# lfunc_search downloaded from the LMFDB on 26 July 2026.
# Search link: https://www.lmfdb.org/L/2/207/207.137
# Query "{'degree': 2, 'conductor': 207}" returned 8338 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.



"2-207-207.160-c0-0-0"	0.32141321941549245	0.1033064576150315	2	207	"207.160"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.33333333333333337	0	1.71818216672499630298919976284	["ModularForm/GL2/Q/holomorphic/207/1/f/a/160/1"]
"2-207-207.160-c0-0-1"	0.32141321941549245	0.1033064576150315	2	207	"207.160"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.0	0	2.31067133706731657237815546333	["ModularForm/GL2/Q/holomorphic/207/1/f/a/160/2"]
"2-207-207.160-c0-0-2"	0.32141321941549245	0.1033064576150315	2	207	"207.160"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.33333333333333337	0	3.59256274110444935456057849803	["ModularForm/GL2/Q/holomorphic/207/1/f/a/160/3"]
"2-207-207.22-c0-0-0"	0.32141321941549245	0.1033064576150315	2	207	"207.22"	[]	[[0.0, 0.0]]	0	true	true	false	false	-0.33333333333333337	0	1.73225099048033422953589967046	["ModularForm/GL2/Q/holomorphic/207/1/f/a/22/3"]
"2-207-207.22-c0-0-1"	0.32141321941549245	0.1033064576150315	2	207	"207.22"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.0	0	2.25393059789021078712292873229	["ModularForm/GL2/Q/holomorphic/207/1/f/a/22/2"]
"2-207-207.22-c0-0-2"	0.32141321941549245	0.1033064576150315	2	207	"207.22"	[]	[[0.0, 0.0]]	0	true	true	false	false	0.33333333333333337	0	2.93369459737726509413576750423	["ModularForm/GL2/Q/holomorphic/207/1/f/a/22/1"]
"2-207-23.22-c0-0-0"	0.32141321941549245	0.1033064576150315	2	207	"23.22"	[]	[[0.0, 0.0]]	0	true	true	true	true	0.0	0	2.70040131053722579925112536657	["ModularForm/GL2/Q/holomorphic/207/1/d/a/91/1", "ModularForm/GL2/Q/holomorphic/207/1/d/a", "ArtinRepresentation/2.207.6t3.a.a", "ArtinRepresentation/2.207.6t3.a"]
"2-207-1.1-c1-0-0"	1.2856528776619702	1.6529033218405047	2	207	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.35438371505727771810386896528	["ModularForm/GL2/Q/holomorphic/207/2/a/d/1/1"]
"2-207-1.1-c1-0-1"	1.2856528776619702	1.6529033218405047	2	207	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.36694706165124286307138591500	["ModularForm/GL2/Q/holomorphic/207/2/a/c/1/1"]
"2-207-1.1-c1-0-2"	1.2856528776619702	1.6529033218405047	2	207	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	1.55622971706613776760962848048	["ModularForm/GL2/Q/holomorphic/207/2/a/e/1/1"]
"2-207-1.1-c1-0-3"	1.2856528776619702	1.6529033218405047	2	207	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	2.20177691065970790790432842988	["ModularForm/GL2/Q/holomorphic/207/2/a/b/1/1"]
"2-207-1.1-c1-0-4"	1.2856528776619702	1.6529033218405047	2	207	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.24040738187388492336580816587	["ModularForm/GL2/Q/holomorphic/207/2/a/d/1/2"]
"2-207-1.1-c1-0-5"	1.2856528776619702	1.6529033218405047	2	207	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.43350663926757041321316798946	["ModularForm/GL2/Q/holomorphic/207/2/a/c/1/2"]
"2-207-1.1-c1-0-6"	1.2856528776619702	1.6529033218405047	2	207	"1.1"	[]	[[0.5, 0.0]]	1	true	true	true	true	0.5	1	2.56565233054647425716584327864	["EllipticCurve/Q/207/a", "ModularForm/GL2/Q/holomorphic/207/2/a/a/1/1", "ModularForm/GL2/Q/holomorphic/207/2/a/a"]
"2-207-1.1-c1-0-7"	1.2856528776619702	1.6529033218405047	2	207	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.0	0	2.62931122275476910363783739075	["ModularForm/GL2/Q/holomorphic/207/2/a/e/1/2"]
"2-207-1.1-c1-0-8"	1.2856528776619702	1.6529033218405047	2	207	"1.1"	[]	[[0.5, 0.0]]	1	true	true	false	true	0.5	1	3.21105387653454934310381798050	["ModularForm/GL2/Q/holomorphic/207/2/a/b/1/2"]
"2-207-207.11-c1-0-0"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2848890211896823	0	0.10833978538818767998953367187	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/3"]
"2-207-207.11-c1-0-1"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.46133089764598856	0	0.25792567856300773414937602247	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/5"]
"2-207-207.11-c1-0-10"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.15786574460182845	0	1.58167147827189632487674051693	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/10"]
"2-207-207.11-c1-0-11"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.10580890748015659	0	2.05686788817164018610653874683	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/19"]
"2-207-207.11-c1-0-12"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.35890022586073606	0	2.08550846086362579606784265669	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/6"]
"2-207-207.11-c1-0-13"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.045097210491059594	0	2.10338271175987192519557051285	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/16"]
"2-207-207.11-c1-0-14"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.24483772303954693	0	2.12183753218060239963901181516	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/4"]
"2-207-207.11-c1-0-15"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.06499781088110326	0	2.30088475091348932245853180241	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/21"]
"2-207-207.11-c1-0-16"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.009968111455168984	0	2.40633199513136122092051197593	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/22"]
"2-207-207.11-c1-0-17"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.35827408382112785	0	2.68914608336531739739076073910	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/12"]
"2-207-207.11-c1-0-18"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.10675767673685403	0	2.81705711401151934833932569723	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/20"]
"2-207-207.11-c1-0-19"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2859566383694382	0	2.89322148302192744870004476013	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/14"]
"2-207-207.11-c1-0-2"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.11170019918428409	0	0.799213469238351928127900293717	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/9"]
"2-207-207.11-c1-0-20"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.06231713256707431	0	2.93725705810328785284474942726	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/18"]
"2-207-207.11-c1-0-21"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.4433392035659325	0	3.58904583852723709667667542238	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/13"]
"2-207-207.11-c1-0-3"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.3145485594119178	0	0.901258777843582052160852181826	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/15"]
"2-207-207.11-c1-0-4"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.03866936992172973	0	0.992619150927682938121678904987	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/2"]
"2-207-207.11-c1-0-5"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1683884347355944	0	1.08666646280188965924704602618	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/1"]
"2-207-207.11-c1-0-6"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2350014106119726	0	1.13452071180619481685951457736	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/7"]
"2-207-207.11-c1-0-7"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.1256907396051219	0	1.34439970310241390289040002913	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/17"]
"2-207-207.11-c1-0-8"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.001786675745629812	0	1.47846563222599345707770276447	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/8"]
"2-207-207.11-c1-0-9"	1.2856528776619702	1.6529033218405047	2	207	"207.11"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.040634125617013225	0	1.48886973188113765631894691008	["ModularForm/GL2/Q/holomorphic/207/2/o/a/11/11"]
"2-207-207.113-c1-0-0"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.4433392035659325	0	0.07316399187973143144094468002	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/13"]
"2-207-207.113-c1-0-1"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.35827408382112785	0	0.28755926499326395076583107792	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/12"]
"2-207-207.113-c1-0-10"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.03866936992172973	0	1.49605198743694194713535155775	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/2"]
"2-207-207.113-c1-0-11"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.040634125617013225	0	2.03505256127745260128384146525	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/11"]
"2-207-207.113-c1-0-12"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2350014106119726	0	2.14737282155048466867538028125	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/7"]
"2-207-207.113-c1-0-13"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.10675767673685403	0	2.17072487229543263351542348028	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/20"]
"2-207-207.113-c1-0-14"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.06231713256707431	0	2.31912401035301126267722924100	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/18"]
"2-207-207.113-c1-0-15"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1256907396051219	0	2.32662100924428680469054160301	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/17"]
"2-207-207.113-c1-0-16"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.009968111455168984	0	2.34865452306744585215167687896	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/22"]
"2-207-207.113-c1-0-17"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.46133089764598856	0	2.49438450231169445127608406436	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/5"]
"2-207-207.113-c1-0-18"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.045097210491059594	0	2.50494481551351236930013470052	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/16"]
"2-207-207.113-c1-0-19"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.06499781088110326	0	2.82968367900942269677149720560	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/21"]
"2-207-207.113-c1-0-2"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.35890022586073606	0	0.56906937813241421929184082509	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/6"]
"2-207-207.113-c1-0-20"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.10580890748015659	0	2.86513526055505551167939363334	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/19"]
"2-207-207.113-c1-0-21"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.3145485594119178	0	2.87038942477033989248449546463	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/15"]
"2-207-207.113-c1-0-3"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.15786574460182845	0	0.65574202484247966472683189640	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/10"]
"2-207-207.113-c1-0-4"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.24483772303954693	0	0.865208629179986896754823279397	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/4"]
"2-207-207.113-c1-0-5"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.2859566383694382	0	0.978413799968160785501014529396	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/14"]
"2-207-207.113-c1-0-6"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.2848890211896823	0	1.19149873917108008552587888706	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/3"]
"2-207-207.113-c1-0-7"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.11170019918428409	0	1.39017261168643784027581020136	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/9"]
"2-207-207.113-c1-0-8"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.1683884347355944	0	1.40992137764010289499366256106	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/1"]
"2-207-207.113-c1-0-9"	1.2856528776619702	1.6529033218405047	2	207	"207.113"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.001786675745629812	0	1.46643583318201835600420497830	["ModularForm/GL2/Q/holomorphic/207/2/o/a/113/8"]
"2-207-207.121-c1-0-0"	1.2856528776619702	1.6529033218405047	2	207	"207.121"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.40304022105176895	0	0.05118815471964467942602839249	["ModularForm/GL2/Q/holomorphic/207/2/m/a/121/10"]
"2-207-207.121-c1-0-1"	1.2856528776619702	1.6529033218405047	2	207	"207.121"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.45279127988037127	0	0.39138323857762693263177358186	["ModularForm/GL2/Q/holomorphic/207/2/m/a/121/7"]
"2-207-207.121-c1-0-10"	1.2856528776619702	1.6529033218405047	2	207	"207.121"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.09994081763715643	0	1.57587936008395445141227236645	["ModularForm/GL2/Q/holomorphic/207/2/m/a/121/11"]
"2-207-207.121-c1-0-11"	1.2856528776619702	1.6529033218405047	2	207	"207.121"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.10882756707986328	0	1.87602022255309150772075829424	["ModularForm/GL2/Q/holomorphic/207/2/m/a/121/20"]
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"2-207-3.2-c12-0-59"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.09795663800765181	0	0.901950078186772608926667970901	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/63"]
"2-207-3.2-c12-0-6"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.4020433619923482	0	0.089467325852013639171542634574	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/50"]
"2-207-3.2-c12-0-60"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.09795663800765181	0	0.923685006645851137211101710074	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/86"]
"2-207-3.2-c12-0-61"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.4020433619923482	0	0.927056348699094235059459778143	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/14"]
"2-207-3.2-c12-0-62"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.09795663800765181	0	0.979088520446552628457061797578	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/45"]
"2-207-3.2-c12-0-63"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.09795663800765181	0	0.980305792788060698194455135432	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/40"]
"2-207-3.2-c12-0-64"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.4020433619923482	0	1.00442551674540575335061363126	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/9"]
"2-207-3.2-c12-0-65"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.4020433619923482	0	1.02692484509772655668156514530	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/29"]
"2-207-3.2-c12-0-66"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.4020433619923482	0	1.06288671145699340310526140741	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/21"]
"2-207-3.2-c12-0-67"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.09795663800765181	0	1.07450030983835343639872691611	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/71"]
"2-207-3.2-c12-0-68"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.09795663800765181	0	1.08658860880890767459582557190	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/57"]
"2-207-3.2-c12-0-69"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.09795663800765181	0	1.10195338572022591375970013991	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/84"]
"2-207-3.2-c12-0-7"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.09795663800765181	0	0.094038347152005246436694447414	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/65"]
"2-207-3.2-c12-0-70"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.09795663800765181	0	1.11378642013815834117032420263	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/44"]
"2-207-3.2-c12-0-71"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.09795663800765181	0	1.13389959647446640793140568719	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/61"]
"2-207-3.2-c12-0-72"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.4020433619923482	0	1.14690953331444486083773529686	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/43"]
"2-207-3.2-c12-0-73"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.4020433619923482	0	1.16474053565787525976253596068	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/34"]
"2-207-3.2-c12-0-74"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.4020433619923482	0	1.16707150821237793043506174790	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/23"]
"2-207-3.2-c12-0-75"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.4020433619923482	0	1.19675989814541739797669940830	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/31"]
"2-207-3.2-c12-0-76"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.09795663800765181	0	1.21480767212600613208330617779	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/64"]
"2-207-3.2-c12-0-77"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.09795663800765181	0	1.31535364291110092539198476335	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/1"]
"2-207-3.2-c12-0-78"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.4020433619923482	0	1.40945694191836123861296396954	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/22"]
"2-207-3.2-c12-0-79"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.4020433619923482	0	1.42666144459750628535253774198	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/37"]
"2-207-3.2-c12-0-8"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.09795663800765181	0	0.11084825635573862680755218365	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/28"]
"2-207-3.2-c12-0-80"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.4020433619923482	0	1.49539332475496311602404964857	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/20"]
"2-207-3.2-c12-0-81"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.4020433619923482	0	1.52073323108898017164706556165	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/56"]
"2-207-3.2-c12-0-82"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.4020433619923482	0	1.58056208219953094836217322957	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/35"]
"2-207-3.2-c12-0-83"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.4020433619923482	0	1.61393724152254009491685906795	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/39"]
"2-207-3.2-c12-0-84"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.4020433619923482	0	1.69146905131243335562677296339	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/59"]
"2-207-3.2-c12-0-85"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.09795663800765181	0	1.74708901236712475300944861637	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/16"]
"2-207-3.2-c12-0-86"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	0.09795663800765181	0	1.83588026811524330114669835955	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/4"]
"2-207-3.2-c12-0-87"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.09795663800765181	0	1.85340542469025470104152352586	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/24"]
"2-207-3.2-c12-0-9"	13.754879867748434	189.19672017619115	2	207	"3.2"	[]	[[6.0, 0.0]]	12	true	true	false	false	-0.4020433619923482	0	0.12549230968012249785994939987	["ModularForm/GL2/Q/holomorphic/207/13/b/a/116/83"]


# 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).