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 94 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-247-247.100-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.100	$0$	✓	✓	$0.435$	$0$	$2.06926$	Character $\chi_{247}(100, \cdot)$
1-247-247.101-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.101	$0$	✓	✓	$-0.143$	$0$	$0.992048$	Character $\chi_{247}(101, \cdot)$
1-247-247.109-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.109	$0$	✓	✓	$0.232$	$0$	$2.05018$	Character $\chi_{247}(109, \cdot)$
1-247-247.110-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.110	$0$	✓	✓	$0.141$	$0$	$1.68800$	Character $\chi_{247}(110, \cdot)$
1-247-247.120-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.120	$0$	✓	✓	$-0.348$	$0$	$2.79698$	Character $\chi_{247}(120, \cdot)$
1-247-247.121-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.121	$0$	✓	✓	$-0.115$	$0$	$1.30434$	Character $\chi_{247}(121, \cdot)$
1-247-247.122-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.122	$0$	✓	✓	$0.145$	$0$	$2.16992$	Character $\chi_{247}(122, \cdot)$
1-247-247.124-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.124	$0$	✓	✓	$-0.325$	$0$	$1.09730$	Character $\chi_{247}(124, \cdot)$
1-247-247.128-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.128	$0$	✓	✓	$-0.141$	$0$	$0.888095$	Character $\chi_{247}(128, \cdot)$
1-247-247.132-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.132	$0$	✓	✓	$-0.420$	$0$	$0.850822$	Character $\chi_{247}(132, \cdot)$
1-247-247.135-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.135	$0$	✓	✓	$0.293$	$0$	$0.449908$	Character $\chi_{247}(135, \cdot)$
1-247-247.136-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.136	$0$	✓	✓	$0.327$	$0$	$2.36708$	Character $\chi_{247}(136, \cdot)$
1-247-247.139-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.139	$0$	✓	✓	$-0.100$	$0$	$0.996500$	Character $\chi_{247}(139, \cdot)$
1-247-247.140-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.140	$0$	✓	✓	$0.0474$	$0$	$1.20291$	Character $\chi_{247}(140, \cdot)$
1-247-247.141-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.141	$0$	✓	✓	$-0.228$	$0$	$0.964496$	Character $\chi_{247}(141, \cdot)$
1-247-247.142-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.142	$0$	✓	✓	$-0.330$	$0$	$1.11658$	Character $\chi_{247}(142, \cdot)$
1-247-247.145-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.145	$0$	✓	✓	$-0.0196$	$0$	$1.88465$	Character $\chi_{247}(145, \cdot)$
1-247-247.148-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.148	$0$	✓	✓	$-0.139$	$0$	$0.770186$	Character $\chi_{247}(148, \cdot)$
1-247-247.15-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.15	$0$	✓	✓	$-0.106$	$0$	$0.761139$	Character $\chi_{247}(15, \cdot)$
1-247-247.151-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.151	$0$	✓	✓	$0.453$	$0$	$0.245479$	Character $\chi_{247}(151, \cdot)$
1-247-247.154-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.154	$0$	✓	✓	$-0.0808$	$0$	$1.34381$	Character $\chi_{247}(154, \cdot)$
1-247-247.159-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.159	$0$	✓	✓	$-0.157$	$0$	$0.907671$	Character $\chi_{247}(159, \cdot)$
1-247-247.16-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.16	$0$	✓	✓	$0.100$	$0$	$1.19680$	Character $\chi_{247}(16, \cdot)$
1-247-247.162-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.162	$0$	✓	✓	$0.0808$	$0$	$1.49527$	Character $\chi_{247}(162, \cdot)$
1-247-247.164-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.164	$0$	✓	✓	$-0.145$	$0$	$1.05740$	Character $\chi_{247}(164, \cdot)$
1-247-247.167-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.167	$0$	✓	✓	$0.486$	$0$	$2.28379$	Character $\chi_{247}(167, \cdot)$
1-247-247.168-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.168	$0$	✓	✓	$-0.275$	$0$	$1.44238$	Character $\chi_{247}(168, \cdot)$
1-247-247.17-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.17	$0$	✓	✓	$-0.249$	$0$	$1.10162$	Character $\chi_{247}(17, \cdot)$
1-247-247.174-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.174	$0$	✓	✓	$0.0468$	$0$	$0.701660$	Character $\chi_{247}(174, \cdot)$
1-247-247.178-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.178	$0$	✓	✓	$0.0901$	$0$	$2.21919$	Character $\chi_{247}(178, \cdot)$
1-247-247.18-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.18	$0$	✓	✓	$-0.453$	$0$	$1.71078$	Character $\chi_{247}(18, \cdot)$
1-247-247.184-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.184	$0$	✓	✓	$0.0791$	$0$	$1.25633$	Character $\chi_{247}(184, \cdot)$
1-247-247.189-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.189	$0$	✓	✓	$0.420$	$0$	$2.05340$	Character $\chi_{247}(189, \cdot)$
1-247-247.193-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.193	$0$	✓	✓	$-0.327$	$0$	$0.565635$	Character $\chi_{247}(193, \cdot)$
1-247-247.194-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.194	$0$	✓	✓	$0.188$	$0$	$1.38061$	Character $\chi_{247}(194, \cdot)$
1-247-247.199-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.199	$0$	✓	✓	$0.0878$	$0$	$0.877661$	Character $\chi_{247}(199, \cdot)$
1-247-247.2-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.2	$0$	✓	✓	$0.325$	$0$	$2.24652$	Character $\chi_{247}(2, \cdot)$
1-247-247.200-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.200	$0$	✓	✓	$-0.199$	$0$	$0.919510$	Character $\chi_{247}(200, \cdot)$
1-247-247.202-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.202	$0$	✓	✓	$-0.178$	$0$	$0.899555$	Character $\chi_{247}(202, \cdot)$
1-247-247.203-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.203	$0$	✓	✓	$-0.0468$	$0$	$0.959636$	Character $\chi_{247}(203, \cdot)$
1-247-247.207-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.207	$0$	✓	✓	$0.330$	$0$	$2.36035$	Character $\chi_{247}(207, \cdot)$
1-247-247.21-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.21	$0$	✓	✓	$0.199$	$0$	$1.45907$	Character $\chi_{247}(21, \cdot)$
1-247-247.218-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.218	$0$	✓	✓	$0.249$	$0$	$1.37244$	Character $\chi_{247}(218, \cdot)$
1-247-247.219-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.219	$0$	✓	✓	$0.426$	$0$	$1.79072$	Character $\chi_{247}(219, \cdot)$
1-247-247.220-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.220	$0$	✓	✓	$-0.466$	$0$	$2.36462$	Character $\chi_{247}(220, \cdot)$
1-247-247.223-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.223	$0$	✓	✓	$0.265$	$0$	$1.46387$	Character $\chi_{247}(223, \cdot)$
1-247-247.225-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.225	$0$	✓	✓	$0.143$	$0$	$1.23958$	Character $\chi_{247}(225, \cdot)$
1-247-247.227-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.227	$0$	✓	✓	$-0.172$	$0$	$1.22459$	Character $\chi_{247}(227, \cdot)$
1-247-247.23-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.23	$0$	✓	✓	$-0.230$	$0$	$1.36202$	Character $\chi_{247}(23, \cdot)$
1-247-247.233-r0-0-0	$1.14$	$1.14$	$1$	$13 \cdot 19$	247.233	$0$	✓	✓	$-0.188$	$0$	$0.731754$	Character $\chi_{247}(233, \cdot)$

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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.