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 171 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\mathbb{Q}$	self-dual	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-173-173.10-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.10	$0$	✓	✓			$0.477$	$0$	$2.36053$	Character $\chi_{173}(10, \cdot)$
1-173-173.100-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.100	$0$	✓	✓			$0.241$	$0$	$1.57404$	Character $\chi_{173}(100, \cdot)$
1-173-173.106-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.106	$0$	✓	✓			$-0.0904$	$0$	$1.31587$	Character $\chi_{173}(106, \cdot)$
1-173-173.109-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.109	$0$	✓	✓			$-0.241$	$0$	$0.688253$	Character $\chi_{173}(109, \cdot)$
1-173-173.113-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.113	$0$	✓	✓			$-0.0699$	$0$	$1.90858$	Character $\chi_{173}(113, \cdot)$
1-173-173.116-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.116	$0$	✓	✓			$-0.289$	$0$	$1.41890$	Character $\chi_{173}(116, \cdot)$
1-173-173.117-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.117	$0$	✓	✓			$-0.0796$	$0$	$1.49413$	Character $\chi_{173}(117, \cdot)$
1-173-173.118-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.118	$0$	✓	✓			$-0.305$	$0$	$0.798454$	Character $\chi_{173}(118, \cdot)$
1-173-173.119-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.119	$0$	✓	✓			$0.0471$	$0$	$1.74891$	Character $\chi_{173}(119, \cdot)$
1-173-173.121-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.121	$0$	✓	✓			$-0.298$	$0$	$3.07108$	Character $\chi_{173}(121, \cdot)$
1-173-173.122-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.122	$0$	✓	✓			$0.290$	$0$	$2.64820$	Character $\chi_{173}(122, \cdot)$
1-173-173.124-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.124	$0$	✓	✓			$-0.0931$	$0$	$0.714748$	Character $\chi_{173}(124, \cdot)$
1-173-173.126-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.126	$0$	✓	✓			$-0.298$	$0$	$1.20956$	Character $\chi_{173}(126, \cdot)$
1-173-173.13-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.13	$0$	✓	✓			$0.0198$	$0$	$1.20456$	Character $\chi_{173}(13, \cdot)$
1-173-173.130-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.130	$0$	✓	✓			$-0.271$	$0$	$1.07340$	Character $\chi_{173}(130, \cdot)$
1-173-173.132-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.132	$0$	✓	✓			$0.163$	$0$	$1.28490$	Character $\chi_{173}(132, \cdot)$
1-173-173.133-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.133	$0$	✓	✓			$-0.126$	$0$	$1.58126$	Character $\chi_{173}(133, \cdot)$
1-173-173.135-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.135	$0$	✓	✓			$-0.163$	$0$	$1.42768$	Character $\chi_{173}(135, \cdot)$
1-173-173.136-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.136	$0$	✓	✓			$0.0913$	$0$	$1.73173$	Character $\chi_{173}(136, \cdot)$
1-173-173.137-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.137	$0$	✓	✓			$0.189$	$0$	$2.13352$	Character $\chi_{173}(137, \cdot)$
1-173-173.138-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.138	$0$	✓	✓			$0.463$	$0$	$1.68117$	Character $\chi_{173}(138, \cdot)$
1-173-173.139-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.139	$0$	✓	✓			$0.0796$	$0$	$2.46569$	Character $\chi_{173}(139, \cdot)$
1-173-173.14-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.14	$0$	✓	✓			$-0.0913$	$0$	$1.33363$	Character $\chi_{173}(14, \cdot)$
1-173-173.140-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.140	$0$	✓	✓			$-0.186$	$0$	$1.14426$	Character $\chi_{173}(140, \cdot)$
1-173-173.142-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.142	$0$	✓	✓			$0.0904$	$0$	$1.34426$	Character $\chi_{173}(142, \cdot)$
1-173-173.144-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.144	$0$	✓	✓			$0.270$	$0$	$1.84002$	Character $\chi_{173}(144, \cdot)$
1-173-173.148-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.148	$0$	✓	✓			$-0.214$	$0$	$1.41392$	Character $\chi_{173}(148, \cdot)$
1-173-173.149-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.149	$0$	✓	✓			$0.268$	$0$	$2.21433$	Character $\chi_{173}(149, \cdot)$
1-173-173.15-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.15	$0$	✓	✓			$0.0875$	$0$	$0.949981$	Character $\chi_{173}(15, \cdot)$
1-173-173.150-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.150	$0$	✓	✓			$-0.0875$	$0$	$1.29900$	Character $\chi_{173}(150, \cdot)$
1-173-173.151-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.151	$0$	✓	✓			$-0.121$	$0$	$1.05594$	Character $\chi_{173}(151, \cdot)$
1-173-173.152-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.152	$0$	✓	✓			$0.186$	$0$	$1.47621$	Character $\chi_{173}(152, \cdot)$
1-173-173.157-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.157	$0$	✓	✓			$0.215$	$0$	$1.66196$	Character $\chi_{173}(157, \cdot)$
1-173-173.158-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.158	$0$	✓	✓			$-0.332$	$0$	$1.24951$	Character $\chi_{173}(158, \cdot)$
1-173-173.159-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.159	$0$	✓	✓			$0.307$	$0$	$2.27899$	Character $\chi_{173}(159, \cdot)$
1-173-173.16-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.16	$0$	✓	✓			$-0.0471$	$0$	$1.67928$	Character $\chi_{173}(16, \cdot)$
1-173-173.160-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.160	$0$	✓	✓			$0.126$	$0$	$1.61799$	Character $\chi_{173}(160, \cdot)$
1-173-173.163-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.163	$0$	✓	✓			$0.298$	$0$	$0.327315$	Character $\chi_{173}(163, \cdot)$
1-173-173.164-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.164	$0$	✓	✓			$-0.345$	$0$	$1.18070$	Character $\chi_{173}(164, \cdot)$
1-173-173.167-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.167	$0$	✓	✓			$-0.270$	$0$	$1.55556$	Character $\chi_{173}(167, \cdot)$
1-173-173.169-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.169	$0$	✓	✓			$-0.341$	$0$	$0.808632$	Character $\chi_{173}(169, \cdot)$
1-173-173.172-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.172	$0$	✓	✓	✓	✓	$0$	$0$	$0.707862$	Character $\chi_{173}(172, \cdot)$
1-173-173.21-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.21	$0$	✓	✓			$0.172$	$0$	$1.92857$	Character $\chi_{173}(21, \cdot)$
1-173-173.22-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.22	$0$	✓	✓			$0.305$	$0$	$2.19233$	Character $\chi_{173}(22, \cdot)$
1-173-173.23-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.23	$0$	✓	✓			$0.332$	$0$	$2.53489$	Character $\chi_{173}(23, \cdot)$
1-173-173.24-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.24	$0$	✓	✓			$-0.189$	$0$	$0.702859$	Character $\chi_{173}(24, \cdot)$
1-173-173.25-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.25	$0$	✓	✓			$0.217$	$0$	$1.42061$	Character $\chi_{173}(25, \cdot)$
1-173-173.29-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.29	$0$	✓	✓			$0.323$	$0$	$0.325799$	Character $\chi_{173}(29, \cdot)$
1-173-173.31-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.31	$0$	✓	✓			$0.0686$	$0$	$1.91845$	Character $\chi_{173}(31, \cdot)$
1-173-173.33-r0-0-0	$0.803$	$0.803$	$1$	$173$	173.33	$0$	✓	✓			$-0.172$	$0$	$0.587936$	Character $\chi_{173}(33, \cdot)$

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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.