2	1700	"1700.179"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.07759447445521349	0	1.52778770849169320632536567422	["ModularForm/GL2/Q/holomorphic/1700/1/cf/a/179/1"]
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"2-1700-85.84-c3-0-34"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.09399762151248438	0	0.55207730460092836936139634207	["ModularForm/GL2/Q/holomorphic/1700/4/g/a/849/3"]
"2-1700-85.84-c3-0-35"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.21657156562354465	0	0.56095702331045018271931856765	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/36"]
"2-1700-85.84-c3-0-36"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.08062844340885511	0	0.56524554449140126854764447660	["ModularForm/GL2/Q/holomorphic/1700/4/g/b/849/10"]
"2-1700-85.84-c3-0-37"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.04226642794954355	0	0.58745779941696178988069010393	["ModularForm/GL2/Q/holomorphic/1700/4/g/c/849/2"]
"2-1700-85.84-c3-0-38"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.09016034590955935	0	0.59034827575841341581447480576	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/23"]
"2-1700-85.84-c3-0-39"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.255159855420423	0	0.60197256369770788806723364497	["ModularForm/GL2/Q/holomorphic/1700/4/g/b/849/5"]
"2-1700-85.84-c3-0-4"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.33590753922860916	0	0.07183198417003166451178891682	["ModularForm/GL2/Q/holomorphic/1700/4/g/b/849/11"]
"2-1700-85.84-c3-0-40"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.35084447668259233	0	0.62477043583519706717413813567	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/4"]
"2-1700-85.84-c3-0-41"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.03100075761206358	0	0.62548127793617868503452414336	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/26"]
"2-1700-85.84-c3-0-42"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.0722702234603667	0	0.62600369106857123237702600489	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/5"]
"2-1700-85.84-c3-0-43"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.11013181445915335	0	0.63706070612254832866222870564	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/16"]
"2-1700-85.84-c3-0-44"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.2422845678904134	0	0.65937117446138696283394099715	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/22"]
"2-1700-85.84-c3-0-45"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.03100075761206358	0	0.68733379919422196576744453991	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/25"]
"2-1700-85.84-c3-0-46"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.0722702234603667	0	0.69578897189793722122959286151	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/6"]
"2-1700-85.84-c3-0-47"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.29358557695175447	0	0.77832454017082117185007251525	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/10"]
"2-1700-85.84-c3-0-48"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.08062844340885511	0	0.78653142421090646493333008993	["ModularForm/GL2/Q/holomorphic/1700/4/g/b/849/9"]
"2-1700-85.84-c3-0-49"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.20550539424700148	0	0.813201940459046035468084315989	["ModularForm/GL2/Q/holomorphic/1700/4/g/c/849/6"]
"2-1700-85.84-c3-0-5"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.2422845678904134	0	0.086751943871544868359503765567	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/21"]
"2-1700-85.84-c3-0-50"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.09016034590955935	0	0.828358927777316755249895402822	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/24"]
"2-1700-85.84-c3-0-51"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.10757623776998974	0	0.849328080513941162652872346227	["ModularForm/GL2/Q/holomorphic/1700/4/g/c/849/14"]
"2-1700-85.84-c3-0-52"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.13765017006896488	0	0.856728583127226564763203450313	["ModularForm/GL2/Q/holomorphic/1700/4/g/c/849/15"]
"2-1700-85.84-c3-0-53"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.10531718970088973	0	0.857422203097544435134381651966	["ModularForm/GL2/Q/holomorphic/1700/4/g/b/849/18"]
"2-1700-85.84-c3-0-54"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.11013181445915335	0	0.924214389026983537958664412014	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/15"]
"2-1700-85.84-c3-0-55"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.33590753922860916	0	0.956763474469270682249360566188	["ModularForm/GL2/Q/holomorphic/1700/4/g/b/849/12"]
"2-1700-85.84-c3-0-56"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.49479924422526195	0	0.980765648808965474869662330102	["ModularForm/GL2/Q/holomorphic/1700/4/g/c/849/3"]
"2-1700-85.84-c3-0-57"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.24158123916291768	0	1.08063133486943784959876211479	["ModularForm/GL2/Q/holomorphic/1700/4/g/a/849/5"]
"2-1700-85.84-c3-0-58"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.35308901189743475	0	1.10837524486881379746427385711	["ModularForm/GL2/Q/holomorphic/1700/4/g/b/849/14"]
"2-1700-85.84-c3-0-59"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.3913125731844938	0	1.15227421662856042004267027224	["ModularForm/GL2/Q/holomorphic/1700/4/g/b/849/7"]
"2-1700-85.84-c3-0-6"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.46110380916507293	0	0.087709103729413635054526848078	["ModularForm/GL2/Q/holomorphic/1700/4/g/c/849/11"]
"2-1700-85.84-c3-0-60"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.0015719056669743988	0	1.15818607421776581320786432673	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/34"]
"2-1700-85.84-c3-0-61"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.0015719056669743988	0	1.16062253163764278316549242021	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/33"]
"2-1700-85.84-c3-0-62"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.44578299738825583	0	1.16447179995906255134255434889	["ModularForm/GL2/Q/holomorphic/1700/4/g/a/849/2"]
"2-1700-85.84-c3-0-63"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.4425767282591261	0	1.17489592612949855090902475639	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/14"]
"2-1700-85.84-c3-0-64"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.10757623776998974	0	1.19819241849666981238049368793	["ModularForm/GL2/Q/holomorphic/1700/4/g/c/849/13"]
"2-1700-85.84-c3-0-65"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.28523378771939817	0	1.20938181236535691235543133777	["ModularForm/GL2/Q/holomorphic/1700/4/g/b/849/3"]
"2-1700-85.84-c3-0-66"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.3935016966555878	0	1.22574999056804236282714793609	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/19"]
"2-1700-85.84-c3-0-67"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.3178324870939913	0	1.25516016349980944084674534109	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/29"]
"2-1700-85.84-c3-0-68"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.10531718970088973	0	1.27499355730228286209582377903	["ModularForm/GL2/Q/holomorphic/1700/4/g/b/849/17"]
"2-1700-85.84-c3-0-69"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.21657156562354465	0	1.28981025363970885295680572740	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/35"]
"2-1700-85.84-c3-0-7"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.4834911568790424	0	0.090458577675298071216326045967	["ModularForm/GL2/Q/holomorphic/1700/4/g/c/849/8"]
"2-1700-85.84-c3-0-70"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.4310120520268887	0	1.30756697182490504798118848206	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/1"]
"2-1700-85.84-c3-0-71"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.4834911568790424	0	1.35568402612623282053019569497	["ModularForm/GL2/Q/holomorphic/1700/4/g/c/849/7"]
"2-1700-85.84-c3-0-72"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.35399804069867885	0	1.38675483801073972492104065152	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/27"]
"2-1700-85.84-c3-0-73"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.46110380916507293	0	1.50068674843046474630410121487	["ModularForm/GL2/Q/holomorphic/1700/4/g/c/849/12"]
"2-1700-85.84-c3-0-74"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.29819937973782257	0	1.52492028294876060006820242725	["ModularForm/GL2/Q/holomorphic/1700/4/g/a/849/7"]
"2-1700-85.84-c3-0-75"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.27743945257123737	0	1.54531101718986478422068839226	["ModularForm/GL2/Q/holomorphic/1700/4/g/c/849/17"]
"2-1700-85.84-c3-0-76"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.34721562657482863	0	1.58289713297625359811172852658	["ModularForm/GL2/Q/holomorphic/1700/4/g/b/849/15"]
"2-1700-85.84-c3-0-77"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.3214156247375032	0	1.72017641354473960361368222514	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/11"]
"2-1700-85.84-c3-0-78"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.25408192099484556	0	1.75525487279282630045833325892	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/17"]
"2-1700-85.84-c3-0-79"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.4246866058099334	0	1.82240300447639497056305189707	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/32"]
"2-1700-85.84-c3-0-8"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.25408192099484556	0	0.10001708447671806336385224419	["ModularForm/GL2/Q/holomorphic/1700/4/g/d/849/18"]
"2-1700-85.84-c3-0-9"	10.01515087304026	100.30324700975909	2	1700	"85.84"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.35308901189743475	0	0.11485673946850121077810963181	["ModularForm/GL2/Q/holomorphic/1700/4/g/b/849/13"]


# 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).


