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 68 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-684-684.103-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.103	$0$	✓	✓	$-0.289$	$0$	$0.380889$	Character $\chi_{684}(103, \cdot)$
1-684-684.11-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.11	$0$	✓	✓	$-0.160$	$0$	$0.542541$	Character $\chi_{684}(11, \cdot)$
1-684-684.119-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.119	$0$	✓	✓	$0.228$	$0$	$1.41074$	Character $\chi_{684}(119, \cdot)$
1-684-684.131-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.131	$0$	✓	✓	$0.136$	$0$	$1.47521$	Character $\chi_{684}(131, \cdot)$
1-684-684.151-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.151	$0$	✓	✓	$0.222$	$0$	$1.37216$	Character $\chi_{684}(151, \cdot)$
1-684-684.211-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.211	$0$	✓	✓	$0.301$	$0$	$1.36782$	Character $\chi_{684}(211, \cdot)$
1-684-684.223-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.223	$0$	✓	✓	$0.352$	$0$	$1.27423$	Character $\chi_{684}(223, \cdot)$
1-684-684.23-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.23	$0$	✓	✓	$-0.228$	$0$	$0.591069$	Character $\chi_{684}(23, \cdot)$
1-684-684.239-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.239	$0$	✓	✓	$-0.105$	$0$	$1.07086$	Character $\chi_{684}(239, \cdot)$
1-684-684.259-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.259	$0$	✓	✓	$0.289$	$0$	$1.51337$	Character $\chi_{684}(259, \cdot)$
1-684-684.263-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.263	$0$	✓	✓	$-0.192$	$0$	$0.325509$	Character $\chi_{684}(263, \cdot)$
1-684-684.275-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.275	$0$	✓	✓	$-0.0808$	$0$	$0.637446$	Character $\chi_{684}(275, \cdot)$
1-684-684.295-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.295	$0$	✓	✓	$-0.301$	$0$	$0.358689$	Character $\chi_{684}(295, \cdot)$
1-684-684.31-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.31	$0$	✓	✓	$-0.154$	$0$	$0.939141$	Character $\chi_{684}(31, \cdot)$
1-684-684.311-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.311	$0$	✓	✓	$0.160$	$0$	$1.11925$	Character $\chi_{684}(311, \cdot)$
1-684-684.319-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.319	$0$	✓	✓	$-0.352$	$0$	$0.151545$	Character $\chi_{684}(319, \cdot)$
1-684-684.331-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.331	$0$	✓	✓	$0.154$	$0$	$1.63077$	Character $\chi_{684}(331, \cdot)$
1-684-684.347-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.347	$0$	✓	✓	$0.283$	$0$	$1.49342$	Character $\chi_{684}(347, \cdot)$
1-684-684.355-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.355	$0$	✓	✓	$0.166$	$0$	$1.32046$	Character $\chi_{684}(355, \cdot)$
1-684-684.439-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.439	$0$	✓	✓	$-0.246$	$0$	$0.349062$	Character $\chi_{684}(439, \cdot)$
1-684-684.443-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.443	$0$	✓	✓	$0.136$	$0$	$1.26748$	Character $\chi_{684}(443, \cdot)$
1-684-684.47-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.47	$0$	✓	✓	$-0.136$	$0$	$1.00235$	Character $\chi_{684}(47, \cdot)$
1-684-684.479-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.479	$0$	✓	✓	$-0.283$	$0$	$0.632000$	Character $\chi_{684}(479, \cdot)$
1-684-684.491-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.491	$0$	✓	✓	$-0.136$	$0$	$0.855160$	Character $\chi_{684}(491, \cdot)$
1-684-684.535-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.535	$0$	✓	✓	$0.388$	$0$	$1.89798$	Character $\chi_{684}(535, \cdot)$
1-684-684.547-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.547	$0$	✓	✓	$0.0919$	$0$	$1.24335$	Character $\chi_{684}(547, \cdot)$
1-684-684.583-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.583	$0$	✓	✓	$-0.388$	$0$	$0.485649$	Character $\chi_{684}(583, \cdot)$
1-684-684.587-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.587	$0$	✓	✓	$0.0808$	$0$	$1.05529$	Character $\chi_{684}(587, \cdot)$
1-684-684.607-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.607	$0$	✓	✓	$-0.222$	$0$	$0.800673$	Character $\chi_{684}(607, \cdot)$
1-684-684.67-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.67	$0$	✓	✓	$0.246$	$0$	$1.37175$	Character $\chi_{684}(67, \cdot)$
1-684-684.671-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.671	$0$	✓	✓	$0.192$	$0$	$1.00388$	Character $\chi_{684}(671, \cdot)$
1-684-684.679-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.679	$0$	✓	✓	$-0.0919$	$0$	$0.905201$	Character $\chi_{684}(679, \cdot)$
1-684-684.79-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.79	$0$	✓	✓	$-0.166$	$0$	$0.805571$	Character $\chi_{684}(79, \cdot)$
1-684-684.83-r0-0-0	$3.17$	$3.17$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.83	$0$	✓	✓	$0.105$	$0$	$1.22657$	Character $\chi_{684}(83, \cdot)$
1-684-684.139-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.139	$1$	✓	✓	$-0.0579$	$0$	$0.540938$	Character $\chi_{684}(139, \cdot)$
1-684-684.155-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.155	$1$	✓	✓	$0.0834$	$0$	$0.539159$	Character $\chi_{684}(155, \cdot)$
1-684-684.167-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.167	$1$	✓	✓	$0.397$	$0$	$0.0200497$	Character $\chi_{684}(167, \cdot)$
1-684-684.175-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.175	$1$	✓	✓	$-0.478$	$0$	$1.33569$	Character $\chi_{684}(175, \cdot)$
1-684-684.187-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.187	$1$	✓	✓	$0.0579$	$0$	$0.836852$	Character $\chi_{684}(187, \cdot)$
1-684-684.203-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.203	$1$	✓	✓	$-0.0834$	$0$	$0.464620$	Character $\chi_{684}(203, \cdot)$
1-684-684.227-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.227	$1$	✓	✓	$0.472$	$0$	$0.0733697$	Character $\chi_{684}(227, \cdot)$
1-684-684.283-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.283	$1$	✓	✓	$-0.113$	$0$	$0.328705$	Character $\chi_{684}(283, \cdot)$
1-684-684.299-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.299	$1$	✓	✓	$-0.397$	$0$	$1.75926$	Character $\chi_{684}(299, \cdot)$
1-684-684.335-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.335	$1$	✓	✓	$-0.460$	$0$	$1.60032$	Character $\chi_{684}(335, \cdot)$
1-684-684.367-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.367	$1$	✓	✓	$0.386$	$0$	$0.0547565$	Character $\chi_{684}(367, \cdot)$
1-684-684.371-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.371	$1$	✓	✓	$-0.0518$	$0$	$1.13682$	Character $\chi_{684}(371, \cdot)$
1-684-684.383-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.383	$1$	✓	✓	$0.138$	$0$	$1.05642$	Character $\chi_{684}(383, \cdot)$
1-684-684.391-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.391	$1$	✓	✓	$-0.355$	$0$	$0.253164$	Character $\chi_{684}(391, \cdot)$
1-684-684.403-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.403	$1$	✓	✓	$-0.0339$	$0$	$0.792029$	Character $\chi_{684}(403, \cdot)$
1-684-684.407-r1-0-0	$73.5$	$73.5$	$1$	$2^{2} \cdot 3^{2} \cdot 19$	684.407	$1$	✓	✓	$0.404$	$0$	$1.19395$	Character $\chi_{684}(407, \cdot)$

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Elliptic curves over $\Q$
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Genus 2 curves over $\Q$
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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.