# lfunc_search downloaded from the LMFDB on 24 June 2026.
# Search link: https://www.lmfdb.org/L/2/18
# Query "{'degree': 2, 'conductor': 18}" returned 2566 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.



"2-18-9.4-c1-0-0"	0.379118350437307	0.14373072363830475	2	18	"9.4"	[]	[[0.5, 0.0]]	1	true	true	false	false	0.05555555555555555	0	5.52147912858687978615646302053	["ModularForm/GL2/Q/holomorphic/18/2/c/a/13/1"]
"2-18-9.7-c1-0-0"	0.379118350437307	0.14373072363830475	2	18	"9.7"	[]	[[0.5, 0.0]]	1	true	true	false	false	-0.05555555555555555	0	4.36179441556210697223984606647	["ModularForm/GL2/Q/holomorphic/18/2/c/a/7/1"]
"2-18-3.2-c2-0-0"	0.7003316898788277	0.4904644758485345	2	18	"3.2"	[]	[[1.0, 0.0]]	2	true	true	false	false	-0.09795663800765181	0	3.36175297440665047564543646315	["ModularForm/GL2/Q/holomorphic/18/3/b/a/17/2"]
"2-18-3.2-c2-0-1"	0.7003316898788277	0.4904644758485345	2	18	"3.2"	[]	[[1.0, 0.0]]	2	true	true	false	false	0.09795663800765181	0	4.71803328341868101997909002331	["ModularForm/GL2/Q/holomorphic/18/3/b/a/17/1"]
"2-18-9.2-c2-0-0"	0.7003316898788277	0.4904644758485345	2	18	"9.2"	[]	[[1.0, 0.0]]	2	true	true	false	false	0.08186450176247415	0	4.16831666093679399606816968694	["ModularForm/GL2/Q/holomorphic/18/3/d/a/11/1"]
"2-18-9.2-c2-0-1"	0.7003316898788277	0.4904644758485345	2	18	"9.2"	[]	[[1.0, 0.0]]	2	true	true	false	false	-0.02630894620691859	0	4.28355042116739765382981373077	["ModularForm/GL2/Q/holomorphic/18/3/d/a/11/2"]
"2-18-9.5-c2-0-0"	0.7003316898788277	0.4904644758485345	2	18	"9.5"	[]	[[1.0, 0.0]]	2	true	true	false	false	-0.08186450176247415	0	3.08266487875230505300547482247	["ModularForm/GL2/Q/holomorphic/18/3/d/a/5/1"]
"2-18-9.5-c2-0-1"	0.7003316898788277	0.4904644758485345	2	18	"9.5"	[]	[[1.0, 0.0]]	2	true	true	false	false	0.02630894620691859	0	4.44660395771464814953646858087	["ModularForm/GL2/Q/holomorphic/18/3/d/a/5/2"]
"2-18-1.1-c3-0-0"	1.0305505228291	1.0620343801033316	2	18	"1.1"	[]	[[1.5, 0.0]]	3	true	true	true	true	0.0	0	3.60929026962551384976945217111	["ModularForm/GL2/Q/holomorphic/18/4/a/a/1/1", "ModularForm/GL2/Q/holomorphic/18/4/a/a"]
"2-18-9.4-c3-0-0"	1.0305505228291	1.0620343801033316	2	18	"9.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.1644114901492248	0	2.49126116116257301076434845504	["ModularForm/GL2/Q/holomorphic/18/4/c/b/13/1"]
"2-18-9.4-c3-0-1"	1.0305505228291	1.0620343801033316	2	18	"9.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.05781073207299744	0	3.33354277687313836026402320475	["ModularForm/GL2/Q/holomorphic/18/4/c/b/13/2"]
"2-18-9.4-c3-0-2"	1.0305505228291	1.0620343801033316	2	18	"9.4"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.2222222222222222	0	4.38699503553042529087882060291	["ModularForm/GL2/Q/holomorphic/18/4/c/a/13/1"]
"2-18-9.7-c3-0-0"	1.0305505228291	1.0620343801033316	2	18	"9.7"	[]	[[1.5, 0.0]]	3	true	true	false	false	-0.2222222222222222	0	1.94503011243440762792153454089	["ModularForm/GL2/Q/holomorphic/18/4/c/a/7/1"]
"2-18-9.7-c3-0-1"	1.0305505228291	1.0620343801033316	2	18	"9.7"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.05781073207299744	0	3.62768242447689383205795706978	["ModularForm/GL2/Q/holomorphic/18/4/c/b/7/2"]
"2-18-9.7-c3-0-2"	1.0305505228291	1.0620343801033316	2	18	"9.7"	[]	[[1.5, 0.0]]	3	true	true	false	false	0.1644114901492248	0	4.67515235124625793810476954388	["ModularForm/GL2/Q/holomorphic/18/4/c/b/7/1"]
"2-18-9.2-c4-0-0"	1.3640598724063393	1.8606593355091985	2	18	"9.2"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.3879404840356162	0	0.35896396520025872083368777390	["ModularForm/GL2/Q/holomorphic/18/5/d/a/11/1"]
"2-18-9.2-c4-0-1"	1.3640598724063393	1.8606593355091985	2	18	"9.2"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.1624683198609998	0	2.18552047483969715815150323590	["ModularForm/GL2/Q/holomorphic/18/5/d/a/11/3"]
"2-18-9.2-c4-0-2"	1.3640598724063393	1.8606593355091985	2	18	"9.2"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.001989258288445687	0	2.28589222508502348599037561037	["ModularForm/GL2/Q/holomorphic/18/5/d/a/11/2"]
"2-18-9.2-c4-0-3"	1.3640598724063393	1.8606593355091985	2	18	"9.2"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.007136009947385263	0	3.20693269571621856355343984246	["ModularForm/GL2/Q/holomorphic/18/5/d/a/11/4"]
"2-18-9.5-c4-0-0"	1.3640598724063393	1.8606593355091985	2	18	"9.5"	[]	[[2.0, 0.0]]	4	true	true	false	false	-0.001989258288445687	0	2.48999694692836780762156599905	["ModularForm/GL2/Q/holomorphic/18/5/d/a/5/2"]
"2-18-9.5-c4-0-1"	1.3640598724063393	1.8606593355091985	2	18	"9.5"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.007136009947385263	0	2.95719226246400729747482457102	["ModularForm/GL2/Q/holomorphic/18/5/d/a/5/4"]
"2-18-9.5-c4-0-2"	1.3640598724063393	1.8606593355091985	2	18	"9.5"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.3879404840356162	0	3.91116000143257416537261368829	["ModularForm/GL2/Q/holomorphic/18/5/d/a/5/1"]
"2-18-9.5-c4-0-3"	1.3640598724063393	1.8606593355091985	2	18	"9.5"	[]	[[2.0, 0.0]]	4	true	true	false	false	0.1624683198609998	0	3.98279971393923136417242305414	["ModularForm/GL2/Q/holomorphic/18/5/d/a/5/3"]
"2-18-1.1-c5-0-0"	1.699090567519475	2.8869087566336518	2	18	"1.1"	[]	[[2.5, 0.0]]	5	true	true	true	true	0.0	0	1.85679263470097699384725873814	["ModularForm/GL2/Q/holomorphic/18/6/a/b/1/1", "ModularForm/GL2/Q/holomorphic/18/6/a/b"]
"2-18-1.1-c5-0-1"	1.699090567519475	2.8869087566336518	2	18	"1.1"	[]	[[2.5, 0.0]]	5	true	true	true	true	0.0	0	2.58758120757187154637192667425	["ModularForm/GL2/Q/holomorphic/18/6/a/c/1/1", "ModularForm/GL2/Q/holomorphic/18/6/a/c"]
"2-18-1.1-c5-0-2"	1.699090567519475	2.8869087566336518	2	18	"1.1"	[]	[[2.5, 0.0]]	5	true	true	true	true	0.5	1	3.68613502464121962042518342836	["ModularForm/GL2/Q/holomorphic/18/6/a/a/1/1", "ModularForm/GL2/Q/holomorphic/18/6/a/a"]
"2-18-9.4-c5-0-0"	1.699090567519475	2.8869087566336518	2	18	"9.4"	[]	[[2.5, 0.0]]	5	true	true	false	false	-0.3859512257471705	0	0.874351368839317877182743688301	["ModularForm/GL2/Q/holomorphic/18/6/c/a/13/1"]
"2-18-9.4-c5-0-1"	1.699090567519475	2.8869087566336518	2	18	"9.4"	[]	[[2.5, 0.0]]	5	true	true	false	false	-0.2278761414320309	0	0.916430588039136972737422307563	["ModularForm/GL2/Q/holomorphic/18/6/c/b/13/2"]
"2-18-9.4-c5-0-2"	1.699090567519475	2.8869087566336518	2	18	"9.4"	[]	[[2.5, 0.0]]	5	true	true	false	false	-0.16960432980838505	0	2.08851336967836819239291254926	["ModularForm/GL2/Q/holomorphic/18/6/c/a/13/2"]
"2-18-9.4-c5-0-3"	1.699090567519475	2.8869087566336518	2	18	"9.4"	[]	[[2.5, 0.0]]	5	true	true	false	false	0.1911975587699587	0	2.87567830729649205634322786998	["ModularForm/GL2/Q/holomorphic/18/6/c/b/13/3"]
"2-18-9.4-c5-0-4"	1.699090567519475	2.8869087566336518	2	18	"9.4"	[]	[[2.5, 0.0]]	5	true	true	false	false	-0.46332141733792787	0	4.56636687833116194394944606844	["ModularForm/GL2/Q/holomorphic/18/6/c/b/13/1"]
"2-18-9.7-c5-0-0"	1.699090567519475	2.8869087566336518	2	18	"9.7"	[]	[[2.5, 0.0]]	5	true	true	false	false	0.46332141733792787	0	0.31637154417658173846555528120	["ModularForm/GL2/Q/holomorphic/18/6/c/b/7/1"]
"2-18-9.7-c5-0-1"	1.699090567519475	2.8869087566336518	2	18	"9.7"	[]	[[2.5, 0.0]]	5	true	true	false	false	-0.1911975587699587	0	1.71573879529527477054922217364	["ModularForm/GL2/Q/holomorphic/18/6/c/b/7/3"]
"2-18-9.7-c5-0-2"	1.699090567519475	2.8869087566336518	2	18	"9.7"	[]	[[2.5, 0.0]]	5	true	true	false	false	0.2278761414320309	0	3.06793779425881685658265795884	["ModularForm/GL2/Q/holomorphic/18/6/c/b/7/2"]
"2-18-9.7-c5-0-3"	1.699090567519475	2.8869087566336518	2	18	"9.7"	[]	[[2.5, 0.0]]	5	true	true	false	false	0.16960432980838505	0	3.27599549842234091842542519150	["ModularForm/GL2/Q/holomorphic/18/6/c/a/7/2"]
"2-18-9.7-c5-0-4"	1.699090567519475	2.8869087566336518	2	18	"9.7"	[]	[[2.5, 0.0]]	5	true	true	false	false	0.3859512257471705	0	4.13378035640076703048240740136	["ModularForm/GL2/Q/holomorphic/18/6/c/a/7/1"]
"2-18-3.2-c6-0-0"	2.0349382067171766	4.140973505157318	2	18	"3.2"	[]	[[3.0, 0.0]]	6	true	true	false	false	-0.4020433619923482	0	0.77636111964462645662059400391	["ModularForm/GL2/Q/holomorphic/18/7/b/a/17/2"]
"2-18-3.2-c6-0-1"	2.0349382067171766	4.140973505157318	2	18	"3.2"	[]	[[3.0, 0.0]]	6	true	true	false	false	0.4020433619923482	0	3.40488705269129499046290458171	["ModularForm/GL2/Q/holomorphic/18/7/b/a/17/1"]
"2-18-9.2-c6-0-0"	2.0349382067171766	4.140973505157318	2	18	"9.2"	[]	[[3.0, 0.0]]	6	true	true	false	false	-0.35835326073128543	0	0.05974136556983953401149895312	["ModularForm/GL2/Q/holomorphic/18/7/d/a/11/2"]
"2-18-9.2-c6-0-1"	2.0349382067171766	4.140973505157318	2	18	"9.2"	[]	[[3.0, 0.0]]	6	true	true	false	false	-0.3822988327173456	0	0.75577935722495958755642441221	["ModularForm/GL2/Q/holomorphic/18/7/d/a/11/4"]
"2-18-9.2-c6-0-2"	2.0349382067171766	4.140973505157318	2	18	"9.2"	[]	[[3.0, 0.0]]	6	true	true	false	false	0.09230359162733376	0	1.65792738516953793636586036853	["ModularForm/GL2/Q/holomorphic/18/7/d/a/11/1"]
"2-18-9.2-c6-0-3"	2.0349382067171766	4.140973505157318	2	18	"9.2"	[]	[[3.0, 0.0]]	6	true	true	false	false	-0.12108284847216458	0	2.10492963411147185629111956060	["ModularForm/GL2/Q/holomorphic/18/7/d/a/11/6"]
"2-18-9.2-c6-0-4"	2.0349382067171766	4.140973505157318	2	18	"9.2"	[]	[[3.0, 0.0]]	6	true	true	false	false	0.17830984105804074	0	2.36328460336228856892955483412	["ModularForm/GL2/Q/holomorphic/18/7/d/a/11/3"]
"2-18-9.2-c6-0-5"	2.0349382067171766	4.140973505157318	2	18	"9.2"	[]	[[3.0, 0.0]]	6	true	true	false	false	0.09112150923542105	0	2.60353758399536868074866720700	["ModularForm/GL2/Q/holomorphic/18/7/d/a/11/5"]
"2-18-9.5-c6-0-0"	2.0349382067171766	4.140973505157318	2	18	"9.5"	[]	[[3.0, 0.0]]	6	true	true	false	false	-0.09230359162733376	0	1.24705781352702887841057263612	["ModularForm/GL2/Q/holomorphic/18/7/d/a/5/1"]
"2-18-9.5-c6-0-1"	2.0349382067171766	4.140973505157318	2	18	"9.5"	[]	[[3.0, 0.0]]	6	true	true	false	false	-0.17830984105804074	0	1.42489293160621109759278876731	["ModularForm/GL2/Q/holomorphic/18/7/d/a/5/3"]
"2-18-9.5-c6-0-2"	2.0349382067171766	4.140973505157318	2	18	"9.5"	[]	[[3.0, 0.0]]	6	true	true	false	false	-0.09112150923542105	0	1.64997347428988153635377497744	["ModularForm/GL2/Q/holomorphic/18/7/d/a/5/5"]
"2-18-9.5-c6-0-3"	2.0349382067171766	4.140973505157318	2	18	"9.5"	[]	[[3.0, 0.0]]	6	true	true	false	false	0.35835326073128543	0	2.51361554893894988813593547435	["ModularForm/GL2/Q/holomorphic/18/7/d/a/5/2"]
"2-18-9.5-c6-0-4"	2.0349382067171766	4.140973505157318	2	18	"9.5"	[]	[[3.0, 0.0]]	6	true	true	false	false	0.12108284847216458	0	2.89893191550281573396473599301	["ModularForm/GL2/Q/holomorphic/18/7/d/a/5/6"]
"2-18-9.5-c6-0-5"	2.0349382067171766	4.140973505157318	2	18	"9.5"	[]	[[3.0, 0.0]]	6	true	true	false	false	0.3822988327173456	0	3.73828622670048338695051379995	["ModularForm/GL2/Q/holomorphic/18/7/d/a/5/4"]
"2-18-1.1-c7-0-0"	2.371271907376755	5.622930458714194	2	18	"1.1"	[]	[[3.5, 0.0]]	7	true	true	true	true	0.0	0	2.04690062189311991864848601401	["ModularForm/GL2/Q/holomorphic/18/8/a/b/1/1", "ModularForm/GL2/Q/holomorphic/18/8/a/b"]
"2-18-1.1-c7-0-1"	2.371271907376755	5.622930458714194	2	18	"1.1"	[]	[[3.5, 0.0]]	7	true	true	true	true	0.5	1	2.81314350215253161204777886583	["ModularForm/GL2/Q/holomorphic/18/8/a/a/1/1", "ModularForm/GL2/Q/holomorphic/18/8/a/a"]
"2-18-9.4-c7-0-0"	2.371271907376755	5.622930458714194	2	18	"9.4"	[]	[[3.5, 0.0]]	7	true	true	false	false	-0.1667999613335228	0	0.50892215003422368349085739070	["ModularForm/GL2/Q/holomorphic/18/8/c/a/13/1"]
"2-18-9.4-c7-0-1"	2.371271907376755	5.622930458714194	2	18	"9.4"	[]	[[3.5, 0.0]]	7	true	true	false	false	-0.3559701719320612	0	0.66563203675177175001608742866	["ModularForm/GL2/Q/holomorphic/18/8/c/b/13/2"]
"2-18-9.4-c7-0-2"	2.371271907376755	5.622930458714194	2	18	"9.4"	[]	[[3.5, 0.0]]	7	true	true	false	false	-0.37860245129437325	0	1.05245353058001881567690469397	["ModularForm/GL2/Q/holomorphic/18/8/c/b/13/3"]
"2-18-9.4-c7-0-3"	2.371271907376755	5.622930458714194	2	18	"9.4"	[]	[[3.5, 0.0]]	7	true	true	false	false	-0.13648938652144868	0	1.06609385576713138706300119940	["ModularForm/GL2/Q/holomorphic/18/8/c/a/13/3"]
"2-18-9.4-c7-0-4"	2.371271907376755	5.622930458714194	2	18	"9.4"	[]	[[3.5, 0.0]]	7	true	true	false	false	0.30328934785497147	0	2.22929812210252177308239351925	["ModularForm/GL2/Q/holomorphic/18/8/c/a/13/2"]
"2-18-9.4-c7-0-5"	2.371271907376755	5.622930458714194	2	18	"9.4"	[]	[[3.5, 0.0]]	7	true	true	false	false	0.010761623425891528	0	2.36866682327249351615346993102	["ModularForm/GL2/Q/holomorphic/18/8/c/b/13/4"]
"2-18-9.4-c7-0-6"	2.371271907376755	5.622930458714194	2	18	"9.4"	[]	[[3.5, 0.0]]	7	true	true	false	false	0.27936655535609844	0	2.60517177887363461421020536330	["ModularForm/GL2/Q/holomorphic/18/8/c/b/13/1"]
"2-18-9.7-c7-0-0"	2.371271907376755	5.622930458714194	2	18	"9.7"	[]	[[3.5, 0.0]]	7	true	true	false	false	-0.27936655535609844	0	0.42995482870247721179003946996	["ModularForm/GL2/Q/holomorphic/18/8/c/b/7/1"]
"2-18-9.7-c7-0-1"	2.371271907376755	5.622930458714194	2	18	"9.7"	[]	[[3.5, 0.0]]	7	true	true	false	false	-0.30328934785497147	0	0.68644292469734592958609609025	["ModularForm/GL2/Q/holomorphic/18/8/c/a/7/2"]
"2-18-9.7-c7-0-2"	2.371271907376755	5.622930458714194	2	18	"9.7"	[]	[[3.5, 0.0]]	7	true	true	false	false	-0.010761623425891528	0	1.78774888370921430682942289530	["ModularForm/GL2/Q/holomorphic/18/8/c/b/7/4"]
"2-18-9.7-c7-0-3"	2.371271907376755	5.622930458714194	2	18	"9.7"	[]	[[3.5, 0.0]]	7	true	true	false	false	0.1667999613335228	0	1.83904679860486403529445483051	["ModularForm/GL2/Q/holomorphic/18/8/c/a/7/1"]
"2-18-9.7-c7-0-4"	2.371271907376755	5.622930458714194	2	18	"9.7"	[]	[[3.5, 0.0]]	7	true	true	false	false	0.13648938652144868	0	2.40868466635140431755997185209	["ModularForm/GL2/Q/holomorphic/18/8/c/a/7/3"]
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"2-18-9.2-c46-0-6"	15.531679353452425	241.23306353846036	2	18	"9.2"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.11639029744418765	0	0.16849832163992538122503445009	["ModularForm/GL2/Q/holomorphic/18/47/d/a/11/17"]
"2-18-9.2-c46-0-7"	15.531679353452425	241.23306353846036	2	18	"9.2"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.49360210878035965	0	0.17291799133095074664794755801	["ModularForm/GL2/Q/holomorphic/18/47/d/a/11/40"]
"2-18-9.2-c46-0-8"	15.531679353452425	241.23306353846036	2	18	"9.2"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.49741184470860045	0	0.20475761645020805299640418356	["ModularForm/GL2/Q/holomorphic/18/47/d/a/11/5"]
"2-18-9.2-c46-0-9"	15.531679353452425	241.23306353846036	2	18	"9.2"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.14424340453180137	0	0.27367352641812171348844421915	["ModularForm/GL2/Q/holomorphic/18/47/d/a/11/28"]
"2-18-9.5-c46-0-0"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.3368463932447943	0	0.01940706002730265564092026280	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/3"]
"2-18-9.5-c46-0-1"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.02313839715118941	0	0.02772927251043464801006787237	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/25"]
"2-18-9.5-c46-0-10"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.47846364208979686	0	0.23797661285681583152660643433	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/21"]
"2-18-9.5-c46-0-11"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.2884421933783183	0	0.24584155059973535467109743026	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/12"]
"2-18-9.5-c46-0-12"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.1549311741691096	0	0.25228431093036135051353754074	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/32"]
"2-18-9.5-c46-0-13"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.09883571851746559	0	0.26632132452767875015678423413	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/11"]
"2-18-9.5-c46-0-14"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.4244742329563082	0	0.27353998226181418302776421198	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/20"]
"2-18-9.5-c46-0-15"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.3591172826729162	0	0.27977275275166290235533820183	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/18"]
"2-18-9.5-c46-0-16"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.020550741416541108	0	0.34850271033091760524468763637	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/1"]
"2-18-9.5-c46-0-17"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.26786630876947476	0	0.34876018457614608055142320688	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/24"]
"2-18-9.5-c46-0-18"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.21885737044586312	0	0.36122313975784948970800628336	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/13"]
"2-18-9.5-c46-0-19"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.17625927690858295	0	0.45563800694880504069632686064	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/2"]
"2-18-9.5-c46-0-2"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.46018920690212933	0	0.04729638818167288060746636414	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/34"]
"2-18-9.5-c46-0-20"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.021492943363932843	0	0.56134573378577855538962043515	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/9"]
"2-18-9.5-c46-0-21"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.17391101035743645	0	0.60975426845859650898029074518	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/22"]
"2-18-9.5-c46-0-22"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.25142106075495596	0	0.62043961214633695769203105922	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/16"]
"2-18-9.5-c46-0-23"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.25289820891010206	0	0.62757842536844835701195376298	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/36"]
"2-18-9.5-c46-0-24"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.14424340453180137	0	0.64136725139017843422560500507	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/28"]
"2-18-9.5-c46-0-25"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.07210326807471142	0	0.69011308717604768601431743035	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/39"]
"2-18-9.5-c46-0-26"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.06041561537682648	0	0.72284229893379140250007379499	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/44"]
"2-18-9.5-c46-0-27"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.09015247051720798	0	0.74738348408146443293675203798	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/10"]
"2-18-9.5-c46-0-28"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.33872640183273767	0	0.76261032790102534145637253577	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/30"]
"2-18-9.5-c46-0-29"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.48990014435460943	0	0.831605640913098099223708597934	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/38"]
"2-18-9.5-c46-0-3"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.32611127232449233	0	0.05988991398296201930633294552	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/14"]
"2-18-9.5-c46-0-30"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.11639029744418765	0	0.938815368632515085207918809117	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/17"]
"2-18-9.5-c46-0-31"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.3064409476244361	0	0.950032620333596430396703674181	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/8"]
"2-18-9.5-c46-0-32"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.3752061185201068	0	0.964473021818574005119667372023	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/45"]
"2-18-9.5-c46-0-33"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.20374013502666738	0	1.00425082072621002783905472904	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/31"]
"2-18-9.5-c46-0-34"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.2004640178033728	0	1.00699014830496045626357203053	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/19"]
"2-18-9.5-c46-0-35"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.49360210878035965	0	1.04546354707607665438711577797	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/40"]
"2-18-9.5-c46-0-36"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.28374259423716575	0	1.11079558568297113156226318585	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/23"]
"2-18-9.5-c46-0-37"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.08806412190811765	0	1.17317867123245130447592488969	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/26"]
"2-18-9.5-c46-0-38"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.37885136075415776	0	1.20722671444247236040526451230	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/4"]
"2-18-9.5-c46-0-39"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.3546589047355748	0	1.24124724939626577575231305381	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/15"]
"2-18-9.5-c46-0-4"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.0850501778182728	0	0.080496846927214486639055358619	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/27"]
"2-18-9.5-c46-0-40"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.49741184470860045	0	1.27760755597522642635350554104	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/5"]
"2-18-9.5-c46-0-41"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.33698471644591316	0	1.27920806483490744465796737538	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/42"]
"2-18-9.5-c46-0-42"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.3491209806585776	0	1.37867727203640589061626692820	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/37"]
"2-18-9.5-c46-0-43"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.349744929909185	0	1.46478710382603224261045973860	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/33"]
"2-18-9.5-c46-0-44"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.40228822468166275	0	1.57317785472112169699468814477	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/7"]
"2-18-9.5-c46-0-45"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.25179326610783753	0	1.79532761117715598803639087703	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/41"]
"2-18-9.5-c46-0-5"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.31254700956737297	0	0.099316760129554003360635095077	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/29"]
"2-18-9.5-c46-0-6"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	0.49335899166706243	0	0.10920832423357295415588837112	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/46"]
"2-18-9.5-c46-0-7"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.31280742905495706	0	0.15039762150811140215517015400	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/43"]
"2-18-9.5-c46-0-8"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.05945487977361745	0	0.19510976996012094294115273392	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/35"]
"2-18-9.5-c46-0-9"	15.531679353452425	241.23306353846036	2	18	"9.5"	[]	[[23.0, 0.0]]	46	true	true	false	false	-0.08773292409609819	0	0.23368231781095536409051764927	["ModularForm/GL2/Q/holomorphic/18/47/d/a/5/6"]


# 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).