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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Results (1-50 of 312 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-1312-1312.1003-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1003	$0$	✓	✓	$-0.120$	$0$	$0.619625$	Character $\chi_{1312}(1003, \cdot)$
1-1312-1312.1005-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1005	$0$	✓	✓	$-0.204$	$0$	$0.648483$	Character $\chi_{1312}(1005, \cdot)$
1-1312-1312.1011-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1011	$0$	✓	✓	$0.0280$	$0$	$1.14479$	Character $\chi_{1312}(1011, \cdot)$
1-1312-1312.1019-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1019	$0$	✓	✓	$-0.184$	$0$	$0.823392$	Character $\chi_{1312}(1019, \cdot)$
1-1312-1312.1021-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1021	$0$	✓	✓	$0.138$	$0$	$1.35763$	Character $\chi_{1312}(1021, \cdot)$
1-1312-1312.1029-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1029	$0$	✓	✓	$0.495$	$0$	$0.349618$	Character $\chi_{1312}(1029, \cdot)$
1-1312-1312.1045-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1045	$0$	✓	✓	$0.164$	$0$	$0.773788$	Character $\chi_{1312}(1045, \cdot)$
1-1312-1312.1051-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1051	$0$	✓	✓	$-0.228$	$0$	$1.98956$	Character $\chi_{1312}(1051, \cdot)$
1-1312-1312.1059-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1059	$0$	✓	✓	$0.434$	$0$	$0.378647$	Character $\chi_{1312}(1059, \cdot)$
1-1312-1312.1061-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1061	$0$	✓	✓	$0.463$	$0$	$1.95463$	Character $\chi_{1312}(1061, \cdot)$
1-1312-1312.1083-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1083	$0$	✓	✓	$-0.106$	$0$	$0.356806$	Character $\chi_{1312}(1083, \cdot)$
1-1312-1312.11-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.11	$0$	✓	✓	$-0.387$	$0$	$0.220470$	Character $\chi_{1312}(11, \cdot)$
1-1312-1312.1109-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1109	$0$	✓	✓	$-0.0456$	$0$	$0.985689$	Character $\chi_{1312}(1109, \cdot)$
1-1312-1312.1117-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1117	$0$	✓	✓	$-0.451$	$0$	$0.0532739$	Character $\chi_{1312}(1117, \cdot)$
1-1312-1312.1125-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1125	$0$	✓	✓	$-0.0780$	$0$	$0.786050$	Character $\chi_{1312}(1125, \cdot)$
1-1312-1312.1131-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1131	$0$	✓	✓	$0.0673$	$0$	$0.653762$	Character $\chi_{1312}(1131, \cdot)$
1-1312-1312.1155-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1155	$0$	✓	✓	$0.00360$	$0$	$0.683936$	Character $\chi_{1312}(1155, \cdot)$
1-1312-1312.1157-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1157	$0$	✓	✓	$-0.290$	$0$	$0.495023$	Character $\chi_{1312}(1157, \cdot)$
1-1312-1312.1163-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1163	$0$	✓	✓	$0.199$	$0$	$1.21497$	Character $\chi_{1312}(1163, \cdot)$
1-1312-1312.1173-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1173	$0$	✓	✓	$-0.323$	$0$	$0.161385$	Character $\chi_{1312}(1173, \cdot)$
1-1312-1312.1181-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1181	$0$	✓	✓	$0.479$	$0$	$1.99486$	Character $\chi_{1312}(1181, \cdot)$
1-1312-1312.1195-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1195	$0$	✓	✓	$0.00360$	$0$	$1.08586$	Character $\chi_{1312}(1195, \cdot)$
1-1312-1312.1197-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1197	$0$	✓	✓	$-0.463$	$0$	$0.537032$	Character $\chi_{1312}(1197, \cdot)$
1-1312-1312.1203-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1203	$0$	✓	✓	$-0.144$	$0$	$0.569974$	Character $\chi_{1312}(1203, \cdot)$
1-1312-1312.1205-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1205	$0$	✓	✓	$-0.359$	$0$	$0.833674$	Character $\chi_{1312}(1205, \cdot)$
1-1312-1312.1211-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1211	$0$	✓	✓	$0.119$	$0$	$1.40841$	Character $\chi_{1312}(1211, \cdot)$
1-1312-1312.1219-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1219	$0$	✓	✓	$0.478$	$0$	$1.59780$	Character $\chi_{1312}(1219, \cdot)$
1-1312-1312.1221-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1221	$0$	✓	✓	$0.102$	$0$	$0.999017$	Character $\chi_{1312}(1221, \cdot)$
1-1312-1312.1227-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1227	$0$	✓	✓	$-0.278$	$0$	$0.514453$	Character $\chi_{1312}(1227, \cdot)$
1-1312-1312.1229-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1229	$0$	✓	✓	$0.0937$	$0$	$1.13412$	Character $\chi_{1312}(1229, \cdot)$
1-1312-1312.1243-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1243	$0$	✓	✓	$0.183$	$0$	$1.14213$	Character $\chi_{1312}(1243, \cdot)$
1-1312-1312.125-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.125	$0$	✓	✓	$-0.358$	$0$	$0.697877$	Character $\chi_{1312}(125, \cdot)$
1-1312-1312.1253-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1253	$0$	✓	✓	$-0.114$	$0$	$1.00251$	Character $\chi_{1312}(1253, \cdot)$
1-1312-1312.1259-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1259	$0$	✓	✓	$0.169$	$0$	$1.12986$	Character $\chi_{1312}(1259, \cdot)$
1-1312-1312.1261-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1261	$0$	✓	✓	$0.495$	$0$	$1.94082$	Character $\chi_{1312}(1261, \cdot)$
1-1312-1312.1269-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1269	$0$	✓	✓	$0.147$	$0$	$1.32962$	Character $\chi_{1312}(1269, \cdot)$
1-1312-1312.1283-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1283	$0$	✓	✓	$-0.0673$	$0$	$0.680131$	Character $\chi_{1312}(1283, \cdot)$
1-1312-1312.1299-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.1299	$0$	✓	✓	$-0.119$	$0$	$0.613074$	Character $\chi_{1312}(1299, \cdot)$
1-1312-1312.133-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.133	$0$	✓	✓	$0.111$	$0$	$0.809812$	Character $\chi_{1312}(133, \cdot)$
1-1312-1312.141-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.141	$0$	✓	✓	$0.109$	$0$	$0.680152$	Character $\chi_{1312}(141, \cdot)$
1-1312-1312.147-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.147	$0$	✓	✓	$0.00484$	$0$	$1.47036$	Character $\chi_{1312}(147, \cdot)$
1-1312-1312.171-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.171	$0$	✓	✓	$-0.191$	$0$	$0.716232$	Character $\chi_{1312}(171, \cdot)$
1-1312-1312.173-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.173	$0$	✓	✓	$-0.102$	$0$	$0.833788$	Character $\chi_{1312}(173, \cdot)$
1-1312-1312.179-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.179	$0$	✓	✓	$0.137$	$0$	$1.21586$	Character $\chi_{1312}(179, \cdot)$
1-1312-1312.189-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.189	$0$	✓	✓	$0.364$	$0$	$0.193230$	Character $\chi_{1312}(189, \cdot)$
1-1312-1312.19-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.19	$0$	✓	✓	$-0.183$	$0$	$0.729965$	Character $\chi_{1312}(19, \cdot)$
1-1312-1312.197-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.197	$0$	✓	✓	$0.0424$	$0$	$1.15850$	Character $\chi_{1312}(197, \cdot)$
1-1312-1312.21-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.21	$0$	✓	✓	$0.358$	$0$	$1.63245$	Character $\chi_{1312}(21, \cdot)$
1-1312-1312.211-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.211	$0$	✓	✓	$-0.0588$	$0$	$0.560635$	Character $\chi_{1312}(211, \cdot)$
1-1312-1312.213-r0-0-0	$6.09$	$6.09$	$1$	$2^{5} \cdot 41$	1312.213	$0$	✓	✓	$0.0992$	$0$	$0.894785$	Character $\chi_{1312}(213, \cdot)$

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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.