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 209 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-633-633.104-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.104	$0$	✓	✓	$0.0911$	$0$	$0.894103$	Character $\chi_{633}(104, \cdot)$
1-633-633.110-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.110	$0$	✓	✓	$-0.112$	$0$	$1.48041$	Character $\chi_{633}(110, \cdot)$
1-633-633.116-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.116	$0$	✓	✓	$0.171$	$0$	$1.01725$	Character $\chi_{633}(116, \cdot)$
1-633-633.128-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.128	$0$	✓	✓	$-0.217$	$0$	$0.839737$	Character $\chi_{633}(128, \cdot)$
1-633-633.131-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.131	$0$	✓	✓	$-0.175$	$0$	$0.776697$	Character $\chi_{633}(131, \cdot)$
1-633-633.140-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.140	$0$	✓	✓	$-0.0911$	$0$	$1.33823$	Character $\chi_{633}(140, \cdot)$
1-633-633.146-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.146	$0$	✓	✓	$0.460$	$0$	$1.70275$	Character $\chi_{633}(146, \cdot)$
1-633-633.149-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.149	$0$	✓	✓	$0.175$	$0$	$1.07338$	Character $\chi_{633}(149, \cdot)$
1-633-633.152-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.152	$0$	✓	✓	$0.349$	$0$	$1.28189$	Character $\chi_{633}(152, \cdot)$
1-633-633.155-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.155	$0$	✓	✓	$-0.0422$	$0$	$1.03743$	Character $\chi_{633}(155, \cdot)$
1-633-633.158-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.158	$0$	✓	✓	$0.116$	$0$	$1.66718$	Character $\chi_{633}(158, \cdot)$
1-633-633.164-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.164	$0$	✓	✓	$0.348$	$0$	$1.31784$	Character $\chi_{633}(164, \cdot)$
1-633-633.167-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.167	$0$	✓	✓	$0.0135$	$0$	$1.30206$	Character $\chi_{633}(167, \cdot)$
1-633-633.17-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.17	$0$	✓	✓	$-0.175$	$0$	$0.603714$	Character $\chi_{633}(17, \cdot)$
1-633-633.191-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.191	$0$	✓	✓	$-0.171$	$0$	$0.964572$	Character $\chi_{633}(191, \cdot)$
1-633-633.197-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.197	$0$	✓	✓	$0.117$	$0$	$1.12628$	Character $\chi_{633}(197, \cdot)$
1-633-633.2-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.2	$0$	✓	✓	$-0.454$	$0$	$0.0518138$	Character $\chi_{633}(2, \cdot)$
1-633-633.200-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.200	$0$	✓	✓	$-0.0887$	$0$	$0.935001$	Character $\chi_{633}(200, \cdot)$
1-633-633.206-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.206	$0$	✓	✓	$-0.0164$	$0$	$0.906401$	Character $\chi_{633}(206, \cdot)$
1-633-633.218-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.218	$0$	✓	✓	$0.174$	$0$	$1.24965$	Character $\chi_{633}(218, \cdot)$
1-633-633.221-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.221	$0$	✓	✓	$0.335$	$0$	$1.86802$	Character $\chi_{633}(221, \cdot)$
1-633-633.23-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.23	$0$	✓	✓	$0.338$	$0$	$0.0699345$	Character $\chi_{633}(23, \cdot)$
1-633-633.233-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.233	$0$	✓	✓	$0.0501$	$0$	$0.926903$	Character $\chi_{633}(233, \cdot)$
1-633-633.239-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.239	$0$	✓	✓	$-0.440$	$0$	$2.12985$	Character $\chi_{633}(239, \cdot)$
1-633-633.242-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.242	$0$	✓	✓	$0.0955$	$0$	$1.56795$	Character $\chi_{633}(242, \cdot)$
1-633-633.251-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.251	$0$	✓	✓	$-0.249$	$0$	$2.70088$	Character $\chi_{633}(251, \cdot)$
1-633-633.26-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.26	$0$	✓	✓	$0.386$	$0$	$1.35610$	Character $\chi_{633}(26, \cdot)$
1-633-633.272-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.272	$0$	✓	✓	$0.217$	$0$	$1.30179$	Character $\chi_{633}(272, \cdot)$
1-633-633.278-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.278	$0$	✓	✓	$0.0877$	$0$	$1.16792$	Character $\chi_{633}(278, \cdot)$
1-633-633.29-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.29	$0$	✓	✓	$0.175$	$0$	$0.978522$	Character $\chi_{633}(29, \cdot)$
1-633-633.296-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.296	$0$	✓	✓	$0.154$	$0$	$1.32226$	Character $\chi_{633}(296, \cdot)$
1-633-633.299-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.299	$0$	✓	✓	$0.337$	$0$	$1.25641$	Character $\chi_{633}(299, \cdot)$
1-633-633.302-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.302	$0$	✓	✓	$-0.372$	$0$	$0.497555$	Character $\chi_{633}(302, \cdot)$
1-633-633.305-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.305	$0$	✓	✓	$0.112$	$0$	$1.28150$	Character $\chi_{633}(305, \cdot)$
1-633-633.308-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.308	$0$	✓	✓	$-0.222$	$0$	$1.01706$	Character $\chi_{633}(308, \cdot)$
1-633-633.317-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.317	$0$	✓	✓	$0.454$	$0$	$1.65618$	Character $\chi_{633}(317, \cdot)$
1-633-633.32-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.32	$0$	✓	✓	$-0.295$	$0$	$0.271614$	Character $\chi_{633}(32, \cdot)$
1-633-633.323-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.323	$0$	✓	✓	$0.157$	$0$	$0.804250$	Character $\chi_{633}(323, \cdot)$
1-633-633.326-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.326	$0$	✓	✓	$0.0887$	$0$	$0.673947$	Character $\chi_{633}(326, \cdot)$
1-633-633.329-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.329	$0$	✓	✓	$-0.349$	$0$	$0.739966$	Character $\chi_{633}(329, \cdot)$
1-633-633.335-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.335	$0$	✓	✓	$0.222$	$0$	$1.71686$	Character $\chi_{633}(335, \cdot)$
1-633-633.338-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.338	$0$	✓	✓	$0.105$	$0$	$1.71737$	Character $\chi_{633}(338, \cdot)$
1-633-633.341-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.341	$0$	✓	✓	$-0.157$	$0$	$0.983933$	Character $\chi_{633}(341, \cdot)$
1-633-633.344-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.344	$0$	✓	✓	$-0.406$	$0$	$0.809413$	Character $\chi_{633}(344, \cdot)$
1-633-633.35-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.35	$0$	✓	✓	$0.322$	$0$	$0.159235$	Character $\chi_{633}(35, \cdot)$
1-633-633.353-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.353	$0$	✓	✓	$-0.175$	$0$	$0.656795$	Character $\chi_{633}(353, \cdot)$
1-633-633.356-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.356	$0$	✓	✓	$-0.0497$	$0$	$1.55697$	Character $\chi_{633}(356, \cdot)$
1-633-633.368-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.368	$0$	✓	✓	$0.150$	$0$	$1.21704$	Character $\chi_{633}(368, \cdot)$
1-633-633.371-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.371	$0$	✓	✓	$0.372$	$0$	$1.34564$	Character $\chi_{633}(371, \cdot)$
1-633-633.377-r0-0-0	$2.93$	$2.93$	$1$	$3 \cdot 211$	633.377	$0$	✓	✓	$-0.186$	$0$	$0.648454$	Character $\chi_{633}(377, \cdot)$

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Classical	Maass
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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.