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 52 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-185-185.102-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.102	$1$	✓	✓	$-0.0934$	$0$	$0.00675223$	Character $\chi_{185}(102, \cdot)$
1-185-185.107-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.107	$1$	✓	✓	$-0.0842$	$0$	$1.09584$	Character $\chi_{185}(107, \cdot)$
1-185-185.108-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.108	$1$	✓	✓	$-0.105$	$0$	$1.36568$	Character $\chi_{185}(108, \cdot)$
1-185-185.109-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.109	$1$	✓	✓	$0.401$	$0$	$2.26440$	Character $\chi_{185}(109, \cdot)$
1-185-185.118-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.118	$1$	✓	✓	$0.0415$	$0$	$0.850859$	Character $\chi_{185}(118, \cdot)$
1-185-185.119-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.119	$1$	✓	✓	$-0.385$	$0$	$0.350369$	Character $\chi_{185}(119, \cdot)$
1-185-185.12-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.12	$1$	✓	✓	$0.105$	$0$	$1.99126$	Character $\chi_{185}(12, \cdot)$
1-185-185.122-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.122	$1$	✓	✓	$0.218$	$0$	$1.29771$	Character $\chi_{185}(122, \cdot)$
1-185-185.123-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.123	$1$	✓	✓	$0.429$	$0$	$1.16893$	Character $\chi_{185}(123, \cdot)$
1-185-185.124-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.124	$1$	✓	✓	$-0.383$	$0$	$0.389501$	Character $\chi_{185}(124, \cdot)$
1-185-185.127-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.127	$1$	✓	✓	$-0.0415$	$0$	$0.724980$	Character $\chi_{185}(127, \cdot)$
1-185-185.129-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.129	$1$	✓	✓	$-0.401$	$0$	$0.692429$	Character $\chi_{185}(129, \cdot)$
1-185-185.132-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.132	$1$	✓	✓	$0.228$	$0$	$0.120302$	Character $\chi_{185}(132, \cdot)$
1-185-185.134-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.134	$1$	✓	✓	$-0.338$	$0$	$0.490041$	Character $\chi_{185}(134, \cdot)$
1-185-185.137-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.137	$1$	✓	✓	$-0.185$	$0$	$0.550671$	Character $\chi_{185}(137, \cdot)$
1-185-185.138-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.138	$1$	✓	✓	$-0.218$	$0$	$1.08035$	Character $\chi_{185}(138, \cdot)$
1-185-185.14-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.14	$1$	✓	✓	$0.385$	$0$	$1.07640$	Character $\chi_{185}(14, \cdot)$
1-185-185.147-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.147	$1$	✓	✓	$-0.161$	$0$	$1.10004$	Character $\chi_{185}(147, \cdot)$
1-185-185.152-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.152	$1$	✓	✓	$-0.230$	$0$	$2.20889$	Character $\chi_{185}(152, \cdot)$
1-185-185.154-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.154	$1$	✓	✓	$-0.138$	$0$	$0.361465$	Character $\chi_{185}(154, \cdot)$
1-185-185.157-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.157	$1$	✓	✓	$-0.239$	$0$	$0.289644$	Character $\chi_{185}(157, \cdot)$
1-185-185.158-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.158	$1$	✓	✓	$0.185$	$0$	$1.04533$	Character $\chi_{185}(158, \cdot)$
1-185-185.173-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.173	$1$	✓	✓	$0.416$	$0$	$1.81040$	Character $\chi_{185}(173, \cdot)$
1-185-185.178-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.178	$1$	✓	✓	$-0.228$	$0$	$2.69331$	Character $\chi_{185}(178, \cdot)$
1-185-185.179-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.179	$1$	✓	✓	$0.138$	$0$	$1.60794$	Character $\chi_{185}(179, \cdot)$
1-185-185.182-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.182	$1$	✓	✓	$-0.429$	$0$	$0.00509826$	Character $\chi_{185}(182, \cdot)$
1-185-185.19-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.19	$1$	✓	✓	$0.0254$	$0$	$1.01187$	Character $\chi_{185}(19, \cdot)$
1-185-185.24-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.24	$1$	✓	✓	$-0.337$	$0$	$1.62748$	Character $\chi_{185}(24, \cdot)$
1-185-185.27-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.27	$1$	✓	✓	$0.457$	$0$	$1.62426$	Character $\chi_{185}(27, \cdot)$
1-185-185.28-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.28	$1$	✓	✓	$0.230$	$0$	$0.0369705$	Character $\chi_{185}(28, \cdot)$
1-185-185.29-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.29	$1$	✓	✓	$0.338$	$0$	$1.82530$	Character $\chi_{185}(29, \cdot)$
1-185-185.3-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.3	$1$	✓	✓	$-0.0929$	$0$	$0.866321$	Character $\chi_{185}(3, \cdot)$
1-185-185.33-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.33	$1$	✓	✓	$0.239$	$0$	$0.846831$	Character $\chi_{185}(33, \cdot)$
1-185-185.39-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.39	$1$	✓	✓	$-0.0254$	$0$	$0.593868$	Character $\chi_{185}(39, \cdot)$
1-185-185.47-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.47	$1$	✓	✓	$-0.138$	$0$	$1.20134$	Character $\chi_{185}(47, \cdot)$
1-185-185.48-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.48	$1$	✓	✓	$-0.457$	$0$	$0.319057$	Character $\chi_{185}(48, \cdot)$
1-185-185.53-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.53	$1$	✓	✓	$0.282$	$0$	$2.20286$	Character $\chi_{185}(53, \cdot)$
1-185-185.54-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.54	$1$	✓	✓	$0.337$	$0$	$0.288917$	Character $\chi_{185}(54, \cdot)$
1-185-185.58-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.58	$1$	✓	✓	$-0.447$	$0$	$1.83431$	Character $\chi_{185}(58, \cdot)$
1-185-185.59-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.59	$1$	✓	✓	$-0.0668$	$0$	$0.926718$	Character $\chi_{185}(59, \cdot)$
1-185-185.62-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.62	$1$	✓	✓	$0.0929$	$0$	$1.40005$	Character $\chi_{185}(62, \cdot)$
1-185-185.63-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.63	$1$	✓	✓	$0.138$	$0$	$1.61993$	Character $\chi_{185}(63, \cdot)$
1-185-185.67-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.67	$1$	✓	✓	$0.447$	$0$	$0.478737$	Character $\chi_{185}(67, \cdot)$
1-185-185.69-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.69	$1$	✓	✓	$0.0668$	$0$	$1.37444$	Character $\chi_{185}(69, \cdot)$
1-185-185.7-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.7	$1$	✓	✓	$-0.282$	$0$	$0.368551$	Character $\chi_{185}(7, \cdot)$
1-185-185.73-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.73	$1$	✓	✓	$0.161$	$0$	$0.703034$	Character $\chi_{185}(73, \cdot)$
1-185-185.77-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.77	$1$	✓	✓	$-0.416$	$0$	$0.297091$	Character $\chi_{185}(77, \cdot)$
1-185-185.78-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.78	$1$	✓	✓	$0.0934$	$0$	$1.18395$	Character $\chi_{185}(78, \cdot)$
1-185-185.79-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.79	$1$	✓	✓	$0.410$	$0$	$2.07278$	Character $\chi_{185}(79, \cdot)$
1-185-185.83-r1-0-0	$19.8$	$19.8$	$1$	$5 \cdot 37$	185.83	$1$	✓	✓	$0.0842$	$0$	$1.07630$	Character $\chi_{185}(83, \cdot)$

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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.