# lfunc_search downloaded from the LMFDB on 13 April 2026.
# Search link: https://www.lmfdb.org/L/2/2352/12.11
# Query "{'degree': 2, 'conductor': 2352}" returned 754 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.



"2-2352-147.107-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.107"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.04081632653061225	0	1.45222423205320220948568015029	["ModularForm/GL2/Q/holomorphic/2352/1/cv/a/401/1"]
"2-2352-147.11-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.11"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.04081632653061225	0	1.53535039062202461880369649963	["ModularForm/GL2/Q/holomorphic/2352/1/cv/a/305/1"]
"2-2352-147.113-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.113"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.04081632653061225	0	1.06123945941217682619177959914	["ModularForm/GL2/Q/holomorphic/2352/1/cj/a/113/1"]
"2-2352-147.134-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.134"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.04081632653061225	0	0.960962460042154568664335431842	["ModularForm/GL2/Q/holomorphic/2352/1/cj/a/1457/1"]
"2-2352-147.137-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.137"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.06802721088435375	0	1.44578204741789146594300336549	["ModularForm/GL2/Q/holomorphic/2352/1/cv/a/1313/1"]
"2-2352-147.2-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.2"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.04081632653061225	0	1.20157051551374921051934288539	["ModularForm/GL2/Q/holomorphic/2352/1/cv/a/737/1"]
"2-2352-147.23-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.23"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.4421768707482993	0	0.27983509071363694380779464788	["ModularForm/GL2/Q/holomorphic/2352/1/cv/a/2081/1"]
"2-2352-147.29-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.29"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.22448979591836735	0	1.04735070427353098130690145083	["ModularForm/GL2/Q/holomorphic/2352/1/cj/a/1793/1"]
"2-2352-147.32-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.32"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.4421768707482993	0	1.75857494847566921037715745747	["ModularForm/GL2/Q/holomorphic/2352/1/cv/a/1649/1"]
"2-2352-147.44-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.44"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.06802721088435375	0	0.826980987394034488163265169230	["ModularForm/GL2/Q/holomorphic/2352/1/cv/a/1073/1"]
"2-2352-147.53-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.53"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.10884353741496598	0	1.14815439704503701051685649368	["ModularForm/GL2/Q/holomorphic/2352/1/cv/a/641/1"]
"2-2352-147.65-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.65"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.4013605442176871	0	1.84097077124193558520606011269	["ModularForm/GL2/Q/holomorphic/2352/1/cv/a/65/1"]
"2-2352-147.71-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.71"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.22448979591836735	0	1.60978297879763721002819278916	["ModularForm/GL2/Q/holomorphic/2352/1/cj/a/2129/1"]
"2-2352-147.74-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.74"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.04081632653061225	0	0.69787180881732726523699471557	["ModularForm/GL2/Q/holomorphic/2352/1/cv/a/1985/1"]
"2-2352-147.8-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.8"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.2653061224489796	0	2.01446713119259575302048543417	["ModularForm/GL2/Q/holomorphic/2352/1/cj/a/449/1"]
"2-2352-147.86-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.86"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.10884353741496598	0	1.36947168206067206064948540954	["ModularForm/GL2/Q/holomorphic/2352/1/cv/a/1409/1"]
"2-2352-147.92-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.92"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.2653061224489796	0	0.78758100573783104460665931067	["ModularForm/GL2/Q/holomorphic/2352/1/cj/a/1121/1"]
"2-2352-147.95-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"147.95"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.4013605442176871	0	0.56987836057923689590271086419	["ModularForm/GL2/Q/holomorphic/2352/1/cv/a/977/1"]
"2-2352-21.11-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"21.11"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.1868396197206128	0	0.875647314138879257351350989160	["ModularForm/GL2/Q/holomorphic/2352/1/bn/a/2321/1"]
"2-2352-21.2-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"21.2"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.1868396197206128	0	1.25098469745794540983897487373	["ModularForm/GL2/Q/holomorphic/2352/1/bn/a/1745/1"]
"2-2352-3.2-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"3.2"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	0.943826337148702968312648393411	["ModularForm/GL2/Q/holomorphic/2352/1/d/a/785/1", "ModularForm/GL2/Q/holomorphic/2352/1/d/a", "ArtinRepresentation/2.2352.6t3.a.a", "ArtinRepresentation/2.2352.6t3.a"]
"2-2352-3.2-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"3.2"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	1.41692071422204198446561443685	["ModularForm/GL2/Q/holomorphic/2352/1/d/b/785/1", "ModularForm/GL2/Q/holomorphic/2352/1/d/b", "ArtinRepresentation/2.2352.6t3.d.a", "ArtinRepresentation/2.2352.6t3.d"]
"2-2352-588.131-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.131"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.015306122448979591	0	0.922406693256429764080668415927	["ModularForm/GL2/Q/holomorphic/2352/1/dj/a/719/1"]
"2-2352-588.131-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.131"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.18197278911564627	0	0.939974867931265672778694289678	["ModularForm/GL2/Q/holomorphic/2352/1/dj/b/719/1"]
"2-2352-588.143-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.143"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.025510204081632654	0	0.73124525254965483192567757554	["ModularForm/GL2/Q/holomorphic/2352/1/dj/b/143/1"]
"2-2352-588.143-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.143"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.1921768707482993	0	1.14374791223363037929337884004	["ModularForm/GL2/Q/holomorphic/2352/1/dj/a/143/1"]
"2-2352-588.167-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.167"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.4744897959183674	0	0.32137833805072084174409341947	["ModularForm/GL2/Q/holomorphic/2352/1/by/b/1343/1"]
"2-2352-588.167-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.167"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.025510204081632654	0	0.983516527678718631536937445676	["ModularForm/GL2/Q/holomorphic/2352/1/by/a/1343/1"]
"2-2352-588.251-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.251"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.015306122448979591	0	1.48657834125496618821922384319	["ModularForm/GL2/Q/holomorphic/2352/1/by/b/2015/1"]
"2-2352-588.251-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.251"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.4846938775510204	0	1.62699963464516046973364997464	["ModularForm/GL2/Q/holomorphic/2352/1/by/a/2015/1"]
"2-2352-588.299-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.299"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.015306122448979591	0	0.797760276661416708732099727987	["ModularForm/GL2/Q/holomorphic/2352/1/dj/a/2063/1"]
"2-2352-588.299-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.299"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.15136054421768708	0	1.14468434830964565516434189602	["ModularForm/GL2/Q/holomorphic/2352/1/dj/b/2063/1"]
"2-2352-588.311-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.311"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.141156462585034	0	0.70739488757119567377894225129	["ModularForm/GL2/Q/holomorphic/2352/1/dj/a/1487/1"]
"2-2352-588.311-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.311"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.025510204081632654	0	1.50637813220103621201778098390	["ModularForm/GL2/Q/holomorphic/2352/1/dj/b/1487/1"]
"2-2352-588.335-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.335"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.4846938775510204	0	0.06115105804545111330799261571	["ModularForm/GL2/Q/holomorphic/2352/1/by/a/335/1"]
"2-2352-588.335-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.335"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.015306122448979591	0	1.34581639210441885381041289027	["ModularForm/GL2/Q/holomorphic/2352/1/by/b/335/1"]
"2-2352-588.383-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.383"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.12414965986394559	0	0.808216166066214732928758217788	["ModularForm/GL2/Q/holomorphic/2352/1/dj/b/383/1"]
"2-2352-588.383-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.383"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.042517006802721094	0	1.46655236902268370341217876297	["ModularForm/GL2/Q/holomorphic/2352/1/dj/a/383/1"]
"2-2352-588.395-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.395"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.18197278911564627	0	1.33353574528254700881290457374	["ModularForm/GL2/Q/holomorphic/2352/1/dj/b/2159/1"]
"2-2352-588.395-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.395"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.015306122448979591	0	1.45517705064671732413871003382	["ModularForm/GL2/Q/holomorphic/2352/1/dj/a/2159/1"]
"2-2352-588.419-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.419"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.025510204081632654	0	1.32103635466629156961269509082	["ModularForm/GL2/Q/holomorphic/2352/1/by/a/1007/1"]
"2-2352-588.419-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.419"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.4744897959183674	0	2.06139177548181627442371401479	["ModularForm/GL2/Q/holomorphic/2352/1/by/b/1007/1"]
"2-2352-588.467-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.467"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.025510204081632654	0	1.25300934939407960684611742031	["ModularForm/GL2/Q/holomorphic/2352/1/dj/b/1055/1"]
"2-2352-588.467-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.467"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.141156462585034	0	1.28376888281546015808384673873	["ModularForm/GL2/Q/holomorphic/2352/1/dj/a/1055/1"]
"2-2352-588.47-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.47"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.37585034013605445	0	0.53751670027556986150188607865	["ModularForm/GL2/Q/holomorphic/2352/1/dj/a/47/1"]
"2-2352-588.47-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.47"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.4574829931972789	0	2.08049248179818631816501538390	["ModularForm/GL2/Q/holomorphic/2352/1/dj/b/47/1"]
"2-2352-588.479-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.479"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.042517006802721094	0	1.18790844415912775965690583255	["ModularForm/GL2/Q/holomorphic/2352/1/dj/a/479/1"]
"2-2352-588.479-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.479"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.12414965986394559	0	1.31357817656027967580070081997	["ModularForm/GL2/Q/holomorphic/2352/1/dj/b/479/1"]
"2-2352-588.503-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.503"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.20918367346938777	0	1.12110407686471615901915732303	["ModularForm/GL2/Q/holomorphic/2352/1/by/a/1679/1"]
"2-2352-588.503-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.503"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.29081632653061223	0	1.46523429046331886913914401604	["ModularForm/GL2/Q/holomorphic/2352/1/by/b/1679/1"]
"2-2352-588.551-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.551"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.025510204081632654	0	1.13160502629059009106341582093	["ModularForm/GL2/Q/holomorphic/2352/1/dj/b/1727/1"]
"2-2352-588.551-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.551"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.1921768707482993	0	1.82905185714119282530934221579	["ModularForm/GL2/Q/holomorphic/2352/1/dj/a/1727/1"]
"2-2352-588.563-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.563"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.4574829931972789	0	0.37826742947040334565485987556	["ModularForm/GL2/Q/holomorphic/2352/1/dj/b/1151/1"]
"2-2352-588.563-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.563"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.37585034013605445	0	1.76611225388265193728008127396	["ModularForm/GL2/Q/holomorphic/2352/1/dj/a/1151/1"]
"2-2352-588.59-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.59"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.015306122448979591	0	0.932992812627650320666213126638	["ModularForm/GL2/Q/holomorphic/2352/1/dj/a/1823/1"]
"2-2352-588.59-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.59"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.15136054421768708	0	1.75809069991171989920483295506	["ModularForm/GL2/Q/holomorphic/2352/1/dj/b/1823/1"]
"2-2352-588.83-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"588.83"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.29081632653061223	0	0.71995210668647087997647662698	["ModularForm/GL2/Q/holomorphic/2352/1/by/b/671/1"]
"2-2352-588.83-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"588.83"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.20918367346938777	0	1.70956979043850597071234646162	["ModularForm/GL2/Q/holomorphic/2352/1/by/a/671/1"]
"2-2352-84.47-c0-0-0"	1.0834209291465722	1.1738009097128217	2	2352	"84.47"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.0934198098603064	0	0.65229264616749066761673331274	["ModularForm/GL2/Q/holomorphic/2352/1/z/a/1391/1"]
"2-2352-84.47-c0-0-1"	1.0834209291465722	1.1738009097128217	2	2352	"84.47"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.26008647652697303	0	0.845557552588317244927063311378	["ModularForm/GL2/Q/holomorphic/2352/1/z/c/1391/1"]
"2-2352-84.47-c0-0-2"	1.0834209291465722	1.1738009097128217	2	2352	"84.47"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.26008647652697303	0	0.876804002733165351353712806347	["ModularForm/GL2/Q/holomorphic/2352/1/z/d/1391/1"]
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"2-2352-1.1-c3-0-41"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.790406109945933608839055154648	["ModularForm/GL2/Q/holomorphic/2352/4/a/bl/1/1"]
"2-2352-1.1-c3-0-42"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.800498491916692887339731902263	["ModularForm/GL2/Q/holomorphic/2352/4/a/cn/1/4"]
"2-2352-1.1-c3-0-43"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.0	0	0.816630057123859507244975008260	["ModularForm/GL2/Q/holomorphic/2352/4/a/r/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/r"]
"2-2352-1.1-c3-0-44"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.817718502839497621070023924337	["ModularForm/GL2/Q/holomorphic/2352/4/a/cm/1/4"]
"2-2352-1.1-c3-0-45"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.818015891927076990246539509357	["ModularForm/GL2/Q/holomorphic/2352/4/a/cj/1/1"]
"2-2352-1.1-c3-0-46"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.832018042557373744609120251695	["ModularForm/GL2/Q/holomorphic/2352/4/a/cf/1/1"]
"2-2352-1.1-c3-0-47"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.840577023316286179968210761963	["ModularForm/GL2/Q/holomorphic/2352/4/a/cd/1/2"]
"2-2352-1.1-c3-0-48"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.845022109851300899617793417665	["ModularForm/GL2/Q/holomorphic/2352/4/a/bn/1/1"]
"2-2352-1.1-c3-0-49"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.852218576134019872757778431108	["ModularForm/GL2/Q/holomorphic/2352/4/a/cq/1/3"]
"2-2352-1.1-c3-0-5"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.34413226614665664911416399725	["ModularForm/GL2/Q/holomorphic/2352/4/a/cn/1/2"]
"2-2352-1.1-c3-0-50"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.860423437823021475524148428582	["ModularForm/GL2/Q/holomorphic/2352/4/a/bm/1/1"]
"2-2352-1.1-c3-0-51"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.864298108556478629796836981150	["ModularForm/GL2/Q/holomorphic/2352/4/a/bo/1/1"]
"2-2352-1.1-c3-0-52"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.871860779336508881357669304978	["ModularForm/GL2/Q/holomorphic/2352/4/a/bq/1/1"]
"2-2352-1.1-c3-0-53"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.878803159018816621674037834486	["ModularForm/GL2/Q/holomorphic/2352/4/a/cm/1/3"]
"2-2352-1.1-c3-0-54"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.903377867021384661796800276563	["ModularForm/GL2/Q/holomorphic/2352/4/a/br/1/1"]
"2-2352-1.1-c3-0-55"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.906878860400957618746392251934	["ModularForm/GL2/Q/holomorphic/2352/4/a/cd/1/1"]
"2-2352-1.1-c3-0-56"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.912029186720007407272693273454	["ModularForm/GL2/Q/holomorphic/2352/4/a/ci/1/2"]
"2-2352-1.1-c3-0-57"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.936793170367792303702327907250	["ModularForm/GL2/Q/holomorphic/2352/4/a/by/1/2"]
"2-2352-1.1-c3-0-58"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.0	0	0.938063913897322390962744523815	["ModularForm/GL2/Q/holomorphic/2352/4/a/s/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/s"]
"2-2352-1.1-c3-0-59"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.0	0	0.940988938597464027050684691460	["ModularForm/GL2/Q/holomorphic/2352/4/a/bh/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/bh"]
"2-2352-1.1-c3-0-6"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.0	0	0.37292761984696651787224378544	["ModularForm/GL2/Q/holomorphic/2352/4/a/u/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/u"]
"2-2352-1.1-c3-0-60"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.942970035270922539394652223855	["ModularForm/GL2/Q/holomorphic/2352/4/a/ck/1/4"]
"2-2352-1.1-c3-0-61"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.947769038879111320623033531694	["ModularForm/GL2/Q/holomorphic/2352/4/a/ce/1/2"]
"2-2352-1.1-c3-0-62"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	0.948705538928507146630026494703	["ModularForm/GL2/Q/holomorphic/2352/4/a/cl/1/1"]
"2-2352-1.1-c3-0-63"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.963459406538530712534210879917	["ModularForm/GL2/Q/holomorphic/2352/4/a/ci/1/3"]
"2-2352-1.1-c3-0-64"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.963753306978551847029839855192	["ModularForm/GL2/Q/holomorphic/2352/4/a/cp/1/4"]
"2-2352-1.1-c3-0-65"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.999518116360043025161050530163	["ModularForm/GL2/Q/holomorphic/2352/4/a/cf/1/2"]
"2-2352-1.1-c3-0-66"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	1.01253358967009164274818646198	["ModularForm/GL2/Q/holomorphic/2352/4/a/cj/1/3"]
"2-2352-1.1-c3-0-67"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.01367905803074433004069681232	["ModularForm/GL2/Q/holomorphic/2352/4/a/cl/1/2"]
"2-2352-1.1-c3-0-68"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.03266015725820616716261505334	["ModularForm/GL2/Q/holomorphic/2352/4/a/bs/1/1"]
"2-2352-1.1-c3-0-69"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.0	0	1.03556745157569230889580165492	["ModularForm/GL2/Q/holomorphic/2352/4/a/q/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/q"]
"2-2352-1.1-c3-0-7"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.38837998064550755926734499113	["ModularForm/GL2/Q/holomorphic/2352/4/a/by/1/1"]
"2-2352-1.1-c3-0-70"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.03897870946516744300063282953	["ModularForm/GL2/Q/holomorphic/2352/4/a/bt/1/1"]
"2-2352-1.1-c3-0-71"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.5	1	1.04394674450421689707309850836	["ModularForm/GL2/Q/holomorphic/2352/4/a/c/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/c"]
"2-2352-1.1-c3-0-72"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.05244787555675405115651522658	["ModularForm/GL2/Q/holomorphic/2352/4/a/bm/1/2"]
"2-2352-1.1-c3-0-73"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.07587806306217472055390805781	["ModularForm/GL2/Q/holomorphic/2352/4/a/ca/1/1"]
"2-2352-1.1-c3-0-74"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.5	1	1.07892985303383290882430112999	["ModularForm/GL2/Q/holomorphic/2352/4/a/i/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/i"]
"2-2352-1.1-c3-0-75"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.5	1	1.10576222542035645039706575422	["ModularForm/GL2/Q/holomorphic/2352/4/a/h/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/h"]
"2-2352-1.1-c3-0-76"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.5	1	1.11133623147651298710133847655	["ModularForm/GL2/Q/holomorphic/2352/4/a/f/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/f"]
"2-2352-1.1-c3-0-77"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.5	1	1.11197674119856643993294489875	["ModularForm/GL2/Q/holomorphic/2352/4/a/j/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/j"]
"2-2352-1.1-c3-0-78"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.5	1	1.14399748812826999310452274977	["ModularForm/GL2/Q/holomorphic/2352/4/a/v/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/v"]
"2-2352-1.1-c3-0-79"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.15364362071065385627114782881	["ModularForm/GL2/Q/holomorphic/2352/4/a/co/1/1"]
"2-2352-1.1-c3-0-8"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.40553889271913398338234579370	["ModularForm/GL2/Q/holomorphic/2352/4/a/cg/1/2"]
"2-2352-1.1-c3-0-80"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.5	1	1.15454793729519640680553043144	["ModularForm/GL2/Q/holomorphic/2352/4/a/y/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/y"]
"2-2352-1.1-c3-0-81"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.15793282097290618238334460836	["ModularForm/GL2/Q/holomorphic/2352/4/a/co/1/2"]
"2-2352-1.1-c3-0-82"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.16128508964478700119890521665	["ModularForm/GL2/Q/holomorphic/2352/4/a/bl/1/2"]
"2-2352-1.1-c3-0-83"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.5	1	1.16666088383296961106763994963	["ModularForm/GL2/Q/holomorphic/2352/4/a/t/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/t"]
"2-2352-1.1-c3-0-84"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	1.18177444876055460447460858930	["ModularForm/GL2/Q/holomorphic/2352/4/a/cq/1/4"]
"2-2352-1.1-c3-0-85"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.0	0	1.18720429367725370322820570190	["ModularForm/GL2/Q/holomorphic/2352/4/a/bj/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/bj"]
"2-2352-1.1-c3-0-86"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.5	1	1.19004964692954393177442849285	["ModularForm/GL2/Q/holomorphic/2352/4/a/k/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/k"]
"2-2352-1.1-c3-0-87"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.19484605574209766719975417736	["ModularForm/GL2/Q/holomorphic/2352/4/a/bz/1/1"]
"2-2352-1.1-c3-0-88"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.22079080493526719760494007877	["ModularForm/GL2/Q/holomorphic/2352/4/a/bu/1/2"]
"2-2352-1.1-c3-0-89"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.22093617224881183511012659946	["ModularForm/GL2/Q/holomorphic/2352/4/a/bn/1/2"]
"2-2352-1.1-c3-0-9"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.0	0	0.43956662763254163552126478447	["ModularForm/GL2/Q/holomorphic/2352/4/a/cq/1/1"]
"2-2352-1.1-c3-0-90"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.22566106239991888515509576555	["ModularForm/GL2/Q/holomorphic/2352/4/a/cl/1/3"]
"2-2352-1.1-c3-0-91"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.22597306770555361957734617123	["ModularForm/GL2/Q/holomorphic/2352/4/a/bx/1/1"]
"2-2352-1.1-c3-0-92"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.5	1	1.22647990755166036226127108245	["ModularForm/GL2/Q/holomorphic/2352/4/a/z/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/z"]
"2-2352-1.1-c3-0-93"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.5	1	1.24037550534884911780788553058	["ModularForm/GL2/Q/holomorphic/2352/4/a/o/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/o"]
"2-2352-1.1-c3-0-94"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.25212773238234968325918313147	["ModularForm/GL2/Q/holomorphic/2352/4/a/cr/1/1"]
"2-2352-1.1-c3-0-95"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.25476943943925019566536326967	["ModularForm/GL2/Q/holomorphic/2352/4/a/bu/1/1"]
"2-2352-1.1-c3-0-96"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.5	1	1.27254971812725897729777756503	["ModularForm/GL2/Q/holomorphic/2352/4/a/n/1/1", "ModularForm/GL2/Q/holomorphic/2352/4/a/n"]
"2-2352-1.1-c3-0-97"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.31068244076930782402594578819	["ModularForm/GL2/Q/holomorphic/2352/4/a/cl/1/4"]
"2-2352-1.1-c3-0-98"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.31498927224312596647926966662	["ModularForm/GL2/Q/holomorphic/2352/4/a/cr/1/2"]
"2-2352-1.1-c3-0-99"	11.78017369708537	138.772492333502	2	2352	"1.1"	[]	[[1.5, 0.0]]	3	true	true	false	true	0.5	1	1.31736988298366637172400569673	["ModularForm/GL2/Q/holomorphic/2352/4/a/bs/1/2"]


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

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


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


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



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

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

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



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

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


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

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


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


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


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

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

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



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


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

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

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



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

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


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


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


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


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


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


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

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


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

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

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


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

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