# lfunc_search downloaded from the LMFDB on 24 August 2026.
# Search link: https://www.lmfdb.org/L/2/2175
# Query "{'degree': 2, 'conductor': 2175}" returned 656 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.



"2-2175-435.434-c0-0-0"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.17620819117478337	0	0.30197695048536623300829006736	["ModularForm/GL2/Q/holomorphic/2175/1/b/d/2174/2"]
"2-2175-435.434-c0-0-1"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.17620819117478337	0	0.52974695487465657582815957331	["ModularForm/GL2/Q/holomorphic/2175/1/b/d/2174/1"]
"2-2175-435.434-c0-0-10"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.42620819117478337	0	1.73563806907604143759868119808	["ModularForm/GL2/Q/holomorphic/2175/1/b/b/2174/1"]
"2-2175-435.434-c0-0-11"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.17620819117478337	0	1.78495838208498490317553901161	["ModularForm/GL2/Q/holomorphic/2175/1/b/d/2174/4"]
"2-2175-435.434-c0-0-12"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.17620819117478337	0	1.79161249331612592450483384027	["ModularForm/GL2/Q/holomorphic/2175/1/b/d/2174/5"]
"2-2175-435.434-c0-0-13"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.17620819117478337	0	1.87237842216213082542263440373	["ModularForm/GL2/Q/holomorphic/2175/1/b/c/2174/3"]
"2-2175-435.434-c0-0-14"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.42620819117478337	0	2.30281055037571072244007421497	["ModularForm/GL2/Q/holomorphic/2175/1/b/a/2174/1"]
"2-2175-435.434-c0-0-15"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.17620819117478337	0	2.46164880092221341098034529901	["ModularForm/GL2/Q/holomorphic/2175/1/b/c/2174/1"]
"2-2175-435.434-c0-0-2"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.17620819117478337	0	0.59307221157721873904594030647	["ModularForm/GL2/Q/holomorphic/2175/1/b/c/2174/6"]
"2-2175-435.434-c0-0-3"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.42620819117478337	0	0.67921307165896043946117356753	["ModularForm/GL2/Q/holomorphic/2175/1/b/a/2174/2"]
"2-2175-435.434-c0-0-4"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.17620819117478337	0	0.811823675829709997785431308179	["ModularForm/GL2/Q/holomorphic/2175/1/b/c/2174/4"]
"2-2175-435.434-c0-0-5"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.42620819117478337	0	0.947433202032195862022651083637	["ModularForm/GL2/Q/holomorphic/2175/1/b/b/2174/2"]
"2-2175-435.434-c0-0-6"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.17620819117478337	0	1.14951364616999161823297943983	["ModularForm/GL2/Q/holomorphic/2175/1/b/c/2174/5"]
"2-2175-435.434-c0-0-7"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.17620819117478337	0	1.16097646635749246192058199182	["ModularForm/GL2/Q/holomorphic/2175/1/b/c/2174/2"]
"2-2175-435.434-c0-0-8"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.17620819117478337	0	1.17871366093912010891378725131	["ModularForm/GL2/Q/holomorphic/2175/1/b/d/2174/3"]
"2-2175-435.434-c0-0-9"	1.0418571890987651	1.0854664024767802	2	2175	"435.434"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.17620819117478337	0	1.56395519216789662685669275993	["ModularForm/GL2/Q/holomorphic/2175/1/b/d/2174/6"]
"2-2175-87.86-c0-0-0"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.375	0	0.33228161875003712152339817706	["ModularForm/GL2/Q/holomorphic/2175/1/h/g/1826/2"]
"2-2175-87.86-c0-0-1"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	0.49730740771534572588371024792	["ModularForm/GL2/Q/holomorphic/2175/1/h/d/1826/2"]
"2-2175-87.86-c0-0-10"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	1.37778745196513544815207440794	["ModularForm/GL2/Q/holomorphic/2175/1/h/a/1826/1", "ModularForm/GL2/Q/holomorphic/2175/1/h/a", "ArtinRepresentation/2.2175.6t3.b.a", "ArtinRepresentation/2.2175.6t3.b"]
"2-2175-87.86-c0-0-11"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.42222125349456273924850061714	["ModularForm/GL2/Q/holomorphic/2175/1/h/f/1826/2"]
"2-2175-87.86-c0-0-12"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.125	0	1.47067445861492531573189272021	["ModularForm/GL2/Q/holomorphic/2175/1/h/g/1826/4"]
"2-2175-87.86-c0-0-13"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.47579939597712814270817544533	["ModularForm/GL2/Q/holomorphic/2175/1/h/c/1826/3"]
"2-2175-87.86-c0-0-14"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.73070337497445164535221643354	["ModularForm/GL2/Q/holomorphic/2175/1/h/d/1826/3"]
"2-2175-87.86-c0-0-15"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.93764703926138004375136775211	["ModularForm/GL2/Q/holomorphic/2175/1/h/e/1826/3", "ArtinRepresentation/2.2175.9t3.a.c"]
"2-2175-87.86-c0-0-16"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.94074726955905458397913084652	["ModularForm/GL2/Q/holomorphic/2175/1/h/f/1826/3"]
"2-2175-87.86-c0-0-17"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.125	0	1.97754050937281310951466859758	["ModularForm/GL2/Q/holomorphic/2175/1/h/g/1826/3"]
"2-2175-87.86-c0-0-2"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	0.62600961268415776705364245821	["ModularForm/GL2/Q/holomorphic/2175/1/h/c/1826/1"]
"2-2175-87.86-c0-0-3"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.02541387754140829046272838321	["ModularForm/GL2/Q/holomorphic/2175/1/h/f/1826/1"]
"2-2175-87.86-c0-0-4"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.05380231752988230136180855778	["ModularForm/GL2/Q/holomorphic/2175/1/h/c/1826/2"]
"2-2175-87.86-c0-0-5"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	1.11917820683913827346747527289	["ModularForm/GL2/Q/holomorphic/2175/1/h/b/1826/1", "ModularForm/GL2/Q/holomorphic/2175/1/h/b", "ArtinRepresentation/2.2175.6t3.d.a", "ArtinRepresentation/2.2175.6t3.d"]
"2-2175-87.86-c0-0-6"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.16696546040772382780751521796	["ModularForm/GL2/Q/holomorphic/2175/1/h/d/1826/1"]
"2-2175-87.86-c0-0-7"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.18432516009006482961781076353	["ModularForm/GL2/Q/holomorphic/2175/1/h/e/1826/2", "ArtinRepresentation/2.2175.9t3.a.a"]
"2-2175-87.86-c0-0-8"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.375	0	1.22802583446277363449727970081	["ModularForm/GL2/Q/holomorphic/2175/1/h/g/1826/1"]
"2-2175-87.86-c0-0-9"	1.0418571890987651	1.0854664024767802	2	2175	"87.86"	[]	[[0.0, 0.0]]	0	true	true	false	true	0.0	0	1.25939835582413232369720352277	["ModularForm/GL2/Q/holomorphic/2175/1/h/e/1826/1", "ArtinRepresentation/2.2175.9t3.a.b"]
"2-2175-1.1-c1-0-0"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.34138934485228128137122512189	["ModularForm/GL2/Q/holomorphic/2175/2/a/ba/1/2"]
"2-2175-1.1-c1-0-1"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.36888289924507259664087467196	["ModularForm/GL2/Q/holomorphic/2175/2/a/bc/1/2"]
"2-2175-1.1-c1-0-10"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.59146369806927440250452264530	["ModularForm/GL2/Q/holomorphic/2175/2/a/bc/1/6"]
"2-2175-1.1-c1-0-11"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.59426077507863089978478871339	["ModularForm/GL2/Q/holomorphic/2175/2/a/v/1/2"]
"2-2175-1.1-c1-0-12"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.64227985210694428018150375061	["ModularForm/GL2/Q/holomorphic/2175/2/a/m/1/1"]
"2-2175-1.1-c1-0-13"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.69959274062441458301279973544	["ModularForm/GL2/Q/holomorphic/2175/2/a/m/1/2"]
"2-2175-1.1-c1-0-14"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.73047933133623116124195629582	["ModularForm/GL2/Q/holomorphic/2175/2/a/bd/1/5"]
"2-2175-1.1-c1-0-15"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.75076362824229183407060510886	["ModularForm/GL2/Q/holomorphic/2175/2/a/y/1/1"]
"2-2175-1.1-c1-0-16"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.75887526150236127825243908358	["ModularForm/GL2/Q/holomorphic/2175/2/a/q/1/1"]
"2-2175-1.1-c1-0-17"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.76989224128822694234011319404	["EllipticCurve/Q/2175/a", "ModularForm/GL2/Q/holomorphic/2175/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/2175/2/a/a"]
"2-2175-1.1-c1-0-18"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.78318140584315882525102430039	["ModularForm/GL2/Q/holomorphic/2175/2/a/u/1/2"]
"2-2175-1.1-c1-0-19"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.804954869493549802355135098687	["ModularForm/GL2/Q/holomorphic/2175/2/a/z/1/1"]
"2-2175-1.1-c1-0-2"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.41388092543812425358550677346	["ModularForm/GL2/Q/holomorphic/2175/2/a/ba/1/5"]
"2-2175-1.1-c1-0-20"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.805173286303730564325945871624	["ModularForm/GL2/Q/holomorphic/2175/2/a/bd/1/4"]
"2-2175-1.1-c1-0-21"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.807133543343497993372000165724	["ModularForm/GL2/Q/holomorphic/2175/2/a/bc/1/1"]
"2-2175-1.1-c1-0-22"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.815274929991884740931393064079	["ModularForm/GL2/Q/holomorphic/2175/2/a/u/1/1"]
"2-2175-1.1-c1-0-23"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.818485184939190777704549822687	["ModularForm/GL2/Q/holomorphic/2175/2/a/y/1/3"]
"2-2175-1.1-c1-0-24"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.822724460421109999941447272957	["ModularForm/GL2/Q/holomorphic/2175/2/a/ba/1/4"]
"2-2175-1.1-c1-0-25"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.834733188292331876571569817971	["ModularForm/GL2/Q/holomorphic/2175/2/a/ba/1/1"]
"2-2175-1.1-c1-0-26"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.850594550508520107148863235659	["EllipticCurve/Q/2175/h", "ModularForm/GL2/Q/holomorphic/2175/2/a/h/1/1", "ModularForm/GL2/Q/holomorphic/2175/2/a/h"]
"2-2175-1.1-c1-0-27"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.881935906972457734636824661786	["ModularForm/GL2/Q/holomorphic/2175/2/a/r/1/1"]
"2-2175-1.1-c1-0-28"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.886981989811700912002777893135	["ModularForm/GL2/Q/holomorphic/2175/2/a/s/1/2"]
"2-2175-1.1-c1-0-29"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.893926187061001652031481912570	["ModularForm/GL2/Q/holomorphic/2175/2/a/bb/1/4"]
"2-2175-1.1-c1-0-3"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.45376784244716733750845202449	["ModularForm/GL2/Q/holomorphic/2175/2/a/bb/1/2"]
"2-2175-1.1-c1-0-30"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.0	0	0.928804870228053909603643886571	["EllipticCurve/Q/2175/i", "ModularForm/GL2/Q/holomorphic/2175/2/a/i/1/1", "ModularForm/GL2/Q/holomorphic/2175/2/a/i"]
"2-2175-1.1-c1-0-31"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.939099081887040149236553067373	["ModularForm/GL2/Q/holomorphic/2175/2/a/bb/1/1"]
"2-2175-1.1-c1-0-32"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.948464654231169835342193876721	["ModularForm/GL2/Q/holomorphic/2175/2/a/bb/1/3"]
"2-2175-1.1-c1-0-33"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.963192479564992882518130036083	["ModularForm/GL2/Q/holomorphic/2175/2/a/bd/1/2"]
"2-2175-1.1-c1-0-34"	4.167428756395062	17.367462439628493	2	2175	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	0.983878420232591295657335447188	["ModularForm/GL2/Q/holomorphic/2175/2/a/bc/1/7"]
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"2-2175-1.1-c3-0-89"	11.328245859906374	128.3291542624859	2	2175	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.71025924470530439797012160699	["ModularForm/GL2/Q/holomorphic/2175/4/a/w/1/3"]
"2-2175-1.1-c3-0-9"	11.328245859906374	128.3291542624859	2	2175	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.18394408220263408509186676857	["ModularForm/GL2/Q/holomorphic/2175/4/a/bb/1/9"]
"2-2175-1.1-c3-0-90"	11.328245859906374	128.3291542624859	2	2175	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.71770530559250330228077940596	["ModularForm/GL2/Q/holomorphic/2175/4/a/u/1/9"]
"2-2175-1.1-c3-0-91"	11.328245859906374	128.3291542624859	2	2175	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.72280154576953020643331859340	["ModularForm/GL2/Q/holomorphic/2175/4/a/t/1/5"]
"2-2175-1.1-c3-0-92"	11.328245859906374	128.3291542624859	2	2175	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.73201168104195665075978011042	["ModularForm/GL2/Q/holomorphic/2175/4/a/ba/1/9"]
"2-2175-1.1-c3-0-93"	11.328245859906374	128.3291542624859	2	2175	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.74507843484202548287814044907	["ModularForm/GL2/Q/holomorphic/2175/4/a/ba/1/1"]
"2-2175-1.1-c3-0-94"	11.328245859906374	128.3291542624859	2	2175	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.74838060992136811466054960655	["ModularForm/GL2/Q/holomorphic/2175/4/a/ba/1/4"]
"2-2175-1.1-c3-0-95"	11.328245859906374	128.3291542624859	2	2175	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.74924883778307658812938837833	["ModularForm/GL2/Q/holomorphic/2175/4/a/k/1/2"]
"2-2175-1.1-c3-0-96"	11.328245859906374	128.3291542624859	2	2175	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.74943572814372988391095990301	["ModularForm/GL2/Q/holomorphic/2175/4/a/bb/1/15"]
"2-2175-1.1-c3-0-97"	11.328245859906374	128.3291542624859	2	2175	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.74972239899724648011194159850	["ModularForm/GL2/Q/holomorphic/2175/4/a/g/1/2"]
"2-2175-1.1-c3-0-98"	11.328245859906374	128.3291542624859	2	2175	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.75023194902620433851689556637	["ModularForm/GL2/Q/holomorphic/2175/4/a/d/1/1"]
"2-2175-1.1-c3-0-99"	11.328245859906374	128.3291542624859	2	2175	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.75327261330094581271618293734	["ModularForm/GL2/Q/holomorphic/2175/4/a/bb/1/10"]


# Label --
#    Each L-function $L$ has a label of the form d-N-q.k-x-y-i, where

#     * $d$ is the degree of $L$.
#     * $N$ is the conductor of $L$.  When $N$ is a perfect power $m^n$ we write $N$ as $m$e$n$, since $N$ can be very large for some imprimitive L-functions.
#     * q.k is the label of the primitive Dirichlet character from which the central character is induced.
#     * x-y is the spectral label encoding the $\mu_j$ and $\nu_j$ in the analytically normalized functional equation.
#     * i is a non-negative integer disambiguating between L-functions that would otherwise have the same label.


#$\alpha$ (root_analytic_conductor) --
#    If $d$ is the degree of the L-function $L(s)$, the **root analytic conductor** $\alpha$ of $L$ is the $d$th root of the analytic conductor of $L$.  It plays a role analogous to the root discriminant for number fields.


#$A$ (analytic_conductor) --
#    The **analytic conductor** of an L-function $L(s)$ with infinity factor $L_{\infty}(s)$ and conductor $N$ is the real number
#    \[
#    A := \mathrm{exp}\left(2\mathrm{Re}\left(\frac{L_{\infty}'(1/2)}{L_{\infty}(1/2)}\right)\right)N.
#    \]



#$d$ (degree) --
#    The **degree** of an L-function is the number $J + 2K$ of Gamma factors occurring in its functional equation

#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s).
#    \]

#    The degree appears as the first component of the Selberg data of $L(s).$ In all known cases it is the degree of the polynomial of the inverse of the Euler factor at any prime not dividing the conductor.



#$N$ (conductor) --
#    The **conductor** of an L-function is the integer $N$  occurring in its functional equation

#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s).
#    \]


#    The conductor of an analytic L-function is the second component in the Selberg data. For a Dirichlet L-function
#     associated with a primitive Dirichlet character, the conductor of the L-function is the same as the conductor of the character. For a primitive L-function associated with a cusp form $\phi$ on $GL(2)/\mathbb Q$, the conductor of the L-function is the same as the level of $\phi$.

#    In the literature, the word _level_ is sometimes used instead of _conductor_.


#$\chi$ (central_character) --
#    An L-function has an Euler product of the form
#    $L(s) = \prod_p L_p(p^{-s})^{-1}$
#    where $L_p(x) = 1 + a_p x + \ldots + (-1)^d \chi(p) x^d$. The character $\chi$ is a Dirichlet character mod $N$ and is called **central character** of the L-function.
#    Here, $N$ is the conductor of $L$.


#$\mu$ (mus) --
#    All known analytic L-functions have a **functional equation** that can be written in the form
#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s),
#    \]
#    where $N$ is an integer, $\Gamma_{\mathbb R}$ and $\Gamma_{\mathbb C}$ are defined in terms of the $\Gamma$-function, $\mathrm{Re}(\mu_j) = 0 \ \mathrm{or} \ 1$ (assuming Selberg's eigenvalue conjecture), and $\mathrm{Re}(\nu_k)$ is a positive integer
#    or half-integer,
#    \[
#    \sum \mu_j + 2 \sum \nu_k \ \ \ \ \text{is real},
#    \]
#    and $\varepsilon$ is the sign of the functional equation.
#    With those restrictions on the spectral parameters, the
#    data in the functional equation is specified uniquely.  The integer $d = J + 2 K$
#    is the degree of the L-function. The integer $N$ is  the conductor (or level)
#    of the L-function.  The pair $[J,K]$ is the signature of the L-function.  The parameters
#    in the functional equation can be used to make up the 4-tuple called the Selberg data.


#    The axioms of the Selberg class are less restrictive than
#    given above.

#    Note that the functional equation above has the central point at $s=1/2$, and relates $s\leftrightarrow 1-s$.

#    For many L-functions there is another normalization which is natural. The corresponding functional equation relates $s\leftrightarrow w+1-s$ for some positive integer $w$,
#    called the motivic weight of the L-function. The central point is at $s=(w+1)/2$, and the arithmetically normalized Dirichlet coefficients $a_n n^{w/2}$ are algebraic integers.



#$\nu$ (nus) --
#    All known analytic L-functions have a **functional equation** that can be written in the form
#    \[
#    \Lambda(s) := N^{s/2}
#    \prod_{j=1}^J \Gamma_{\mathbb R}(s+\mu_j) \prod_{k=1}^K \Gamma_{\mathbb C}(s+\nu_k)
#    \cdot L(s) = \varepsilon \overline{\Lambda}(1-s),
#    \]
#    where $N$ is an integer, $\Gamma_{\mathbb R}$ and $\Gamma_{\mathbb C}$ are defined in terms of the $\Gamma$-function, $\mathrm{Re}(\mu_j) = 0 \ \mathrm{or} \ 1$ (assuming Selberg's eigenvalue conjecture), and $\mathrm{Re}(\nu_k)$ is a positive integer
#    or half-integer,
#    \[
#    \sum \mu_j + 2 \sum \nu_k \ \ \ \ \text{is real},
#    \]
#    and $\varepsilon$ is the sign of the functional equation.
#    With those restrictions on the spectral parameters, the
#    data in the functional equation is specified uniquely.  The integer $d = J + 2 K$
#    is the degree of the L-function. The integer $N$ is  the conductor (or level)
#    of the L-function.  The pair $[J,K]$ is the signature of the L-function.  The parameters
#    in the functional equation can be used to make up the 4-tuple called the Selberg data.


#    The axioms of the Selberg class are less restrictive than
#    given above.

#    Note that the functional equation above has the central point at $s=1/2$, and relates $s\leftrightarrow 1-s$.

#    For many L-functions there is another normalization which is natural. The corresponding functional equation relates $s\leftrightarrow w+1-s$ for some positive integer $w$,
#    called the motivic weight of the L-function. The central point is at $s=(w+1)/2$, and the arithmetically normalized Dirichlet coefficients $a_n n^{w/2}$ are algebraic integers.



#$w$ (motivic_weight) --
#    The **motivic weight** (or **arithmetic weight**) of an arithmetic L-function with analytic normalization $L_{an}(s)=\sum_{n=1}^\infty a_nn^{-s}$ is the least nonnegative integer $w$ for which $a_nn^{w/2}$ is an algebraic integer for all $n\ge 1$.

#    If the L-function arises from a motive, then the weight of the motive has the
#    same parity as the motivic weight of the L-function, but the weight of the motive
#    could be larger.  This apparent discrepancy comes from the fact that a Tate twist
#    increases the weight of the motive.  This corresponds to the change of variables
#    $s \mapsto s + j$ in the L-function of the motive.


#prim (primitive) --
#    An L-function is <b>primitive</b> if it cannot be written as a product of nontrivial L-functions.  The "trivial L-function" is the constant function $1$.


#arith (algebraic) --
#    An L-function $L(s) = \sum_{n=1}^{\infty} a_n n^{-s}$  is called **arithmetic** if its Dirichlet coefficients $a_n$ are algebraic numbers.


#$\mathbb{Q}$ (rational) --
#    A **rational** L-function $L(s)$ is an arithmetic L-function with coefficient field $\Q$; equivalently, its Euler product in the arithmetic normalization can be written as a product over rational primes
#    \[
#    L(s)=\prod_pL_p(p^{-s})^{-1}
#    \]
#    with $L_p\in \Z[T]$.


#self-dual (self_dual) --
#    An L-function $L(s) = \sum_{n=1}^{\infty} \frac{a_n}{n^s}$ is called **self-dual** if its Dirichlet coefficients $a_n$ are real.


#$\operatorname{Arg}(\epsilon)$ (root_angle) --
#    The **root angle** of an L-function is the argument of its root number, as a real number $\alpha$ with $-0.5 < \alpha \le 0.5$.


#$r$ (order_of_vanishing) --
#    The **analytic rank** of an L-function $L(s)$ is its order of vanishing at its central point.

#    When the analytic rank $r$ is positive, the value listed in the LMFDB is typically an upper bound that is believed to be tight (in the sense that there are known to be $r$ zeroes located very near to the central point).


#First zero (z1) --
#    The **zeros** of an L-function $L(s)$ are the complex numbers $\rho$ for which $L(\rho)=0$.

#    Under the Riemann Hypothesis, every non-trivial zero $\rho$ lies on the critical line $\Re(s)=1/2$ (in the analytic normalization).

#    The **lowest zero** of an L-function $L(s)$ is the least $\gamma>0$ for which $L(1/2+i\gamma)=0$. Note that even when $L(1/2)=0$, the lowest zero is by definition a positive real number.


#Origin (instance_urls) --
#    L-functions arise from many different sources. Already in degree 2 we have examples of
#    L-functions associated with holomorphic cusp forms, with Maass forms, with elliptic curves, with characters of number fields (Hecke characters), and with 2-dimensional representations of the Galois group of a number field (Artin L-functions).

#    Sometimes an L-function may arise from more than one source. For example, the L-functions associated with elliptic curves are also associated with weight 2 cusp forms. A goal of the Langlands program ostensibly is to prove that any degree $d$ L-function is associated with an automorphic form on $\mathrm{GL}(d)$. Because of this representation theoretic genesis, one can associate an L-function not only to an automorphic representation but also to symmetric powers, or exterior powers of that representation, or to the tensor product of two representations (the Rankin-Selberg product of two L-functions).