LMFDB - L-function search results

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Lowest zero	Conductor	Analytic conductor	Central character	Analytic rank

Degree	Bad $p$	Root analytic conductor	Motivic weight	Spectral label

Root angle	Primitive	Origin	Exclude origin	Self-dual

Arithmetic

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-6369-6369.1004-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1004	$0$	✓	✓	$0.380$	$0$	$1.02258$	Character $\chi_{6369}(1004, \cdot)$
1-6369-6369.1007-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1007	$0$	✓	✓	$0.388$	$0$	$1.06414$	Character $\chi_{6369}(1007, \cdot)$
1-6369-6369.101-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.101	$0$	✓	✓	$0.289$	$0$	$0.574044$	Character $\chi_{6369}(101, \cdot)$
1-6369-6369.1010-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1010	$0$	✓	✓	$-0.212$	$0$	$0.653809$	Character $\chi_{6369}(1010, \cdot)$
1-6369-6369.1016-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1016	$0$	✓	✓	$-0.414$	$0$	$0.134266$	Character $\chi_{6369}(1016, \cdot)$
1-6369-6369.1019-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1019	$0$	✓	✓	$0.295$	$0$	$0.336995$	Character $\chi_{6369}(1019, \cdot)$
1-6369-6369.104-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.104	$0$	✓	✓	$0.465$	$0$	$0.0626925$	Character $\chi_{6369}(104, \cdot)$
1-6369-6369.1040-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1040	$0$	✓	✓	$-0.101$	$0$	$0.755663$	Character $\chi_{6369}(1040, \cdot)$
1-6369-6369.1043-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1043	$0$	✓	✓	$-0.159$	$0$	$0.527325$	Character $\chi_{6369}(1043, \cdot)$
1-6369-6369.1058-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1058	$0$	✓	✓	$0.475$	$0$	$0.182508$	Character $\chi_{6369}(1058, \cdot)$
1-6369-6369.107-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.107	$0$	✓	✓	$-0.279$	$0$	$1.48904$	Character $\chi_{6369}(107, \cdot)$
1-6369-6369.1070-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1070	$0$	✓	✓	$-0.0655$	$0$	$0.869534$	Character $\chi_{6369}(1070, \cdot)$
1-6369-6369.1073-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1073	$0$	✓	✓	$0.0552$	$0$	$0.791481$	Character $\chi_{6369}(1073, \cdot)$
1-6369-6369.1076-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1076	$0$	✓	✓	$-0.213$	$0$	$0.441065$	Character $\chi_{6369}(1076, \cdot)$
1-6369-6369.1082-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1082	$0$	✓	✓	$-0.0158$	$0$	$0.798090$	Character $\chi_{6369}(1082, \cdot)$
1-6369-6369.1091-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1091	$0$	✓	✓	$0.128$	$0$	$0.683588$	Character $\chi_{6369}(1091, \cdot)$
1-6369-6369.113-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.113	$0$	✓	✓	$-0.137$	$0$	$0.714492$	Character $\chi_{6369}(113, \cdot)$
1-6369-6369.1130-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1130	$0$	✓	✓	$-0.296$	$0$	$1.43379$	Character $\chi_{6369}(1130, \cdot)$
1-6369-6369.1136-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1136	$0$	✓	✓	$0.140$	$0$	$0.788588$	Character $\chi_{6369}(1136, \cdot)$
1-6369-6369.1148-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1148	$0$	✓	✓	$-0.0891$	$0$	$0.794184$	Character $\chi_{6369}(1148, \cdot)$
1-6369-6369.1151-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1151	$0$	✓	✓	$-0.140$	$0$	$0.288781$	Character $\chi_{6369}(1151, \cdot)$
1-6369-6369.1154-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1154	$0$	✓	✓	$0.428$	$0$	$1.22094$	Character $\chi_{6369}(1154, \cdot)$
1-6369-6369.1157-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1157	$0$	✓	✓	$0.246$	$0$	$0.0907830$	Character $\chi_{6369}(1157, \cdot)$
1-6369-6369.1169-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1169	$0$	✓	✓	$0.306$	$0$	$0.0997203$	Character $\chi_{6369}(1169, \cdot)$
1-6369-6369.1172-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1172	$0$	✓	✓	$-0.350$	$0$	$0.714901$	Character $\chi_{6369}(1172, \cdot)$
1-6369-6369.1175-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1175	$0$	✓	✓	$-0.122$	$0$	$0.642491$	Character $\chi_{6369}(1175, \cdot)$
1-6369-6369.119-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.119	$0$	✓	✓	$-0.418$	$0$	$0.161924$	Character $\chi_{6369}(119, \cdot)$
1-6369-6369.1190-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1190	$0$	✓	✓	$0.405$	$0$	$0.459644$	Character $\chi_{6369}(1190, \cdot)$
1-6369-6369.1193-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1193	$0$	✓	✓	$-0.276$	$0$	$0.294130$	Character $\chi_{6369}(1193, \cdot)$
1-6369-6369.1202-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1202	$0$	✓	✓	$0.00302$	$0$	$1.03844$	Character $\chi_{6369}(1202, \cdot)$
1-6369-6369.1217-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1217	$0$	✓	✓	$0.302$	$0$	$0.992674$	Character $\chi_{6369}(1217, \cdot)$
1-6369-6369.1220-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1220	$0$	✓	✓	$0.257$	$0$	$0.899422$	Character $\chi_{6369}(1220, \cdot)$
1-6369-6369.1223-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1223	$0$	✓	✓	$0.489$	$0$	$0.118639$	Character $\chi_{6369}(1223, \cdot)$
1-6369-6369.1226-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1226	$0$	✓	✓	$-0.224$	$0$	$0.260028$	Character $\chi_{6369}(1226, \cdot)$
1-6369-6369.1235-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1235	$0$	✓	✓	$-0.459$	$0$	$1.36421$	Character $\chi_{6369}(1235, \cdot)$
1-6369-6369.1247-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1247	$0$	✓	✓	$-0.0440$	$0$	$0.983150$	Character $\chi_{6369}(1247, \cdot)$
1-6369-6369.125-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.125	$0$	✓	✓	$0.0655$	$0$	$0.346932$	Character $\chi_{6369}(125, \cdot)$
1-6369-6369.1250-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1250	$0$	✓	✓	$0.279$	$0$	$0.0656008$	Character $\chi_{6369}(1250, \cdot)$
1-6369-6369.1253-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1253	$0$	✓	✓	$0.185$	$0$	$0.0266191$	Character $\chi_{6369}(1253, \cdot)$
1-6369-6369.1256-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1256	$0$	✓	✓	$0.00377$	$0$	$0.640728$	Character $\chi_{6369}(1256, \cdot)$
1-6369-6369.1274-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1274	$0$	✓	✓	$-0.433$	$0$	$0.760741$	Character $\chi_{6369}(1274, \cdot)$
1-6369-6369.128-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.128	$0$	✓	✓	$-0.146$	$0$	$0.357235$	Character $\chi_{6369}(128, \cdot)$
1-6369-6369.1280-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1280	$0$	✓	✓	$-0.230$	$0$	$0.353068$	Character $\chi_{6369}(1280, \cdot)$
1-6369-6369.1286-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1286	$0$	✓	✓	$-0.185$	$0$	$1.55203$	Character $\chi_{6369}(1286, \cdot)$
1-6369-6369.1289-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1289	$0$	✓	✓	$0.360$	$0$	$0.881721$	Character $\chi_{6369}(1289, \cdot)$
1-6369-6369.1295-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1295	$0$	✓	✓	$0.325$	$0$	$0.795867$	Character $\chi_{6369}(1295, \cdot)$
1-6369-6369.1307-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1307	$0$	✓	✓	$0.264$	$0$	$1.04388$	Character $\chi_{6369}(1307, \cdot)$
1-6369-6369.131-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.131	$0$	✓	✓	$0.114$	$0$	$0.548447$	Character $\chi_{6369}(131, \cdot)$
1-6369-6369.1313-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1313	$0$	✓	✓	$0.160$	$0$	$0.573034$	Character $\chi_{6369}(1313, \cdot)$
1-6369-6369.1319-r0-0-0	$29.5$	$29.5$	$1$	$3 \cdot 11 \cdot 193$	6369.1319	$0$	✓	✓	$-0.103$	$0$	$0.487640$	Character $\chi_{6369}(1319, \cdot)$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.